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<h3 class="toggler-37"><a href="javascript:void(0)" style="color: black;">LAL: Linear Algebra (December 2021-April 2022) </a></h3>
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<h2><strong>Announcements</strong></h2>
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<h2><strong>Announcements</strong></h2>
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<li> <strong>Introductory Class: </strong>The class is scheduled for Monday (20/12/2021) at 9 AM.</li>
<!--<strong>Introductory Class: </strong>The class will be scheduled in the evening.-->
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<li> <a href="./LAL/syllabus.pdf" target="_blank"><strong>Syllabus</strong> </a> </li>
<li> <a href="./LAL/lecture_schedule.pdf" target="_blank"><strong>LAL-Sections & Lecture-Schedule</strong> </a> </li>
<li> <a href="./LAL/tutorial_schedule.pdf" target="_blank"><strong> Tutorial-Schedule</strong> </a> </li>
<li> <a href="./LAL/assessment_plan.pdf" target="_blank"><strong>Assessment Plan</strong> </a> </li>
</li>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> Lecture 1: <a href="./Lecture_1.pdf" target="_blank"> Groups & Fields</a> </li>
<li> Lecture 2: <a href="./Lecture_2.pdf" target="_blank"> System of Linear Equations</a> </li>
<li> Lecture 3: <a href="./Lecture_3.pdf" target="_blank"> Elementary Matrices & Row Reduced Echelon Form</a> </li>
<li> Lecture 4: <a href="./Lecture_4.pdf" target="_blank"> Invertible Matrix & Gauss-Jordan Method</a> </li>
<li> Lecture 5: <a href="./Lecture_5.pdf" target="_blank"> Determinant Function & Its Properties</a> </li>
<li> Lecture 6: <a href="./Lecture_6.pdf" target="_blank"> Vector Space & Its Properties</a> </li>
<li> Lecture 7: <a href="./Lecture_7.pdf" target="_blank"> Linear Combination, Linear Span, Linear Dependence & Independence</a> </li>
<li> Lecture 8: <a href="./Lecture_8.pdf" target="_blank"> Basis & Dimension</a> </li>
<li> Lecture 9: <a href="./Lecture_9.pdf" target="_blank"> Direct Sum & Its Basis and Dimension</a> </li>
<li> Lecture 10: <a href="./Lecture_10.pdf" target="_blank"> Linear Transformation</a> </li>
<li> Lecture 11: <a href="./Lecture_11.pdf" target="_blank">Rank-Nullity Theorem & Vector Space Isomorphism</a> </li>
<li> Lecture 12: <a href="./Lecture_12.pdf" target="_blank">Matrix Representation of a Linear Transformation & Similar Matrices</a> </li>
Lecture 13: <a href="./Lecture_13.pdf" target="_blank"> Rank of a matrix & System of Linear Equations</a> </li>
<li> Lecture 14: <a href="./Lecture_14.pdf" target="_blank"> Eigenvalue & Eigenvector</a> </li>
<li> Lecture 15: <a href="./Lecture_15.pdf" target="_blank"> Diagonalizability</a> </li>
<li> Lecture 16: <a href="./Lecture_16.pdf" target="_blank"> Minimal polynomial & Diagonalizability</a> </li>
<li> Lecture 17: <a href="./Lecture_17.pdf" target="_blank"> Inner Product Space</a> </li>
<li> Lecture 18: <a href="./Lecture_18.pdf" target="_blank"> Orthogonal Projection & Shortest Distance</a> </li>
<li> Lecture 19: <a href="./Lecture_19.pdf" target="_blank"> Fundamental Theorem of Linear Algebra & Least-Square Approximation</a> </li>
<li> Lecture 20: <a href="./Lecture_20.pdf" target="_blank"> Spectral Theorem</a> </li>
<li> Lecture 21: <a href="./Lecture_21.pdf" target="_blank"> Projection</a> </li>
<li> Lecture 22: <a href="./Lecture_22.pdf" target="_blank"> SVD</a> </li>
<li> Lecture 23: <a href="./Lecture_23.pdf" target="_blank"> Classification of Cones and Surfaces</a> </li>
<li> Lecture 24: <a href="./Lecture_24.pdf" target="_blank"> Jordan Form</a> </li>
</ul>
</br>
<li><strong>Problem Sets</strong></li>
<ul>
<li> <a href="./problem_set_1.pdf" target="_blank">Problem Set 1</a> </li>
<li> <a href="./problem_set_2.pdf" target="_blank">Problem Set 2</a> </li>
<li> <a href="./problem_set_3.pdf" target="_blank">Problem Set 3</a> </li>
<li> <a href="./problem_set_4.pdf" target="_blank">Problem Set 4</a> </li>
<li> <a href="./problem_set_5.pdf" target="_blank">Problem Set 5</a> </li>
<li> <a href="./problem_set_6.pdf" target="_blank">Problem Set 6</a> </li>
</ul>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C3 Review: <a href="./c3_ms.pdf" target="_blank"> Tentative Marking Scheme</a></li>
</ul>
<li><strong>C3 Marks </strong></li>
<ul>
<li> <a href="./c3_review_result.php" target="_blank"> C3 Marks After Rechecking</a> </li>
</ul>
<!--<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C1 Review Test Marking Scheme: <a href="./c1_ms.pdf" target="_blank"> Tentative Marking Scheme</a></li>
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<li><strong>C1 Marks</strong></li>
<ul>
<li> <a href="./c1_review_result.php" target="_blank"> C1 Marks </a> </li>-->
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<li><strong>Question Papers and Answer Keys</strong></li>
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<li> C3 Review Test: <a href="./c3_ms.pdf" target="_blank"> Tentative Marking Scheme</a></li>
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<li><strong>C3 Marks</strong></li>
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<li> <a href="./c3_result.php" target="_blank"> C3 Marks After Rechecking </a> </li>
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<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">DMF13210: Mathematical Foundation for Data Science (January - June 2021) </a></h3>
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<!-- <<strong>Quiz 1: </strong>The first quiz will be held on August 23, 2020.-->
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<li> <a href="./DMF/DMF_Syllabus.pdf" target="_blank"><strong>Syllabus</strong> </a> </li>
<li> <a href="./DMF/Time_Table.pdf" target="_blank"><strong>Time-Table</strong> </a> </li>
</br>
<!--
<li><strong>Lecture Notes</strong></li>
<ul>
<li> Lecture 0: <a href="./Lecture_0.pdf" target="_blank"> System of Linear Equations</a> </li>
<li> Lecture 1: <a href="./Lecture1.pdf" target="_blank"> Vector Space</a> </li>
<li> Lecture 2: <a href="./Lecture2.pdf" target="_blank"> Linear Combination & Linear Dependence and Independence</a> </li>
<li> Lecture 3: <a href="./Lecture3.pdf" target="_blank"> Basis & Dimension</a> </li>
<li> Lecture 4: <a href="./Lecture4.pdf" target="_blank"> Direct Sum</a> </li>
<li> Lecture 5: <a href="./Lecture5.pdf" target="_blank"> Linear Transformation</a> </li>
<li> Lecture 6: <a href="./Lecture6.pdf" target="_blank"> Rank-Nullity Theorem</a> </li>
<li> Lecture 7: <a href="./Lecture_7.pdf" target="_blank">Rank-Nullity Theorem & Vector Space Isomorphism</a> </li>
<li> Lecture 8: <a href="./Lecture_8.pdf" target="_blank">Matrix Representation of a Linear Transformation & Similar Matrices</a> </li>
