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.
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