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September 23, 2023

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This course includes:

Unlimited Duration

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Description

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)

Course Curriculum

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

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