<li> Lecture 9: <a href="./Lecture_9.pdf" target="_blank"> Rank of a matrix & System of Linear Equations</a> </li>
<li> Lecture 10: <a href="./Lecture_14.pdf" target="_blank"> Eigenvalue & Eigenvector</a> </li>
<li> Lecture 11: <a href="./Lecture_15.pdf" target="_blank"> Diagonalizability</a> </li>
<li> Lecture 12: <a href="./Lecture_16.pdf" target="_blank"> Minimal polynomial & Diagonalizability</a> </li>
<li> Lecture 13: <a href="./Lecture_17.pdf" target="_blank"> Inner Product Space</a> </li>
<li> Lecture 14: <a href="./Lecture_18.pdf" target="_blank"> Orthogonal Projection & Shortest Distance</a> </li>
<li> Lecture 15: <a href="./Lecture_19.pdf" target="_blank"> Fundamental Theorem of Linear Algebra & Least-Square Approximation</a> </li>
<li> Lecture 16: <a href="./Lecture_20.pdf" target="_blank"> Spectral Theorem</a> </li>
<li> Lecture 17: <a href="./Lecture_21.pdf" target="_blank"> Projection</a> </li>
<li> Lecture 18: <a href="./Lecture_22.pdf" target="_blank"> SVD</a> </li>
</br>
</ul>
<li><strong>Problem Sets</strong></li>
<ul>
<li> <a href="./problem_set1.pdf" target="_blank">Problem Set 1</a> </li>
<li> <a href="./DMF/problem_set2.pdf" target="_blank">Problem Set 2</a> </li>
<li> <a href="./problem_set3.pdf" target="_blank">Problem Set 3</a> </li>
<li> <a href="./DMF/problem_set_4.pdf" target="_blank">Problem Set 4</a> </li>
<li> <a href="./DMF/problem_set_5.pdf" target="_blank">Problem Set 5</a> </li>
</ul>
<!--
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C2 Review Test: <a href="./c2_ms.pdf" target="_blank"> Tentative Marking Scheme</a></li>
</ul>-->
<li><strong>Marks</strong></li>
<ul>
<li> <a href="./dmf_result.php" target="_blank"> C3 Marks </a> </li>
-->
</ul>
</ul>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">LAL: Linear Algebra (July-December 2020) </a></h3>
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<h2><strong>Announcements</strong></h2>
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<h2><strong>Announcements</strong></h2>
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<li> Assessment Plan updated! </li>
<!--<strong>Introductory Class: </strong>The class will be scheduled in the evening.-->
</div>
</div>
<li> <a href="./LAL/syllabus.pdf" target="_blank"><strong>Syllabus</strong> </a> </li>
<li> <a href="./LAL/Lecture_schedule.pdf" target="_blank"><strong>LAL-Sections & Lecture-Schedule</strong> </a> </li>
<li> <a href="./LAL/Tutorial_schedule.pdf" target="_blank"><strong>Tutorial-Batches & Tutorial-Schedule</strong> </a> </li>
<li> <a href="./LAL/assessment.pdf" target="_blank"><strong>Assessment Plan</strong> </a> </li>
</li>
</br>
<!--
<li><strong>Lecture Notes</strong></li>
<ul>
<li> Lecture 1: <a href="./Lecture_1.pdf" target="_blank"> Groups & Fields</a> </li>
<li> Lecture 2: <a href="./Lecture_2.pdf" target="_blank"> System of Linear Equations</a> </li>
<li> Lecture 3: <a href="./Lecture_3.pdf" target="_blank"> Elementary Matrices & Row Reduced Echelon Form</a> </li>
<li> Lecture 4: <a href="./Lecture_4.pdf" target="_blank"> Invertible Matrix & Gauss-Jordan Method</a> </li>
<li> Lecture 5: <a href="./Lecture_5.pdf" target="_blank"> Determinant Function & Its Properties</a> </li>
<li> Lecture 6: <a href="./Lecture_6.pdf" target="_blank"> Vector Space & Its Properties</a> </li>
<li> Lecture 7: <a href="./Lecture_7.pdf" target="_blank"> Linear Combination, Linear Span, Linear Dependence & Independence</a> </li>
<li> Lecture 8: <a href="./Lecture_8.pdf" target="_blank"> Basis & Dimension</a> </li>
<li> Lecture 9: <a href="./Lecture_9.pdf" target="_blank"> Direct Sum & Its Basis and Dimension</a> </li>
<li> Lecture 10: <a href="./Lecture_10.pdf" target="_blank"> Linear Transformation</a> </li>
<li> Lecture 11: <a href="./Lecture_11.pdf" target="_blank">Rank-Nullity Theorem & Vector Space Isomorphism</a> </li>
<li> Lecture 12: <a href="./Lecture_12.pdf" target="_blank">Matrix Representation of a Linear Transformation & Similar Matrices</a> </li>
<li> Lecture 13: <a href="./Lecture_13.pdf" target="_blank"> Rank of a matrix & System of Linear Equations</a> </li>
<li> Lecture 14: <a href="./Lecture_14.pdf" target="_blank"> Eigenvalue & Eigenvector</a> </li>
<li> Lecture 15: <a href="./Lecture_15.pdf" target="_blank"> Diagonalizability</a> </li>
<li> Lecture 16: <a href="./Lecture_16.pdf" target="_blank"> Minimal polynomial & Diagonalizability</a> </li>
<li> Lecture 17: <a href="./Lecture_17.pdf" target="_blank"> Inner Product Space</a> </li>
<li> Lecture 18: <a href="./Lecture_18.pdf" target="_blank"> Orthogonal Projection & Shortest Distance</a> </li>
<li> Lecture 19: <a href="./Lecture_19.pdf" target="_blank"> Fundamental Theorem of Linear Algebra & Least-Square Approximation</a> </li>
<li> Lecture 20: <a href="./Lecture_20.pdf" target="_blank"> Spectral Theorem</a> </li>
<li> Lecture 21: <a href="./Lecture_21.pdf" target="_blank"> Projection</a> </li>
<li> Lecture 22: <a href="./Lecture_22.pdf" target="_blank"> SVD</a> </li>
<li> Lecture 23: <a href="./Lecture_23.pdf" target="_blank"> Classification of Cones and Surfaces</a> </li>
<li> Lecture 24: <a href="./Lecture_24.pdf" target="_blank"> Jordan Form</a> </li>
</ul>
</br>
<li><strong>Problem Sets</strong></li>
<ul>
<li> <a href="./problem_set_1.pdf" target="_blank">Problem Set 1</a> </li>
<li> <a href="./problem_set_2.pdf" target="_blank">Problem Set 2</a> </li>
<li> <a href="./problem_set_3.pdf" target="_blank">Problem Set 3</a> </li>
<li> <a href="./problem_set_4.pdf" target="_blank">Problem Set 4</a> </li>
<li> <a href="./problem_set_5.pdf" target="_blank">Problem Set 5</a> </li>
<li> <a href="./problem_set_6.pdf" target="_blank">Problem Set 6</a> </li>
</ul>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C3 Review Test: <a href="./c3_ms.pdf" target="_blank"> Tentative Marking Scheme</a></li>
</ul>
<li><strong>C3 Marks</strong></li>
<ul>
<li> <a href="./c3_result.php" target="_blank"> C3 Marks After Rechecking </a> </li>
</ul>
-->
</ul>
</ul>
</ul> <!-- for ending the page of the course-->
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Probability & Statistics (July - December 2020) </a></h3>
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<div class="container">
<h2><strong>Announcements</strong></h2>
<div class="alert alert-info">
<<strong>Quiz 1: </strong>The first quiz will be held on August 23, 2020.
</div>
</div>
<li> <a href="./PAS/PAS_Syllabus.pdf" target="_blank"><strong>Syllabus</strong> </a> </li>
<li> <a href="./PAS/Time_Table.pdf" target="_blank"><strong>Time Table</strong> </a> </li>
<li> <a href="./PAS/Time_Table.pdf" target="_blank"><strong>Time Table</strong> </a> </li>
<li> For Lecture notes and Problem sets, visit the <a href="https://profile.iiita.ac.in/abdullah/Teaching.php" target="_blank">Course Page</a>.
