| I. Linear Algebra |
Lecture 1
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Review of Groups, Fields and Matrices
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Lecture 2
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Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors
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Lecture 3
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Basis, Dimension, Rank and Matrix Inverse
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Lecture 4
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Linear Transformation, Isomorphism and Matrix Representation
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Lecture 5
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System of Linear Equations, Eigenvalues and Eigenvectors
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Lecture 6
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Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices
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Lecture 7
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Jordan Canonical Form, Cayley Hamilton Theorem
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Lecture 8
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Inner Product Spaces, Cauchy-Schwarz Inequality
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Lecture 9
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Orthogonality, Gram-Schmidt Orthogonalization Process
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Lecture 10
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Spectrum of special matrices,positive/negative definite matrices
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| II. Theory of Complex Variables |
Lecture 11
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Concept of Domain, Limit, Continuity and Differentiability
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Lecture 12
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Analytic Functions, CR Equations
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Lecture 13
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Harmonic Functions
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Lecture 14
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Line Integral in the Complex Plane
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Lecture 15
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Cauchy Integral Theorem
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Lecture 16
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Cauchy Integral Theorem (Contd.)
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Lecture 17
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Cauchy Integral Formula
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Lecture 18
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Power and Taylor's Series of Complex Numbers
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Lecture 19
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Power and Taylor's Series of Complex Numbers (Contd.)
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Lecture 20
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Taylor's, Laurent Series of f(z) and Singularities
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Lecture 21
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Classification of Singularities, Residue and Residue Theorem
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| III. Laplace and Fourier Transforms |
Lecture 22
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Laplace Transform and its Existence
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Lecture 23
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Properties of Laplace Transform
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Lecture 24
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Evaluation of Laplace and Inverse Laplace Transform
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Lecture 25
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Applications of Laplace Transform to Integral Equations and ODEs
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Lecture 26
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Applications of Laplace Transform to PDEs
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Lecture 27
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Fourier Series
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Lecture 28
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Fourier Series (Contd.)
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Lecture 29
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Fourier Integral Representation of a Function
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Lecture 30
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Introduction to Fourier Transform
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Lecture 31
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Applications of Fourier Transform to PDEs
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| IV. Probability and Statistics |
Lecture 32
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Laws of Probability I
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Lecture 33
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Laws of Probability II
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Lecture 34
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Problems in Probability
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Lecture 35
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Random Variables
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Lecture 36
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Special Discrete Distributions
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Lecture 37
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Special Continuous Distributions
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Lecture 38
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Joint Distributions and Sampling Distributions
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Lecture 39
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Point Estimation
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Lecture 40
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Interval Estimation
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Lecture 41
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Basic Concepts of Testing of Hypothesis
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Lecture 42
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Tests for Normal Populations
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