Contents:
Linear Algebra : Review: Groups, Fields, & Matrices – Vector Spaces, Subspaces, Linearly dependent / independent of vectors – Basis, Dimension, Rank and Matrix Inverse – Linear Transformation, Isomorphism & Matrix Representation – System of Linear Equations, Eigenvalues and Eigenvectors – Method to find Eigenvalues and Eigenvectors, Diagonalization of Matrices – Jordan Canonical Form, Cayley Hamilton Theorem – Innerproduct Spaces, Cauchy-Schwarz Inequality – Orthogonality, Gram-Schmidt Orthogonalization Process – Spectrum of Special Matrices, Positive / Negative Definite Matrices.

Theory of Complex Variables : Concept of Domain, Limit, Continuity & Differentiability – Analytic Functions, C-R Equations – Harmonic Functions – Line Integral in the complex – Cauchy Integral Theorem – Cauchy Integral Formula – Power & Taylor’s Series of Complex Numbers – Power & Taylor’s Series of Complex Numbers (Contd.) – Taylor’s Laurent Series of f(z) & Singularities – Classification of Singularities , Residue and Residue Theorem.

Transform Calculus : Laplace Transform and its Existence – Properties of Laplace Transform – Evaluation of Laplace and Inverse Laplace Transform – Applications of Laplace Transform to Integral Equations and ODEs – Applications of Laplace Transform to PDEs – Fourier Series – Fourier Integral Representation of a Function – Introduction to Fourier Transform – Applications of Fourier Transform t PDEs.

Probability & Statistics : Laws of Probability – Problems in Probability – Random Variables – Special Discrete Distributions – Special Continuous Distributions – Joint Distributions and Sampling Distributions – Point Estimation – Interval Estimation – Basic Concepts of Testing of Hypothesis – Tests for Normal Populations.

Other Resources

Course Curriculum

Mod-01 Lec-01 Review Groups, Fields and Matrices Details 58:15
Mod-01 Lec-02 Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors Details 1:3:30
Mod-01 Lec-03 Basis, Dimension, Rank and Matrix Inverse Details 1:2:9
Mod-01 Lec-04 Linear Transformation, Isomorphism and Matrix Representation Details 51:33
Mod-01 Lec-05 System of Linear Equations, Eigenvalues and Eigenvectors Details 58:34
Mod-01 Lec-06 Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices Details 56:16
Mod-01 Lec-07 Jordan Canonical Form, Cayley Hamilton Theorem Details 1:1
Mod-01 Lec-08 Inner Product Spaces, Cauchy-Schwarz Inequality Details 56:16
Mod-01 Lec-09 Orthogonality, Gram-Schmidt Orthogonalization Process Details 59:22
Mod-01 Lec-10 Spectrum of special matrices,positive/negative definite matrices Details 53:48
Mod-02 Lec-11 Concept of Domain, Limit, Continuity and Differentiability Details 53:10
Mod-02 Lec-12 Analytic Functions, C-R Equations Details 54:8
Mod-02 Lec-13 Harmonic Functions Details 55:19
Mod-02 Lec-14 Line Integral in the Complex Details 54:24
Mod-02 Lec-15 Cauchy Integral Theorem Details 52:54
Mod-02 Lec-16 Cauchy Integral Theorem (Contd.) Details 52:48
Mod-02 Lec-17 Cauchy Integral Formula Details 54:3
Mod-02 Lec-18 Power and Taylor’s Series of Complex Numbers Details 54:11
Mod-02 Lec-19 Power and Taylor’s Series of Complex Numbers (Contd.) Details 55:1
Mod-02 Lec-20 Taylor’s, Laurent Series of f(z) and Singularities Details 55:12
Mod-02 Lec-21 Classification of Singularities, Residue and Residue Theorem Details 55:56
Mod-03 Lec-22 Laplace Transform and its Existence Details 59:5
Mod-03 Lec-23 Properties of Laplace Transform Details 57:40
Mod-03 Lec-24 Evaluation of Laplace and Inverse Laplace Transform Details 58:2
Mod-03 Lec-25 Applications of Laplace Transform to Integral Equations and ODEs Details 57:43
Mod-03 Lec-26 Applications of Laplace Transform to PDEs Details 57:26
Mod-03 Lec-27 Fourier Series Details 57:24
Mod-03 Lec-28 Fourier Series (Contd.) Details 0:58
Mod-03 Lec-29 Fourier Integral Representation of a Function Details 57:56
Mod-03 Lec-30 Introduction to Fourier Transform Details 57:57
Mod-03 Lec-31 Applications of Fourier Transform to PDEs Details 57:53
Mod-04 Lec-32 Laws of Probability – I Details 57:10
Mod-04 Lec-33 Laws of Probability – II Details 57:20
Mod-04 Lec-34 Problems in Probability Details 59:25
Mod-04 Lec-35 Random Variables Details 59:26
Mod-04 Lec-36 Special Discrete Distributions Details 58:1
Mod-04 Lec-37 Special Continuous Distributions Details 58:6
Mod-04 Lec-38 Joint Distributions and Sampling Distributions Details 58:29
Mod-04 Lec-39 Point Estimation Details 55:38
Mod-04 Lec-40 Interval Estimation Details 57:22
Mod-04 Lec-41 Basic Concepts of Testing of Hypothesis Details 54:48
Mod-04 Lec-42 Tests for Normal Populations Details 59:50

These video tutorials are delivered by IIT Kharagpur as part of NPTEL online courses program.

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