</li>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Univariate and Multivariate Calculus (January-July 2020) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> The first quiz will be held on January 20, 2020. The Syllabus of the quiz will cover Lectures 1, 2 & 3. </li>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem,
maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
<li>Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating
series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates,
applications of Power series.</li>
<li>Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional
derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals,
change of variables.</li>
<li>Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem
and applications, Divergence theorem, Stokes’ theorem and applications.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>G. B. Thomas, M. D. Weir, and J. Hass,<i> Thomas' Calculus</i>, Pearson.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>T. M. Apostol, <i>Calculus, Vol. 1</i>, Wiley.</li>
<li>T. M. Apostol, <i>Calculus, Vol. 2</i>, Wiley.</li>
<li>Ajit Kumar and S. Kumaresan, <i>A Basic Course in Real Analysis</i>, CRC Press, Taylor & Francis Group.</li>
</ul>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> The Real Number System: <a href="./Lecture_1.pdf" target="_blank"> Lecture 1</a> </li>
<li> Convergence of a Sequence, Monotone Sequences: <a href="./Lecture_2.pdf" target="_blank"> Lecture 2 </a> </li>
<li> Cauchy Criterion, Bolzano - Weierstrass Theorem: <a href="./Lecture_3.pdf" target="_blank"> Lecture 3</a> </li>
<li> Continuity and Limits: <a href="./Lecture_4.pdf" target="_blank"> Lecture 4</a> </li>
<li> Existence of Maxima, Intermediate Value Property, Differentiabilty: <a href="./Lecture_5.pdf" target="_blank"> Lecture 5</a> </li>
<li> Rolle's Theorem, Mean Value Theorem: <a href="./Lecture_6.pdf" target="_blank"> Lecture 6</a> </li>
<li> Cauchy Mean Value Theorem, L'Hopital Rule: <a href="./Lecture_7.pdf" target="_blank"> Lecture 7</a> </li>
<li> Fixed Point Iteration Method, Newton's Method: <a href="./Lecture_8.pdf" target="_blank"> Lecture 8</a> </li>
<li> Sufficient Conditions for Local Maximum, Point of Inflection: <a href="./Lecture_9.pdf" target="_blank"> Lecture 9</a> </li>
<li> Taylor's Theorem: <a href="./Lecture_10.pdf" target="_blank"> Lecture 10</a> </li>
<li> Infinite Series: <a href="./Lecture_11.pdf" target="_blank"> Lecture 11-13</a> </li>
</ul>
</br>
<li><strong>Problems</strong></li>
<ul>
<li> The Real Number System: <a href="./Problem_1.pdf" target="_blank"> Problem Set 01</a> </li>
<li> Convergence of Sequences, Monotone Sequences: <a href="./Problem_2.pdf" target="_blank"> Problem Set 02</a> </li>
<li> Cauchy criterion, Subsequence: <a href="./Problem_3.pdf" target="_blank"> Problem Set 03</a> </li>
<li> Continuity and Limits: <a href="./Problem_4.pdf" target="_blank"> Problem Set 04</a> </li>
<li> IVP, Existence of maxima/minima: <a href="./Problem_5.pdf" target="_blank"> Problem Set 05</a> </li>
<li> Differentiability, Rolle’s theorem: <a href="./Problem_6.pdf" target="_blank"> Problem Set 06</a> </li>
<li> Mean Value Theorem: <a href="./Problem_7.pdf" target="_blank"> Problem Set 07</a> </li>
<li> Fixed point iteration method, Newton’s method: <a href="./Problem_8.pdf" target="_blank"> Problem Set 08</a> </li>
<li> Maxima/minima, Curve tracing: <a href="./Problem_9.pdf" target="_blank"> Problem Set 09</a> </li>
<li> Taylor's Theorem: <a href="./Problem_10.pdf" target="_blank"> Problem Set 10</a> </li>
<li> Series: Definition of convergence, Necessary and sufficient conditions for convergence: <a href="./Problem_11.pdf" target="_blank"> Problem Set 11</a> </li>
</ul>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">LAL: Linear Algebra (July - December 2019) </a></h3>
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<!-- <li>First year: <a href="./result_1st_yr.php"><strong>C3 Marks</strong></a> </li>
<li>Second Year: <a href="./result_2nd_yr.php"><strong>Marks</strong></a></li>
-->
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT430C: Convex Optimization (February-June 2019) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Convex Analysis: convex sets, convex functions, calculus of convex functions. </li>
<li>Optimality of Convex Programs: 1st order necessary and sufficient conditions, KKT conditions. </li>
<li>Duality: Lagrange and conic duality. </li>
<li>Linear and Quadratic Programs.</li>
<li>Conic Programs: QCQPs, SOCPs, SDPs.</li>
<li>Smooth Problems: gradient descent, Nesterov's accelerated method, Newton's methods.</li>
<li>Non-smooth Problems: sub-gradient descent.</li>
<li>Special topics: active set and cutting planes methods, proximal point method.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>S. Boyd and L.Vandenberghe, Convex Optimization. Cambridge University Press, 2004.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>R. T. Rockafellar. Convex Analysis. Princeton University Press, 1996.</li>
<li>G. C. Calafiore and L. El Ghaoui, Optimization Models, Cambridge University Press, 2014.</li>
</ul>
<!--
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Probability & Statistics (July - December 2019) </a></h3>
<ul class="panel-37">
<li>C3: <a href="./result_2nd_yr.php"><strong>Marks</strong></a>
</li>
</ul>
-->
<!--
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Univariate and Multivariate Calculus (January-July 2019) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> </li>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem,
maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
<li>Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating
series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates,
applications of Power series.</li>
<li>Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional
derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals,
change of variables.</li>
<li>Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem
and applications, Divergence theorem, Stokes’ theorem and applications.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>G. B. Thomas, M. D. Weir, and J. Hass,<i> Thomas' Calculus</i>, Pearson.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>T. M. Apostol, <i>Calculus, Vol. 1</i>, Wiley.</li>
<li>T. M. Apostol, <i>Calculus, Vol. 2</i>, Wiley.</li>
<li>J. Stewart, <i>Calculus</i>, Thompson Press.</li>
<li>Ajit Kumar and S. Kumaresan, <i>A Basic Course in Real Analysis</i>, CRC Press, Taylor & Francis Group.</li>
</ul>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> The Real Number System: <a href="./Lecture_1.pdf" target="_blank"> Lecture 1</a> </li>
<li> Convergence of a Sequence, Monotone Sequences: <a href="./Lecture_2.pdf" target="_blank"> Lecture 2 </a> </li>
<li> Cauchy Criterion, Bolzano - Weierstrass Theorem: <a href="./Lecture_3.pdf" target="_blank"> Lecture 3</a> </li>
<li> Continuity and Limits: <a href="./Lecture_4.pdf" target="_blank"> Lecture 4</a> </li>
<li> Existence of Maxima, Intermediate Value Property, Differentiabilty: <a href="./Lecture_5.pdf" target="_blank"> Lecture 5</a> </li>
<li> Rolle's Theorem, Mean Value Theorem: <a href="./Lecture_6.pdf" target="_blank"> Lecture 6</a> </li>
<li> Cauchy Mean Value Theorem, L'Hopital Rule: <a href="./Lecture_7.pdf" target="_blank"> Lecture 7</a> </li>
<li> Fixed Point Iteration Method, Newton's Method: <a href="./Lecture_8.pdf" target="_blank"> Lecture 8</a> </li>
<li> Sufficient Conditions for Local Maximum, Point of Inflection: <a href="./Lecture_9.pdf" target="_blank"> Lecture 9</a> </li>
<li> Taylor's Theorem: <a href="./Lecture_10.pdf" target="_blank"> Lecture 10</a> </li>
<li> Infinite Series: <a href="./Lecture_11.pdf" target="_blank"> Lecture 11-13</a> </li>
<li> Power Series, Taylor Series: <a href="./Lecture_14.pdf" target="_blank"> Lecture 14</a> </li>
