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<h3 class="toggler-37"><a href="javascript:void(0)" style="color: black;">Linear Algebra (November 2022 - March 2023) </a></h3>
<ul class="panel-37">
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C3 Review Test: <a href="./C3_MS_22.pdf" target="_blank">Tentaive marking scheme </a> </li>
</ul>
</br>
<li><strong>Marks</strong></li>
<ul>
<li>C3 Review Test:: <a href="./results2.php"><strong>Marks</strong></a> </li>
</ul>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Univariate and Multivariate Calculus (April 2022 - July 2022) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> </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>
<li><a href="./C1_Assessment_Plan.pdf" target="_blank"><strong>C1 Assessment Plan</strong></a>
</li>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> Lecture 01: <a href="./Lecture_1_Quantifiers.pdf" target="_blank"> Quantifiers </a> </li>
<li> Lecture 02: <a href="./Lecture_2_The_Real_Number_System.pdf" target="_blank"> The Real Number System </a> </li>
<li> Lecture 03: <a href="./Lecture_3_Sequences_and_Their_Convergence.pdf" target="_blank"> Sequences and Their Convergence </a> </li>
<li> Lecture 04: <a href="./Lecture_4_Cauchy_Sequences_and_Subsequences.pdf" target="_blank"> Cauchy Sequences and Subsequences </a> </li>
<li> Lecture 05: <a href="./Lecture_5_Continuity.pdf" target="_blank"> Continuity </a> </li>
<li> Lecture 06: <a href="./Lecture_6_Limits.pdf" target="_blank"> Limits </a> </li>
<li> Lecture 07: <a href="./Lecture_7_Properties_of_Continuous_Functions.pdf" target="_blank"> Properties of Continuous Functions </a> </li>
<li> Lecture 08: <a href="./Lecture_8_Differentiability.pdf" target="_blank"> Differentiability </a> </li>
<li> Lecture 09: <a href="./Lecture_9_Mean_Value_Theorem.pdf" target="_blank"> Mean Value Theorem </a> </li>
<li> Lecture 10: <a href="./Lecture_10_L’Hospital’s_Rules.pdf" target="_blank"> L'Hopital's Rules </a> </li>
<li> Lecture 11: <a href="./Lecture_11_Local_Extrema_and_Points_of_Inflection.pdf" target="_blank"> Local Extrema and Points of Inflection </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"> Fundamental Theorems of Calculus </a> </li>
<li> Lecture 18: <a href="./Lecture_18_Improper_Integrals.pdf" target="_blank"> Improper Integrals</a> </li>
<li> Lecture 19: <a href="./Lecture_19_The_Euclidean_Spaces.pdf" target="_blank"> The Euclidean Spaces</a> </li>
<li> Lecture 20: <a href="./Lecture_20_Limits_and_Continuity_of_Functions_of_Several_Variables.pdf" target="_blank"> Limits and Continuity of Functions of Several Variables </a> </li>
<li> Lecture 21: <a href="./Lecture_21_Differentiability_of_Functions_of_Several_Variables.pdf" target="_blank"> Differentiability of Functions of Several Variables</a> </li>
<li> Lecture 22: <a href="./L22_Local_Extrema_and_Saddle_Points.pdf" target="_blank"> Local Extrema and Saddle Points</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>
<li> Convergence Tests I: Comparison, Limit comparison and Cauchy condensation tests: <a href="./Problem_Set_11.pdf" target="_blank">Problem Set 11 </a> </li>
<li> Convergence Tests II: Ratio, Root and Leibniz’s tests: <a href="./Problem_Set_12.pdf" target="_blank">Problem Set 12 </a> </li>
<li> Power Series: <a href="./Problem_Set_13.pdf" target="_blank">Problem Set 13 </a> </li>
<li> Riemann Integration: <a href="./Problem_Set_14.pdf" target="_blank">Problem Set 14 </a> </li>
<li> FTC, Riemann Sum and Improper Integrals: <a href="./Problem_Set_15.pdf" target="_blank">Problem Set 15 </a> </li>
<li> Functions of Several Variables: <a href="./Problem_Set_16.pdf" target="_blank">Problem Set 16 </a> </li>
<li> Local Extrema and Lagrange Multiplier Method: <a href="./Problem_Set_17.pdf" target="_blank">Problem Set 17 </a> </li>
