# InfoCoBuild

Advanced Engineering Mathematics. Instructors: Dr. Pratima Panigrahi, Prof. P.D. Srivastava, Prof. Somesh Kumar, and Prof. Jitendra Kumar, Department of Mathematics, IIT Kharagpur. This is a course suitable for B.Tech / M.Tech students of various discipline. It deals with some advanced topics in Engineering Mathematics usually covered in a degree course: linear algebra, theory of complex variables, Laplace transform, Fourier series and transform, probability and statistics. (from nptel.ac.in)

 Lecture 19 - Power and Taylor's Series of Complex Numbers (cont.)

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 Linear Algebra Lecture 01 - Review Groups, Fields, and Matrices Lecture 02 - Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors Lecture 03 - Basis, Dimension, Rank and Matrix Inverse Lecture 04 - Linear Transformation, Isomorphism and Matrix Representation Lecture 05 - System of Linear Equations, Eigenvalues and Eigenvectors Lecture 06 - Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices Lecture 07 - Jordan Canonical Form, Cayley Hamilton Theorem Lecture 08 - Inner Product Spaces, Cauchy-Schwarz Inequality Lecture 09 - Orthogonality, Gram-Schmidt Orthogonalization Process Lecture 10 - Spectrum of Special Matrices, Positive/Negative Definite Matrices Theory of Complex Variables Lecture 11 - Concept of Domain, Limit, Continuity and Differentiability Lecture 12 - Analytic Functions, C-R Equations Lecture 13 - Harmonic Functions Lecture 14 - Line Integral in the Complex Lecture 15 - Cauchy Integral Theorem Lecture 16 - Cauchy Integral Theorem (cont.) Lecture 17 - Cauchy Integral Formula Lecture 18 - Power and Taylor's Series of Complex Numbers Lecture 19 - Power and Taylor's Series of Complex Numbers (cont.) Lecture 20 - Taylor's, Laurent Series of f(z) and Singularities Lecture 21 - Classification of Singularities, Residue and Residue Theorem Transform Calculus Lecture 22 - Laplace Transform and its Existence Lecture 23 - Properties of Laplace Transform Lecture 24 - Evaluation of Laplace and Inverse Laplace Transform Lecture 25 - Applications of Laplace Transform to Integral Equations and ODEs Lecture 26 - Applications of Laplace Transform to PDEs Lecture 27 - Fourier Series Lecture 28 - Fourier Series (cont.) Lecture 29 - Fourier Integral Representation of a Function Lecture 30 - Introduction to Fourier Transform Lecture 31 - Applications of Fourier Transform to PDEs Probability and Statistics Lecture 32 - Laws of Probability I Lecture 33 - Laws of Probability II Lecture 34 - Problems in Probability Lecture 35 - Random Variables Lecture 36 - Special Discrete Distributions Lecture 37 - Special Continuous Distributions Lecture 38 - Joint Distributions and Sampling Distributions Lecture 39 - Point Estimation Lecture 40 - Interval Estimation Lecture 41 - Basic Concepts of Testing of Hypothesis Lecture 42 - Tests for Normal Populations