<li> Riemann Integration: <a href="./Lecture_15.pdf" target="_blank"> Lecture 15-16</a> </li>
<li> Fundamental Theorems of Calculus, Riemann Sum: <a href="./Lecture_17.pdf" target="_blank"> Lecture 17</a> </li>
<li> Improper Integrals: <a href="./Lecture_18.pdf" target="_blank"> Lecture 18</a> </li>
<li> Area Between Two Curves; Polar Coordinates: <a href="./Lecture_19.pdf" target="_blank"> Lecture 19</a> </li>
<li> Area in Polar Coordinates, Volume of Solids: <a href="./Lecture_20.pdf" target="_blank"> Lecture 20</a> </li>
<li> Washer and Shell Methods, Length of a plane curve : <a href="./Lecture_21.pdf" target="_blank"> Lecture 21</a> </li>
<li> Areas of Surfaces of Revolution; Pappus's Theorems: <a href="./Lecture_22.pdf" target="_blank"> Lecture 22</a> </li>
<li> Review of vectors, equations of lines and planes; sequences in R^3: <a href="./Lecture_23.pdf" target="_blank"> Lecture 23</a> </li>
<li> Calculus of Vector Valued Functions: <a href="./Lecture_24.pdf" target="_blank"> Lecture 24</a> </li>
<li> Principal Normal; Curvature: <a href="./Lecture_25.pdf" target="_blank"> Lecture 25</a> </li>
<li> Functions of Several Variables - Continuity and Differentiability: <a href="./Lecture_26.pdf" target="_blank"> Lecture 26-27</a> </li>
<li> Directional Derivatives, Gradient, Tangent Plane: <a href="./Lecture_28.pdf" target="_blank"> Lecture 28</a> </li>
<li> Mixed derivative Theorem, MVT: <a href="./Lecture_29.pdf" target="_blank"> Lecture 29</a> </li>
<li> Maxima, Minima, Second Derivative Test: <a href="./Lecture_30.pdf" target="_blank"> Lecture 30</a> </li>
<li> Lagrange Multiplier Method: <a href="./Lecture_31.pdf" target="_blank"> Lecture 31</a> </li>
<li> Double integrals: <a href="./Lecture_32.pdf" target="_blank"> Lecture 32</a> </li>
<li> Change of Variable in a Double Integral, Triple Integrals: <a href="./Lecture_33.pdf" target="_blank"> Lecture 33</a> </li>
<li> Change of Variables in a Triple Integral: <a href="./Lecture_34.pdf" target="_blank"> Lecture 34</a> </li>
</ul>
</br>
<li><strong>Problems</strong></li>
<ul>
<li> The Real Number System: <a href="./Problem_1.pdf" target="_blank"> Problem Set 01</a> </li>
<li> Convergence of Sequences, Monotone Sequences: <a href="./Problem_2.pdf" target="_blank"> Problem Set 02</a> </li>
<li> Cauchy criterion, Subsequence: <a href="./Problem_3.pdf" target="_blank"> Problem Set 03</a> </li>
<li> Continuity and Limits: <a href="./Problem_4.pdf" target="_blank"> Problem Set 04</a> </li>
<li> IVP, Existence of maxima/minima: <a href="./Problem_5.pdf" target="_blank"> Problem Set 05</a> </li>
<li> Differentiability, Rolle’s theorem: <a href="./Problem_6.pdf" target="_blank"> Problem Set 06</a> </li>
<li> Mean Value Theorem: <a href="./Problem_7.pdf" target="_blank"> Problem Set 07</a> </li>
<li> Fixed point iteration method, Newton’s method: <a href="./Problem_8.pdf" target="_blank"> Problem Set 08</a> </li>
<li> Maxima/minima, Curve tracing: <a href="./Problem_9.pdf" target="_blank"> Problem Set 09</a> </li>
<li> Taylor's Theorem: <a href="./Problem_10.pdf" target="_blank"> Problem Set 10</a> </li>
<li> Series: Definition of convergence, Necessary and sufficient conditions for convergence: <a href="./Problem_11.pdf" target="_blank"> Problem Set 11</a> </li>
<li> Comparison, Limit comparison and Cauchy condensation tests: <a href="./Problem_12.pdf" target="_blank"> Problem Set 12</a> </li>
<li> Ratio and Root tests, Leibniz's Test: <a href="./Problem_13.pdf" target="_blank"> Problem Set 13</a> </li>
<li> Functions of Several Variables: <a href="./FoSV.pdf" target="_blank"> Problem </a> </li>
</ul>
</br>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C3 Review Test: <a href="./C3_UMC.pdf" target="_blank"> Question Paper</a>
<a href="./C3_UMC_MS.pdf" target="_blank"> Tentative Marking Scheme</a></li>
</ul>
<li><a href="./result.php"><strong>C3 Marks</strong></a></li>
</ul>
-->
<!--
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT130C: Mathematics - I (July-December 2017) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> One more book, viz. A Basic Course in Real Analysis, is added in the Reference Books. Go through Appendix A: Quantifiers. </li>
<li> A link for Practice Problems is added below. Solve as many questions as you can. Hints are also given for each problem set. </li>
<li> Quiz 1 marking scheme is uploaded. </li>
<li> The syllabus for the Mid Semester Examination is from the beginning of the course up to Power Series (Lecture 14). </li>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem,
maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
<li>Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating
series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates,
applications of Power series.</li>
<li>Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional
derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals,
change of variables.</li>
<li>Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem
and applications, Divergence theorem, Stokes’ theorem and applications.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>G. B. Thomas, M. D. Weir, and J. Hass,<i> Thomas' Calculus</i>, Pearson.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>T. M. Apostol, <i>Calculus, Vol. 1</i>, Wiley.</li>
<li>T. M. Apostol, <i>Calculus, Vol. 2</i>, Wiley.</li>
<li>J. Stewart, <i>Calculus</i>, Thompson Press.</li>
<li>Ajit Kumar and S. Kumaresan, <i>A Basic Course in Real Analysis</i>, CRC Press, Taylor & Francis Group.</li>
</ul>
</br>
</ul>
-->
<!--
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT430C: Convex Optimization (January-June 2017) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Convex Analysis: convex sets, convex functions, calculus of convex functions. </li>
<li>Optimality of Convex Programs: 1st order necessary and sufficient conditions, KKT conditions. </li>
<li>Duality: Lagrange and conic duality. </li>
<li>Linear and Quadratic Programs.</li>
<li>Conic Programs: QCQPs, SOCPs, SDPs.</li>
<li>Smooth Problems: gradient descent, Nesterov's accelerated method, Newton's methods.</li>
<li>Non-smooth Problems: sub-gradient descent.</li>
<li>Special topics: active set and cutting planes methods, proximal point method.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>S. Boyd and L.Vandenberghe, Convex Optimization. Cambridge University Press, 2004.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>R. T. Rockafellar. Convex Analysis. Princeton University Press, 1996.</li>
<li>G. C. Calafiore and L. El Ghaoui, Optimization Models, Cambridge University Press, 2014.</li>
</ul>
</br>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> Quiz I: <a href="./2017_Q1.pdf" target="_blank"> Question Paper</a>
<a href="./2017_Q1_MS.pdf" target="_blank"> Marking Scheme</a></li>
<li> Mid-Sem: <a href="./2017_MS.pdf" target="_blank"> Question Paper</a>
<a href="./2017_MS_MS.pdf" target="_blank"> Marking Scheme</a></li>
<li> Quiz II: <a href="./2017_Q2.pdf" target="_blank"> Question Paper</a>
<a href="./2017_Q2_MS.pdf" target="_blank"> Marking Scheme</a></li>
<li> End-Sem: <a href="./2017_ES.pdf" target="_blank"> Question Paper</a>
<a href="./2017_ES_MS.pdf" target="_blank"> Marking Scheme</a></li>
</ul>
<li><a href="./results.php"><strong>Marks</strong></a>
(Formula for Total Marks = Q1 + MS + 0.8*Q2 + ES) </li>
</ul>
-->
<!--
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT130C: Mathematics - I (July-December 2016) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> Problem set 11 is uploaded.</li>
<li> The syllabus for the Mid Semester Examination will be from Lecture 5 to Lecture 12-13. Sequence, Series and Fundamental
theorem of calculus are not included.</li>
<li> Grading Policy: Quiz I: 20 points, Mid-sem Exam: 35 points, Quiz II: 20 points, End-sem Exam: 75 points, Total: 150 points.