<li> Double Integrals: <a href="./Problem_Set_18.pdf" target="_blank">Problem Set 18 </a> </li>
<li> Triple Integrals: <a href="./Problem_Set_19.pdf" target="_blank">Problem Set 19 </a> </li>
</ul>
</br>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> Make Up Exam: <a href="./Make_Up_MS.pdf" target="_blank">Tentaive marking scheme </a> </li>
</ul>
</br>
<li><strong>Marks</strong></li>
<ul>
<li>C3 Make Up Exam: <a href="./results2.php"><strong>Marks</strong></a> </li>
</ul>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Univariate and Multivariate Calculus (April 2021 - July 2021) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> Problem set 04 is uploaded. </li>
<li> Lecture 06 is updated. </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>
<li><a href="./C.pdf" target="_blank"><strong>C1 assessment plan (TBA)</strong></a>
</li>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> Lecture 01: <a href="./Lecture_1_Quantifiers.pdf" target="_blank"> Quantifiers </a> </li>
<li> Lecture 02: <a href="./Lecture_2_The_Real_Number_System.pdf" target="_blank"> The Real Number System </a> </li>
<li> Lecture 03: <a href="./Lecture_3_Sequences_and_Their_Convergence.pdf" target="_blank"> Sequences and Their Convergence </a> </li>
<li> Lecture 04: <a href="./Lecture_4_Cauchy_Sequences_and_Subsequences.pdf" target="_blank"> Cauchy Sequences and Subsequences </a> </li>
<li> Lecture 05: <a href="./Lecture_5_Continuity.pdf" target="_blank"> Continuity </a> </li>
<li> Lecture 06: <a href="./Lecture_6_Limits.pdf" target="_blank"> Limits </a> </li>
<li> Lecture 07: <a href="./Lecture_5.pdf" target="_blank"> Existence of Maxima, Intermediate Value Property, Differentiability</a> </li>
<li> Lecture 08: <a href="./Lecture_6.pdf" target="_blank"> Rolle's Theorem, Mean Value Theorem</a> </li>
<li> Lecture 09: <a href="./Lecture_7.pdf" target="_blank"> Cauchy Mean Value Theorem, L'Hopital Rule</a> </li>
<li> Lecture 10: <a href="./Lecture_9.pdf" target="_blank"> Sufficient Conditions for Local Maximum, Point of Inflection</a> </li>
<li> Lecture 11: <a href="./Lecture_11_Taylor's_Theorem.pdf" target="_blank"> Taylor's Theorem</a> </li>
<li> Lecture 12: <a href="./Lecture_11.pdf" target="_blank"> Infinite Series, Convergence Tests, Leibniz's Theorem </a> </li>
<li> Lecture 13: <a href="./Lecture_14.pdf" target="_blank"> Power Series, Taylor Series </a> </li>
<li> Lecture 14: <a href="./Lecture_14_Riemann_Integration.pdf" target="_blank"> Riemann Integration </a> </li>
<li> Lecture 15: <a href="./Lecture_15_The Fundamental_Theorems_of_Calculus.pdf" target="_blank"> Fundamental Theorems of Calculus </a> </li>
<li> Lecture 16: <a href="./Lecture_18.pdf" target="_blank"> Improper Integrals</a> </li>
<li> Lecture 17: <a href="./Lecture_19.pdf" target="_blank"> Area Between Two Curves; Polar Coordinates </a> </li>
<li> Lecture 18: <a href="./Lecture_20.pdf" target="_blank"> Area in Polar Coordinates, Volume of Solids </a> </li>
<li> Lecture 19: <a href="./Lecture_21.pdf" target="_blank"> Washer and Shell Methods, Length of a plane curve </a> </li>
<li> Lecture 20: <a href="./Lecture_22.pdf" target="_blank"> Areas of Surfaces of Revolution; Pappus's Theorems </a> </li>
<li> Lecture 21: <a href="./Lecture_26.pdf" target="_blank"> Functions of Several Variables - Continuity and Differentiability </a> </li>
<li> Lecture 22: <a href="./Lecture_28.pdf" target="_blank"> Directional Derivatives, Gradient, Tangent Plane </a> </li>
<li> Lecture 23: <a href="./Lecture_30.pdf" target="_blank"> Maxima, Minima, Second Derivative Test</a> </li>
<li> Lecture 24: <a href="./Lecture_32.pdf" target="_blank"> Double integrals</a> </li>
<li> Lecture 25: <a href="./Lecture_33.pdf" target="_blank"> Change of Variable in a Double Integral, Triple Integrals</a> </li>
