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Advanced Engineering Mathematics

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 22 - Laplace Transform and its Existence

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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