Note that marks will be rescaled (linearly) depending on the full marks of the examination. </li>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem,
maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
<li>Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating
series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates,
applications of Power series.</li>
<li>Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional
derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals,
change of variables.</li>
<li>Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem
and applications, Divergence theorem, Stokes’ theorem and applications.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>G. B. Thomas, M. D. Weir, and J. Hass,<i> Thomas' Calculus</i>, Pearson.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>T. M. Apostol, <i>Calculus, Vol. 1</i>, Wiley.</li>
<li>T. M. Apostol, <i>Calculus, Vol. 2</i>, Wiley.</li>
<li>J. Stewart, <i>Calculus</i>, Thompson Press.</li>
</ul>
</br>
</ul>
-->
<!--
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SPAS230C: Probability and Statistics (January-June 2016) </a></h3>
<ul class="panel-37">
<li><strong>Course Outline</strong></li>
<ul>
<li>Probability: Axiomatic definition, Properties, Conditional probability, Bayes rule and independence of events.</li>
<li>Random Variable: Random Variables, Distribution function, Discrete and Continuous random variables, Probability mass and density functions, Expectation, Function of random variable, Moments, Moment generating function, Chebyshev's inequality.</li>
<li>Special discrete distributions: Bernoulli, Binomial, Geometric, Negative binomial, Hypergeometric, Poisson, Uniform.</li>
<li>Special continuous distributions: Uniform, Exponential, Gamma, Normal.</li>
<li>Random vector: Joint distributions, Marginal and conditional distributions, Moments, Independence of random variables, Covariance, Correlation, Functions of random variables.</li>
<li>Law of Large Numbers: Weak law of large numbers, Levy's Central limit theorem (i.i.d. finite variance case), Normal and Poisson approximations to Binomial.</li>
<li>Statistics: Introduction: Population, Sample, Parameters.</li>
<li>Point Estimation: Method of moments, Maximum likelihood estimation, Unbiasedness, Consistency.</li>
<li>Interval Estimation: Confidence interval.</li>
<li>Tests of Hypotheses: Null and Alternative hypothesis, Type-I and Type-II errors, Level of significance, p-value, Likelihood ratio test, Chi-square goodness of fit tests.</li>
<li>Regression Analysis: Scatter diagram, Simple linear regression, Least square estimation, Tests for slope, prediction problem, Graphical residual analysis, Q-Q plot to test for normality of residuals.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>Rohatgi, V. K. and Saleh, A. K. (2000), <i>An Introduction to Probability and Statistics</i>, 2nd Edition, Wiley-interscience.</li>
<li>Montgomery, D. C., Peck, E. A. and Vining, G. G. (2012), <i>An Introduction to Linear Regression Analysis</i>, 5th Edition, Wiley.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>Bertsekas, D. P. and Tsitsiklis, J. N. (2008), <i>Introduction to Probability</i>, Athena Scientific, Massachusetts.</li>
<li>Seber, G. A. F. and Lee, A. J. (2003), <i>Linear Regression Analysis</i>, 2nd Edition, Wiley-interscience.</li>
</ul>
</br>
<li><strong>Questions and Keys</strong></li>
<ul>
<li> Back Paper Examination: <a href="spas_back_paper.pdf" target="_blank"> Question Paper</a> <a href="spas_marking.pdf"
target="_blank"> Marking Scheme </a>
</ul>
</ul>
-->
<!--
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT330: Complex Analysis and Integral Transformations (July-December 2015) </a></h3>
<ul class="panel-37">
<li><strong>Course Outline</strong></li>
<ul>
<li>Laplace Transforms: Definition and properties, Sufficient condition of Existence,
Transforms of derivatives and integrals, Derivatives and integrals of transforms, Inverse
Laplace Transforms, Exponential shifts, Convolutions, Applications: Differential and Integral
Equations.</li>
<li>Fourier Series: Periodic functions, fundamental period, Trigonometric series, Fourier
series, Bessel's inequality, Orthonormal and orthogonal set, Euler formulas, Functions with
arbitrary periods, Even and odd functions , Half range expansions, Fourier coefficients
without integration, Approximation by trigonometric polynomials, Application to differential
equation.</li>
<li>Fourier Transforms: Fourier integral theorem, Sine and Cosine Integrals, Inverse
Transforms, Transforms of Elementary Functions, Properties, Convolution, Parsevals relation,
Transform of Dirac Delta Function, Multiple Fourier transform, Finite Fourier transform.</li>
<li>Z Transforms: Z-transforms, properties, Inverse Z- transforms, relationship with Fourier
transforms.</li>
<li>Complex Analysis: Complex numbers, Modulus, Argument, Curves and regions in complex
plane, Functions, Limits, Derivatives, Analytic functions, Cauchy-Riemann equations, Complex
exponential logarithms and trigonometric function, General powers, Line integrals, Cauchy's
theorem, Cauchys integral theorem, Cauchys integral formula, Taylor and Laurent series ,
Zeros and singularities, Residues, Residues theorem, Evaluation of real improper
integrals.</li>
</ul>
<br>
<li><strong>Text Book</strong></li>
<ul>
<li>E. Kreyszig, <i>Advanced Engineering Mathematics</i>, Wiley.</li>
</ul>
<br>
<li><strong>Reference Books</strong></li>
<ul>
<li>M. Braun, <i>Differential Equations and Their Applications</i>, Springer-Verlag, New
York.</li>
<li><a style="color: black;" href="./TRENCH_DIFF_EQNS_I.PDF" target="_blank">W. Trench, <i>Elementary Differential Equations</i></a>.