<li> Lecture 26: <a href="./Lecture_34.pdf" target="_blank"> Change of Variables in a Triple Integral</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> 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> Maxima/minima, Curve tracing: <a href="./Problem_9.pdf" target="_blank"> Problem Set 08</a> </li>
<li> Taylor's Theorem: <a href="./Problem_10.pdf" target="_blank"> Problem Set 9</a> </li>
<li> Series: Definition of convergence, Necessary and sufficient conditions for convergence: <a href="./Problem_11.pdf" target="_blank"> Problem Set 10</a> </li>
<li> Comparison, Limit comparison and Cauchy condensation tests: <a href="./Problem_12.pdf" target="_blank"> Problem Set 11</a> </li>
<li> Ratio and Root tests, Leibniz's Test: <a href="./Problem_13.pdf" target="_blank"> Problem Set 12</a> </li>
</ul>
</br>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C3 Review Test: <a href="./C3_MS_21.pdf" target="_blank">Tentaive marking scheme </a> </li>
</ul>
</br>
<li><strong>Marks</strong></li>
<ul>
<li>C3 Review Test: <a href="./results2.php"><strong>Marks</strong></a> </li>
</ul>
</ul>
<h3 class="toggler-37"><a href="javascript:void(0)" style="color: grey;">Probability & Statistics (July-December 2020) </a></h3>
<ul class="panel-37">
<li><strong>Announcements</strong></li>
<ul>
<li> We would like to express our deepest appreciation to Professor Neeraj Mishra, IIT Kanpur for many insightful discussions while teaching this course in the past couple of years. The modules for the same course available on his personal web page were very helpful in preparing our lecture notes. </li>
<li> First lecture on basic probability is uploaded. We will upload problem set 01 soon. </li>
<li> Problem Set 01 is uploaded. </li>
<li> Lecture 03 is uploaded. </li>
<li> Lecture 04 is uploaded. </li>
<li> Lecture 05 and problem set 02 are uploaded. We have slightly modified lectures 03 & 04. Download the latest ones.</li>
<li> The syllabus of the quiz this weekend consists of lectures 01, 02 & 03. Exact time and mode will be emailed later. </li>
<li> Lecture 09 is uploaded. </li>
<li> Lecture 10 is uploaded. </li>
<li> Check the detailed assessment plan for C2 & C3 </li>
<li> Problem set 04 is uploaded. </li>
<li> Lecture 15 is uploaded. </li>
<li> Lecture 16 is uploaded. </li>
<li> Lecture 17 is uploaded. </li>
<li> Lecture 18 is uploaded. </li>
<li> Lecture 19 is uploaded. </li>
<li> Lecture 20 and problem set 05 are uploaded. </li>
<li> Lecture 21 & 22 are uploaded. </li>
</ul>
<li><a href="./PAS_Syllabus.pdf" target="_blank"><strong>Syllabus</strong></a>
</li>
<li><a href="./Time_Table.pdf" target="_blank"><strong>Time Table and component-wise plan</strong></a>
</li>
<li><a href="./Groups.pdf" target="_blank"><strong>Groups (TBA)</strong></a>
</li>
<li><a href="./C2_C3.pdf" target="_blank"><strong>C2 & C2 assessment plan</strong></a>
</li>
<li><a href="./z_table.pdf" target="_blank"><strong>z-table</strong></a>
</li>
</br>
<li><strong>Lecture Notes</strong></li>
<ul>
<li> Lecture 01: <a href="./Basic_Probability.pdf" target="_blank">Basic Probability </a> </li>
<li> Lecture 02: <a href="./Conditional_Probability.pdf" target="_blank">Conditional Probability </a> </li>
<li> Lecture 03: <a href="./Random_Variable.pdf" target="_blank">Random Variable </a> </li>
<li> Lecture 04: <a href="./Types_of_Random_Variables.pdf" target="_blank">Types of Random Variables</a> </li>
<li> Lecture 05: <a href="./Function_of_Random_Variables.pdf" target="_blank">Function of Random Variables</a> </li>
<li> Lecture 06: <a href="./Expectation.pdf" target="_blank">Expectation, Variance and Standard Deviation</a> </li>
<li> Lecture 07: <a href="./Moment_generating_function.pdf" target="_blank">Moment generating function</a> </li>
