Mathematics - Advanced Engineering Mathematics (English)

1    Monday, March 31, 2025   

Starting a new Lecture Notes Series on Mathematics - Advanced Engineering Mathematics

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Lecture 1: Mod-01 Lec-01 Review Groups, Fields and Matrices

Lecture 2: Mod-01 Lec-02 Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors

Lecture 3: Mod-01 Lec-03 Basis, Dimension, Rank and Matrix Inverse

Lecture 4: Mod-01 Lec-04 Linear Transformation, Isomorphism and Matrix Representation

Lecture 5: Mod-01 Lec-05 System of Linear Equations, Eigenvalues and Eigenvectors

Lecture 6: Mod-01 Lec-06 Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices

Lecture 7: Mod-01 Lec-07 Jordan Canonical Form, Cayley Hamilton Theorem

Lecture 8: Mod-01 Lec-08 Inner Product Spaces, Cauchy-Schwarz Inequality

Lecture 9: Mod-01 Lec-09 Orthogonality, Gram-Schmidt Orthogonalization Process

Lecture 10: Mod-01 Lec-10 Spectrum of special matrices,positive/negative definite matrices

Lecture 11: Mod-02 Lec-11 Concept of Domain, Limit, Continuity and Differentiability

Lecture 12: Mod-02 Lec-12 Analytic Functions, C-R Equations

Lecture 13: Mod-02 Lec-13 Harmonic Functions

Lecture 14: Mod-02 Lec-14 Line Integral in the Complex

Lecture 15: Mod-02 Lec-15 Cauchy Integral Theorem

Lecture 16: Mod-02 Lec-16 Cauchy Integral Theorem (Contd.)

Lecture 17: Mod-02 Lec-17 Cauchy Integral Formula

Lecture 18: Mod-02 Lec-18 Power and Taylor's Series of Complex Numbers

Lecture 19: Mod-02 Lec-19 Power and Taylor's Series of Complex Numbers (Contd.)

Lecture 20: Mod-02 Lec-20 Taylor's, Laurent Series of f(z) and Singularities

Lecture 21: Mod-02 Lec-21 Classification of Singularities, Residue and Residue Theorem

Lecture 22: Mod-03 Lec-22 Laplace Transform and its Existence

Lecture 23: Mod-03 Lec-23 Properties of Laplace Transform

Lecture 24: Mod-03 Lec-24 Evaluation of Laplace and Inverse Laplace Transform

Lecture 25: Mod-03 Lec-25 Applications of Laplace Transform to Integral Equations and ODEs

Lecture 26: Mod-03 Lec-26 Applications of Laplace Transform to PDEs

Lecture 27: Mod-03 Lec-27 Fourier Series

Lecture 28: Mod-03 Lec-28 Fourier Series (Contd.)

Lecture 29: Mod-03 Lec-29 Fourier Integral Representation of a Function

Lecture 30: Mod-03 Lec-30 Introduction to Fourier Transform

Lecture 31: Mod-03 Lec-31 Applications of Fourier Transform to PDEs

Lecture 32: Mod-04 Lec-32 Laws of Probability - I

Lecture 33: Mod-04 Lec-33 Laws of Probability - II

Lecture 34: Mod-04 Lec-34 Problems in Probability

Lecture 35: Mod-04 Lec-35 Random Variables

Lecture 36: Mod-04 Lec-36 Special Discrete Distributions

Lecture 37: Mod-04 Lec-37 Special Continuous Distributions

Lecture 38: Mod-04 Lec-38 Joint Distributions and Sampling Distributions

Lecture 39: Mod-04 Lec-39 Point Estimation

Lecture 40: Mod-04 Lec-40 Interval Estimation

Lecture 41: Mod-04 Lec-41 Basic Concepts of Testing of Hypothesis

Lecture 42: Mod-04 Lec-42 Tests for Normal Populations