</li><li>J. Schiff, <i>The Laplace Transform: Theory and Applications</i>, Springer.</li>
<li>J. Brown and R. Churchill, <i>Complex Variables and Application</i>, McGraw-Hill.</li>
<li>G. F. Simmons, <i>Differential Equations</i>, Tata Mcgraw Hill.</li>
<li>R. Jain and S. Iyenger, <i>Advanced Engineering Mathematics</i>, Narosa.</li>
</ul>
<li><strong>Questions and Keys</strong></li>
<ul>
<li> Back Paper Examination: <a href="smat_back_paper.pdf" target="_blank"> Question Paper</a> <a href="smat_marking.pdf"
target="_blank"> Marking Scheme </a>
</ul>
</ul>
-->
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<!--<content>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: black;">Univariate and Multivariate Calculus (January-July 2020) </a></h3>
<ul class="panel-37">
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem,
maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
<li>Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating
series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates,
applications of Power series.</li>
<li>Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional
derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals,
change of variables.</li>
<li>Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem
and applications, Divergence theorem, Stokes’ theorem and applications.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>G. B. Thomas, M. D. Weir, and J. Hass,<i> Thomas' Calculus</i>, Pearson.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>T. M. Apostol, <i>Calculus, Vol. 1</i>, Wiley.</li>
<li>T. M. Apostol, <i>Calculus, Vol. 2</i>, Wiley.</li>
<li>Ajit Kumar and S. Kumaresan, <i>A Basic Course in Real Analysis</i>, CRC Press, Taylor & Francis Group.</li>
</ul>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> The Real Number System: <a href="./Lecture_1.pdf" target="_blank"> Lecture 1</a> </li>
<li> Convergence of a Sequence, Monotone Sequences: <a href="./Lecture_2.pdf" target="_blank"> Lecture 2 </a> </li>
<li> Cauchy Criterion, Bolzano - Weierstrass Theorem: <a href="./Lecture_3.pdf" target="_blank"> Lecture 3</a> </li>
<li> Continuity and Limits: <a href="./Lecture_4.pdf" target="_blank"> Lecture 4</a> </li>
<li> Existence of Maxima, Intermediate Value Property, Differentiabilty: <a href="./Lecture_5.pdf" target="_blank"> Lecture 5</a> </li>
<li> Rolle's Theorem, Mean Value Theorem: <a href="./Lecture_6.pdf" target="_blank"> Lecture 6</a> </li>
<li> Cauchy Mean Value Theorem, L'Hopital Rule: <a href="./Lecture_7.pdf" target="_blank"> Lecture 7</a> </li>
<li> Fixed Point Iteration Method, Newton's Method: <a href="./Lecture_8.pdf" target="_blank"> Lecture 8</a> </li>
<li> Sufficient Conditions for Local Maximum, Point of Inflection: <a href="./Lecture_9.pdf" target="_blank"> Lecture 9</a> </li>
<li> Taylor's Theorem: <a href="./Lecture_10.pdf" target="_blank"> Lecture 10</a> </li>
<li> Infinite Series: <a href="./Lecture_11.pdf" target="_blank"> Lecture 11-13</a> </li>
</ul>
</br>
<li><strong>Problems</strong></li>
<ul>
<li> The Real Number System: <a href="./Problem_1.pdf" target="_blank"> Problem Set 01</a> </li>
<li> Convergence of Sequences, Monotone Sequences: <a href="./Problem_2.pdf" target="_blank"> Problem Set 02</a> </li>
<li> Cauchy criterion, Subsequence: <a href="./Problem_3.pdf" target="_blank"> Problem Set 03</a> </li>
<li> Continuity and Limits: <a href="./Problem_4.pdf" target="_blank"> Problem Set 04</a> </li>
<li> IVP, Existence of maxima/minima: <a href="./Problem_5.pdf" target="_blank"> Problem Set 05</a> </li>
<li> Differentiability, Rolle’s theorem: <a href="./Problem_6.pdf" target="_blank"> Problem Set 06</a> </li>
<li> Mean Value Theorem: <a href="./Problem_7.pdf" target="_blank"> Problem Set 07</a> </li>
<li> Fixed point iteration method, Newton’s method: <a href="./Problem_8.pdf" target="_blank"> Problem Set 08</a> </li>
<li> Maxima/minima, Curve tracing: <a href="./Problem_9.pdf" target="_blank"> Problem Set 09</a> </li>
<li> Taylor's Theorem: <a href="./Problem_10.pdf" target="_blank"> Problem Set 10</a> </li>
<li> Series: Definition of convergence, Necessary and sufficient conditions for convergence: <a href="./Problem_11.pdf" target="_blank"> Problem Set 11</a> </li>
</ul>
</ul>
<center><h3 class="toggler-37">Marks </h3></center>
<ul class="panel-37">
<?php
if(isset($_POST['username']) && isset($_POST['password'])){
$adServer = "ldap://pldap.iiita.ac.in";
$ldap = ldap_connect($adServer);
$username = $_POST['username'];
$password = $_POST['password'];
ldap_set_option($ldap, LDAP_OPT_PROTOCOL_VERSION, 3);
$a = ldap_search($ldap,"dc=iiita,dc=ac,dc=in", "uid=$username");
$b = ldap_get_entries($ldap, $a);
$dn = $b[0]["dn"];
//******************************************************
if(trim($username)==='' || trim($password)==='')
{
echo "Username and Password cannot be blank.";
}
elseif (ldap_bind($ldap, $dn, $password))
{
$username = strtoupper($username);
if (($handle = fopen("C3.csv", "r")) !== FALSE)
{
$flag=0;
if((($data0 = fgetcsv($handle, 1000, ",")) !== FALSE))
{
while (($data = fgetcsv($handle, 1000, ",")) !== FALSE)
{
$num = count($data);
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if ($num>0 && $fileuser==$username)
{
$flag = 1;
?>
<h2>Enrolment Number: <?php echo $data[0];?> Name : <?php echo $data[1];?></h2>
<br/>
<table class="fixed">
<col width="250px" />
<col width="100px" />
<thead>
<tr><td><b><u>Exam </u></b></td><td><b><u>Mark</u></b></td></tr>
</thead>
<tbody>
<?php
for ($c=2; $c < $num; $c++)
{
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<tr>
<td><?php echo $data0[$c];?></td>
<td><?php echo $data[$c];?></td>
</tr>
<?php
}
break;
}
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</tbody>
</table>
<?php
}
if($flag==0)
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echo "No data found for this user. Please make sure that you are attending a valid course this semester";
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else
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echo "Primary data not found. Please inform at seemak@iiita.ac.in";
}
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else
echo "Wrong Username/Password";
ldap_close($ds);
}
else
{
?>
<h4>Log-In using your LDAP credentials</h4>
<form action="#" method="POST">
<label for="username">Username: </label><br>
<input id="username" type="text" name="username" /><br>
<label for="password">Password: </label><br>
<input id="password" type="password" name="password" /><br><br>
<input type="submit" name="submit" value="Submit" /><br>
</form>
<?php } ?>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Probability & Statistics (July - December 2019) </a></h3>
<ul class="panel-37">
<li>C3: <a href="./Backpaper_marks.php"><strong>Marks</strong></a>
</li>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Univariate and Multivariate Calculus (January-July 2019) </a></h3>
<ul class="panel-37">
<li><strong>Announcements result_2nd_yr </strong></li>
<ul>
<li> </li>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem,
maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
<li>Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating
series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates,
applications of Power series.</li>
<li>Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional
derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals,
change of variables.</li>
<li>Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem
and applications, Divergence theorem, Stokes’ theorem and applications.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>G. B. Thomas, M. D. Weir, and J. Hass,<i> Thomas' Calculus</i>, Pearson.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>T. M. Apostol, <i>Calculus, Vol. 1</i>, Wiley.</li>
<li>T. M. Apostol, <i>Calculus, Vol. 2</i>, Wiley.</li>
<li>J. Stewart, <i>Calculus</i>, Thompson Press.</li>
<li>Ajit Kumar and S. Kumaresan, <i>A Basic Course in Real Analysis</i>, CRC Press, Taylor & Francis Group.</li>
</ul>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> The Real Number System: <a href="./Lecture_1.pdf" target="_blank"> Lecture 1</a> </li>
<li> Convergence of a Sequence, Monotone Sequences: <a href="./Lecture_2.pdf" target="_blank"> Lecture 2 </a> </li>
<li> Cauchy Criterion, Bolzano - Weierstrass Theorem: <a href="./Lecture_3.pdf" target="_blank"> Lecture 3</a> </li>
<li> Continuity and Limits: <a href="./Lecture_4.pdf" target="_blank"> Lecture 4</a> </li>
<li> Existence of Maxima, Intermediate Value Property, Differentiabilty: <a href="./Lecture_5.pdf" target="_blank"> Lecture 5</a> </li>
<li> Rolle's Theorem, Mean Value Theorem: <a href="./Lecture_6.pdf" target="_blank"> Lecture 6</a> </li>