<li> Lecture 08: <a href="./Bernoulli_Binomial_Uniform.pdf" target="_blank">Special Discrete Distribution I: Bernoulli, Binomial and Uniform</a> </li>
<li> Lecture 09: <a href="./Negative_Binomial_and_Geometric.pdf" target="_blank">Special Discrete Distribution II: Negative Binomial and Geometric</a> </li>
<li> Lecture 10: <a href="./Hypergeometric_and_Poisson.pdf" target="_blank">Special Discrete Distribution III: Hypergeometric and Poisson</a> </li>
<li> Lecture 11: <a href="./Uniform_and_Normal.pdf" target="_blank">Special Continuous Distribution I: Uniform and Normal</a> </li>
<li> Lecture 12: <a href="./Gamma_and_Exponential.pdf" target="_blank">Special Continuous Distribution II: Gamma and Exponential</a> </li>
<li> Lecture 13: <a href="./Random_Vector.pdf" target="_blank">Random Vector</a> </li>
<li> Lecture 14: <a href="./Types_Random_Vector.pdf" target="_blank">Types of Random Vector</a> </li>
<li> Lecture 15: <a href="./Conditional_Distributions_and_Independent_Random_Variables.pdf" target="_blank">Conditional Distributions and Independent Random Variables</a> </li>
<li> Lecture 16: <a href="./Momets_Covariance_Correlation.pdf" target="_blank">Momets, Covariance & Correlation Coefficient</a> </li>
<li> Lecture 17: <a href="./Conditional_Expectation_Variance.pdf" target="_blank">Conditional Expectation and Variance</a> </li>
<li> Lecture 18: <a href="./Joint_Moment_generating_function.pdf" target="_blank">Joint Moment generating function</a> </li>
<li> Lecture 19: <a href="./Functions_of_several_Random_Variables.pdf" target="_blank">Functions of several Random Variables</a> </li>
<li> Lecture 20: <a href="./Law_of_Large_Numbers_CLT_Normal_Approximation.pdf" target="_blank">Law of Large Numbers, CLT and Normal Approximation</a> </li>
<li> Lecture 21: <a href="./Point_Estimation.pdf" target="_blank">Point Estimation</a> </li>
<li> Lecture 22: <a href="./Testing_Statistical_Hypothesis.pdf" target="_blank">Testing Statistical Hypothesis</a> </li>
</ul>
</br>
<li><strong>Problems</strong></li>
<ul>
<li> <a href="./PS_I.pdf" target="_blank">Problem Set 01 </a> </li>
<li> <a href="./PS_II.pdf" target="_blank">Problem Set 02 </a> </li>
<li> <a href="./PS_III.pdf" target="_blank">Problem Set 03 </a> </li>
<li> <a href="./PS_IV.pdf" target="_blank">Problem Set 04 </a> </li>
<li> <a href="./PS_V.pdf" target="_blank">Problem Set 05 </a> </li>
</ul>
</br>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> C3 Review Test: <a href="./C3_Review_Test_MS.pdf" target="_blank"> Tentative Marking Scheme</a></li>
</ul>
</br>
<li><strong>C3 Marks</strong></li>
<ul>
<li>C3 Review Test: <a href="./C3_Marks.php"><strong>Marks</strong></a> </li>
</ul>
</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>
<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> Maxima, Minima, Second Derivative Test: <a href="./Lecture_30.pdf" target="_blank"> Lecture 29</a> </li>
<li> Double integrals: <a href="./Lecture_32.pdf" target="_blank"> Lecture 30</a> </li>
<li> Change of Variable in a Double Integral, Triple Integrals: <a href="./Lecture_33.pdf" target="_blank"> Lecture 31</a> </li>
<li> Change of Variables in a Triple Integral: <a href="./Lecture_34.pdf" target="_blank"> Lecture 32</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>
</ul>
</br>
<li><strong>Question Papers and Answer Keys</strong></li>
<ul>
<li> Quiz 1: <a href="./Q1.pdf" target="_blank"> Question Paper</a>
<a href="./Q1_MS.pdf" target="_blank"> Tentative Marking Scheme</a></li>
<li> C1 Review Test: <a href="./C1.pdf" target="_blank"> Question Paper</a>
<a href="./C1_MS.pdf" target="_blank"> Tentative Marking Scheme</a></li>
</ul>
<li><a href="./result_1st_yr.php"><strong>C3 Make Up Marks</strong></a></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_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>
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