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<h3 class="toggler-37"><a href="javascript:void(0)" style="color: black;">Univariate and Multivariate Calculus (March 2023 - June 2023) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> Welcome to the Univariate and Multivariate Calculus webpage. You have to visit this page reguarly for any announcement regarding this course. </li>
<li> </li>
</ul>
<li><a href="./UMC_Syllabus.pdf" target="_blank"><strong>Syllabus</strong></a>
</li>
<li><a href="./Lecture_Schedule.pdf" target="_blank"><strong>Lecture Schedule</strong></a>
</li>
<li><a href="./Tutorial_Schedule.pdf" target="_blank"><strong>Tutorial Schedule</strong></a>
</li>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> Lecture 0: <a href="./Lecture_0_Quantifiers.pdf" target="_blank"> Quantifiers </a> </li>
<li> Lecture 1: <a href="./Lecture_1_The_Real_Number_System.pdf" target="_blank"> The Real Number System </a> </li>
<li> Lecture 2: <a href="./Lecture_2_Sequences_and_Their_Convergence.pdf" target="_blank"> Sequences and Their Convergence </a> </li>
<li> Lecture 3: <a href="./Lecture_3_Cauchy_Sequences_and_Subsequences.pdf" target="_blank"> Cauchy Sequences and Subsequences </a> </li>
<li> Lecture 4: <a href="./Lecture_4_Continuity.pdf" target="_blank"> Continuity </a> </li>
<li> Lecture 5: <a href="./Lecture_5_Limits.pdf" target="_blank"> Limits </a> </li>
<li> Lecture 6: <a href="./Lecture_6_Properties_of_Continuous_Functions.pdf" target="_blank"> Properties of Continuous Functions </a> </li>
<li> Lecture 7: <a href="./Lecture_7_Differentiability.pdf" target="_blank"> Differentiability </a> </li>
<li> Lecture 8: <a href="./Lecture_8_Mean_Value_Theorem.pdf" target="_blank"> Mean Value Theorem </a> </li>
<li> Lecture 9: <a href="./Lecture_9_L’Hospital’s_Rules.pdf" target="_blank"> L’Hospital’s Rules </a> </li>
<li> Lecture 10: <a href="./Lecture_10_Local_Extrema_and_Points_of_Inflection.pdf" target="_blank"> Local Extrema and Points of Inflection </a> </li>
<li> Lecture 11: <a href="./Lecture_11_The_Picard_and_Newton_Methods.pdf" target="_blank"> The Picard and Newton Methods </a> </li>
<li> Lecture 12: <a href="./Lecture_12_Taylor's_Theorem.pdf" target="_blank"> Taylor's Theorem </a> </li>
<li> Lecture 13: <a href="./Lecture_13_Series.pdf" target="_blank"> Series </a> </li>
<li> Lecture 14: <a href="./Lecture_14_Convergence_Tests_for_Series.pdf" target="_blank"> Convergence Tests for Series </a> </li>
<li> Lecture 15: <a href="./Lecture_15_Power_Series.pdf" target="_blank"> Power Series </a> </li>
<li> Lecture 16: <a href="./Lecture_16_Riemann_Integration.pdf" target="_blank"> Riemann Integration </a> </li>
<li> Lecture 17: <a href="./Lecture_17_The_Fundamental_Theorems_of_Calculus.pdf" target="_blank"> The Fundamental Theorems of Calculus </a> </li>
<li> Lecture 18: <a href="./Lecture_18_Improper_Riemann_Integrals.pdf" target="_blank"> Improper Riemann Integrals (TBA) </a> </li>
<li> Lecture 19: <a href="./Lecture_19_The_Euclidean_Spaces.pdf" target="_blank"> The Euclidean Spaces </a> </li>
</ul>
</br>
<li><strong>Problems</strong></li>
<ul>
<li> The Real Number System: <a href="./Problem_Set_1.pdf" target="_blank">Problem Set 01 </a> </li>
<li> Sequences and Their Convergence: <a href="./Problem_Set_2.pdf" target="_blank">Problem Set 02 </a> </li>
<li> Cauchy Sequences and Subsequence: <a href="./Problem_Set_3.pdf" target="_blank">Problem Set 03 </a> </li>
<li> Continuity and Limits: <a href="./Problem_Set_4.pdf" target="_blank">Problem Set 04 </a> </li>
<li> Properties of Continuous Functions: <a href="./Problem_Set_5.pdf" target="_blank">Problem Set 05 </a> </li>
<li> Differentiability: <a href="./Problem_Set_6.pdf" target="_blank">Problem Set 06 </a> </li>
<li> Mean Value Theorem: <a href="./Problem_Set_7.pdf" target="_blank">Problem Set 07 </a> </li>
<li> Local Extrema and Points of Inflection: <a href="./Problem_Set_8.pdf" target="_blank">Problem Set 08 </a> </li>
<li> Taylor's Theorem <a href="./Problem_Set_9.pdf" target="_blank">Problem Set 09 </a> </li>
<li> Series <a href="./Problem_Set_10.pdf" target="_blank">Problem Set 10 </a> </li>
</ul>
<li><strong>Question Papers and Answer Keys </strong></li>
<ul>
<li> Section A: <a href="./Section_A.pdf" target="_blank">Tentaive marking scheme </a> </li>
<li> Section B: <a href="./Section_B.pdf" target="_blank">Tentaive marking scheme </a> </li>
<li> Section C: <a href="./Section_C.pdf" target="_blank">Tentaive marking scheme </a> </li>
<li> Section D: <a href="./Section_D.pdf" target="_blank">Tentaive marking scheme </a> </li>
<li> IFE: <a href="./IFE.pdf" target="_blank">Tentaive marking scheme </a> </li>
<li> C1 Review Test: <a href="./C1_MS.pdf" target="_blank">Tentaive marking scheme </a> </li>
</ul>
</br>
<li><strong>Marks</strong></li>
<ul>
<li>Assessment I & C1 Review Test: <a href="./results2.php"><strong>Marks</strong></a> </li>
</ul>
</ul>
</ul>
</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;">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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