<li> Cauchy Mean Value Theorem, L'Hopital Rule: <a href="./Lecture_7.pdf" target="_blank"> Lecture 7</a> </li>
<li> Fixed Point Iteration Method, Newton's Method: <a href="./Lecture_8.pdf" target="_blank"> Lecture 8</a> </li>
<li> Sufficient Conditions for Local Maximum, Point of Inflection: <a href="./Lecture_9.pdf" target="_blank"> Lecture 9</a> </li>
<li> Taylor's Theorem: <a href="./Lecture_10.pdf" target="_blank"> Lecture 10</a> </li>
<li> Infinite Series: <a href="./Lecture_11.pdf" target="_blank"> Lecture 11-13</a> </li>
<li> Power Series, Taylor Series: <a href="./Lecture_14.pdf" target="_blank"> Lecture 14</a> </li>
<li> Riemann Integration: <a href="./Lecture_15.pdf" target="_blank"> Lecture 15-16</a> </li>
<li> Fundamental Theorems of Calculus, Riemann Sum: <a href="./Lecture_17.pdf" target="_blank"> Lecture 17</a> </li>
<li> Improper Integrals: <a href="./Lecture_18.pdf" target="_blank"> Lecture 18</a> </li>
<li> Area Between Two Curves; Polar Coordinates: <a href="./Lecture_19.pdf" target="_blank"> Lecture 19</a> </li>
<li> Area in Polar Coordinates, Volume of Solids: <a href="./Lecture_20.pdf" target="_blank"> Lecture 20</a> </li>
<li> Washer and Shell Methods, Length of a plane curve : <a href="./Lecture_21.pdf" target="_blank"> Lecture 21</a> </li>
<li> Areas of Surfaces of Revolution; Pappus's Theorems: <a href="./Lecture_22.pdf" target="_blank"> Lecture 22</a> </li>
<li> Review of vectors, equations of lines and planes; sequences in R^3: <a href="./Lecture_23.pdf" target="_blank"> Lecture 23</a> </li>
<li> Calculus of Vector Valued Functions: <a href="./Lecture_24.pdf" target="_blank"> Lecture 24</a> </li>
<li> Principal Normal; Curvature: <a href="./Lecture_25.pdf" target="_blank"> Lecture 25</a> </li>
<li> Functions of Several Variables - Continuity and Differentiability: <a href="./Lecture_26.pdf" target="_blank"> Lecture 26-27</a> </li>
<li> Directional Derivatives, Gradient, Tangent Plane: <a href="./Lecture_28.pdf" target="_blank"> Lecture 28</a> </li>
<li> Mixed derivative Theorem, MVT: <a href="./Lecture_29.pdf" target="_blank"> Lecture 29</a> </li>
<li> Maxima, Minima, Second Derivative Test: <a href="./Lecture_30.pdf" target="_blank"> Lecture 30</a> </li>
<li> Lagrange Multiplier Method: <a href="./Lecture_31.pdf" target="_blank"> Lecture 31</a> </li>
<li> Double integrals: <a href="./Lecture_32.pdf" target="_blank"> Lecture 32</a> </li>
<li> Change of Variable in a Double Integral, Triple Integrals: <a href="./Lecture_33.pdf" target="_blank"> Lecture 33</a> </li>
<li> Change of Variables in a Triple Integral: <a href="./Lecture_34.pdf" target="_blank"> Lecture 34</a> </li>
</ul>
</br>
<li><strong>Problems</strong></li>
<ul>
<li> The Real Number System: <a href="./Problem_1.pdf" target="_blank"> Problem Set 01</a> </li>
<li> Convergence of Sequences, Monotone Sequences: <a href="./Problem_2.pdf" target="_blank"> Problem Set 02</a> </li>
<li> Cauchy criterion, Subsequence: <a href="./Problem_3.pdf" target="_blank"> Problem Set 03</a> </li>
<li> Continuity and Limits: <a href="./Problem_4.pdf" target="_blank"> Problem Set 04</a> </li>
<li> IVP, Existence of maxima/minima: <a href="./Problem_5.pdf" target="_blank"> Problem Set 05</a> </li>
<li> Differentiability, Rolle’s theorem: <a href="./Problem_6.pdf" target="_blank"> Problem Set 06</a> </li>
<li> Mean Value Theorem: <a href="./Problem_7.pdf" target="_blank"> Problem Set 07</a> </li>
<li> Fixed point iteration method, Newton’s method: <a href="./Problem_8.pdf" target="_blank"> Problem Set 08</a> </li>
<li> Maxima/minima, Curve tracing: <a href="./Problem_9.pdf" target="_blank"> Problem Set 09</a> </li>
<li> Taylor's Theorem: <a href="./Problem_10.pdf" target="_blank"> Problem Set 10</a> </li>
<li> Series: Definition of convergence, Necessary and sufficient conditions for convergence: <a href="./Problem_11.pdf" target="_blank"> Problem Set 11</a> </li>
<li> Comparison, Limit comparison and Cauchy condensation tests: <a href="./Problem_12.pdf" target="_blank"> Problem Set 12</a> </li>
<li> Ratio and Root tests, Leibniz's Test: <a href="./Problem_13.pdf" target="_blank"> Problem Set 13</a> </li>
<li> Functions of Several Variables: <a href="./FoSV.pdf" target="_blank"> Problem </a> </li>
</ul>
</br>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C3 Review Test: <a href="./C3_UMC.pdf" target="_blank"> Question Paper</a>
<a href="./C3_UMC_MS.pdf" target="_blank"> Tentative Marking Scheme</a></li>
</ul>
<li><a href="./result_1st_yr.php"><strong>C3 Marks</strong></a></li>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">LAL/SMAT330C: Linear Algebra (July - December 2018) </a></h3>
<ul class="panel-37">
<li>First year: <a href="./result_1st_yr.php"><strong>C3 Marks</strong></a> </li>
<li>Second Year: <a href="./result_2nd_yr.php"><strong>Marks</strong></a></li>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT130C: Mathematics - I (July-December 2017) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> One more book, viz. A Basic Course in Real Analysis, is added in the Reference Books. Go through Appendix A: Quantifiers. </li>
<li> A link for Practice Problems is added below. Solve as many questions as you can. Hints are also given for each problem set. </li>
<li> Quiz 1 marking scheme is uploaded. </li>
<li> The syllabus for the Mid Semester Examination is from the beginning of the course up to Power Series (Lecture 14). </li>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem,
maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
<li>Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating
series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates,
applications of Power series.</li>
<li>Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional
derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals,
change of variables.</li>
<li>Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem
and applications, Divergence theorem, Stokes’ theorem and applications.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>G. B. Thomas, M. D. Weir, and J. Hass,<i> Thomas' Calculus</i>, Pearson.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>T. M. Apostol, <i>Calculus, Vol. 1</i>, Wiley.</li>
<li>T. M. Apostol, <i>Calculus, Vol. 2</i>, Wiley.</li>
<li>J. Stewart, <i>Calculus</i>, Thompson Press.</li>
<li>Ajit Kumar and S. Kumaresan, <i>A Basic Course in Real Analysis</i>, CRC Press, Taylor & Francis Group.</li>
</ul>
</br>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT430C: Convex Optimization (January-June 2017) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Convex Analysis: convex sets, convex functions, calculus of convex functions. </li>
<li>Optimality of Convex Programs: 1st order necessary and sufficient conditions, KKT conditions. </li>
<li>Duality: Lagrange and conic duality. </li>
<li>Linear and Quadratic Programs.</li>
<li>Conic Programs: QCQPs, SOCPs, SDPs.</li>
<li>Smooth Problems: gradient descent, Nesterov's accelerated method, Newton's methods.</li>
<li>Non-smooth Problems: sub-gradient descent.</li>
<li>Special topics: active set and cutting planes methods, proximal point method.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>S. Boyd and L.Vandenberghe, Convex Optimization. Cambridge University Press, 2004.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>R. T. Rockafellar. Convex Analysis. Princeton University Press, 1996.</li>
<li>G. C. Calafiore and L. El Ghaoui, Optimization Models, Cambridge University Press, 2014.</li>
</ul>
</br>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> Quiz I: <a href="./2017_Q1.pdf" target="_blank"> Question Paper</a>
<a href="./2017_Q1_MS.pdf" target="_blank"> Marking Scheme</a></li>
<li> Mid-Sem: <a href="./2017_MS.pdf" target="_blank"> Question Paper</a>
<a href="./2017_MS_MS.pdf" target="_blank"> Marking Scheme</a></li>
<li> Quiz II: <a href="./2017_Q2.pdf" target="_blank"> Question Paper</a>
<a href="./2017_Q2_MS.pdf" target="_blank"> Marking Scheme</a></li>
<li> End-Sem: <a href="./2017_ES.pdf" target="_blank"> Question Paper</a>
<a href="./2017_ES_MS.pdf" target="_blank"> Marking Scheme</a></li>
</ul>
<li><a href="./results.php"><strong>Marks</strong></a>
(Formula for Total Marks = Q1 + MS + 0.8*Q2 + ES) </li>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT130C: Mathematics - I (July-December 2016) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> Problem set 11 is uploaded.</li>
<li> The syllabus for the Mid Semester Examination will be from Lecture 5 to Lecture 12-13. Sequence, Series and Fundamental
theorem of calculus are not included.</li>
<li> Grading Policy: Quiz I: 20 points, Mid-sem Exam: 35 points, Quiz II: 20 points, End-sem Exam: 75 points, Total: 150 points.
Note that marks will be rescaled (linearly) depending on the full marks of the examination. </li>
</ul>
</br>
<li><strong>Course Outline</strong></li>
<ul>
<li>Univariate Calculus: Function of one variable, Limit, Continuity and Differentiability of functions, Rolle’s theorem, Mean value theorem,
maxima, minima, Riemann integral, Fundamental theorem of calculus, applications to length, area, volume, surface area of revolution.
<li>Infinite Sequences and Series: Sequences, Infinite series, The Integral test, Comparison tests, The Ratio and Root tests, alternating
series, absolute and conditional convergence, Power series. Taylor and Maclaurin series, Convergence of Taylor Series, Error Estimates,
applications of Power series.</li>
<li>Multivariate Calculus: Functions of several variables, Limit, Continuity and Partial derivatives, Chain rule, Gradient, Directional
derivative, and Differentiation, Tangent planes and normals. maxima, minima, saddle points, Lagrange multipliers, Double and Triple integrals,
change of variables.</li>
<li>Calculus on Vector Field: Vector fields, Gradient, Curl and Divergence, Curves, Line integrals and their applications, Green’s theorem
and applications, Divergence theorem, Stokes’ theorem and applications.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>G. B. Thomas, M. D. Weir, and J. Hass,<i> Thomas' Calculus</i>, Pearson.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>T. M. Apostol, <i>Calculus, Vol. 1</i>, Wiley.</li>
<li>T. M. Apostol, <i>Calculus, Vol. 2</i>, Wiley.</li>
<li>J. Stewart, <i>Calculus</i>, Thompson Press.</li>
</ul>
</br>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SPAS230C: Probability and Statistics (January-June 2016) </a></h3>
<ul class="panel-37">
<li><strong>Course Outline</strong></li>
<ul>
<li>Probability: Axiomatic definition, Properties, Conditional probability, Bayes rule and independence of events.</li>
<li>Random Variable: Random Variables, Distribution function, Discrete and Continuous random variables, Probability mass and density functions, Expectation, Function of random variable, Moments, Moment generating function, Chebyshev's inequality.</li>
<li>Special discrete distributions: Bernoulli, Binomial, Geometric, Negative binomial, Hypergeometric, Poisson, Uniform.</li>
<li>Special continuous distributions: Uniform, Exponential, Gamma, Normal.</li>
<li>Random vector: Joint distributions, Marginal and conditional distributions, Moments, Independence of random variables, Covariance, Correlation, Functions of random variables.</li>
<li>Law of Large Numbers: Weak law of large numbers, Levy's Central limit theorem (i.i.d. finite variance case), Normal and Poisson approximations to Binomial.</li>
<li>Statistics: Introduction: Population, Sample, Parameters.</li>
<li>Point Estimation: Method of moments, Maximum likelihood estimation, Unbiasedness, Consistency.</li>
<li>Interval Estimation: Confidence interval.</li>
<li>Tests of Hypotheses: Null and Alternative hypothesis, Type-I and Type-II errors, Level of significance, p-value, Likelihood ratio test, Chi-square goodness of fit tests.</li>
<li>Regression Analysis: Scatter diagram, Simple linear regression, Least square estimation, Tests for slope, prediction problem, Graphical residual analysis, Q-Q plot to test for normality of residuals.</li>
</ul>
</br>
<li><strong>Text Books</strong></li>
<ul>
<li>Rohatgi, V. K. and Saleh, A. K. (2000), <i>An Introduction to Probability and Statistics</i>, 2nd Edition, Wiley-interscience.</li>
<li>Montgomery, D. C., Peck, E. A. and Vining, G. G. (2012), <i>An Introduction to Linear Regression Analysis</i>, 5th Edition, Wiley.</li>
</ul>
</br>
<li><strong>Reference Books</strong></li>
<ul>
<li>Bertsekas, D. P. and Tsitsiklis, J. N. (2008), <i>Introduction to Probability</i>, Athena Scientific, Massachusetts.</li>
<li>Seber, G. A. F. and Lee, A. J. (2003), <i>Linear Regression Analysis</i>, 2nd Edition, Wiley-interscience.</li>
</ul>
</br>
<li><strong>Questions and Keys</strong></li>
<ul>
<li> Back Paper Examination: <a href="spas_back_paper.pdf" target="_blank"> Question Paper</a> <a href="spas_marking.pdf"
target="_blank"> Marking Scheme </a>
</ul>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">SMAT330: Complex Analysis and Integral Transformations (July-December 2015) </a></h3>
<ul class="panel-37">
<li><strong>Course Outline</strong></li>
<ul>
<li>Laplace Transforms: Definition and properties, Sufficient condition of Existence,
Transforms of derivatives and integrals, Derivatives and integrals of transforms, Inverse
Laplace Transforms, Exponential shifts, Convolutions, Applications: Differential and Integral
Equations.</li>
<li>Fourier Series: Periodic functions, fundamental period, Trigonometric series, Fourier
series, Bessel's inequality, Orthonormal and orthogonal set, Euler formulas, Functions with
arbitrary periods, Even and odd functions , Half range expansions, Fourier coefficients
without integration, Approximation by trigonometric polynomials, Application to differential
equation.</li>
<li>Fourier Transforms: Fourier integral theorem, Sine and Cosine Integrals, Inverse
Transforms, Transforms of Elementary Functions, Properties, Convolution, Parsevals relation,
Transform of Dirac Delta Function, Multiple Fourier transform, Finite Fourier transform.</li>
<li>Z Transforms: Z-transforms, properties, Inverse Z- transforms, relationship with Fourier
transforms.</li>
<li>Complex Analysis: Complex numbers, Modulus, Argument, Curves and regions in complex
plane, Functions, Limits, Derivatives, Analytic functions, Cauchy-Riemann equations, Complex
exponential logarithms and trigonometric function, General powers, Line integrals, Cauchy's
theorem, Cauchys integral theorem, Cauchys integral formula, Taylor and Laurent series ,
Zeros and singularities, Residues, Residues theorem, Evaluation of real improper
integrals.</li>
</ul>
<br>
<li><strong>Text Book</strong></li>
<ul>
<li>E. Kreyszig, <i>Advanced Engineering Mathematics</i>, Wiley.</li>
</ul>
<br>
<li><strong>Reference Books</strong></li>
<ul>
<li>M. Braun, <i>Differential Equations and Their Applications</i>, Springer-Verlag, New
York.</li>
<li><a style="color: black;" href="./TRENCH_DIFF_EQNS_I.PDF" target="_blank">W. Trench, <i>Elementary Differential Equations</i></a>.
</li><li>J. Schiff, <i>The Laplace Transform: Theory and Applications</i>, Springer.</li>
<li>J. Brown and R. Churchill, <i>Complex Variables and Application</i>, McGraw-Hill.</li>
<li>G. F. Simmons, <i>Differential Equations</i>, Tata Mcgraw Hill.</li>
<li>R. Jain and S. Iyenger, <i>Advanced Engineering Mathematics</i>, Narosa.</li>
</ul>
<li><strong>Questions and Keys</strong></li>
<ul>
<li> Back Paper Examination: <a href="smat_back_paper.pdf" target="_blank"> Question Paper</a> <a href="smat_marking.pdf"
target="_blank"> Marking Scheme </a>
</ul>
</ul>
</content>
</div>
<br><br>
-->