About This Course

Applied Linear Algebra. Nonlinear Optimization. Numerical Methods. Vector and Complex Analysis. Differential Equations and Applications. Approximation Techniques....

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Course Curriculum

8 Sections | 40 Lecture | 37h 41min total length

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Module I. Solution of Linear Systems

| 04h 31min total length

Introduction
52m
Basic Ideas of Applied Linear Algebra
52m
Systems of Linear Equations
51m
Square Non-Singular Systems
59m
Ill-Conditioned and Ill-Posed Systems
55m

Module II. The Algebraic Eigenvalue Problem

| 04h 44min total length

The Algebraic Eigenvalue Problem
55m
Canonical Forms, Symmetric Matrices
55m
Methods of Plane Rotations
56m
Householder Method, Tridiagonal Matrices
1h 60 min
QR Decomposition, General Matrices
57m

Module III. Selected Topics in Linear Algebra and Calculus

| 04h 50min total length

Singular Value Decomposition
57m
Vector Space: Concepts
54m
Multivariate Calculus
56m
Vector Calculus in Geometry
1h 63 min
Vector Calculus in Physics
59m

Module IV. An Introductory Outline of Optimization Techniques

| 04h 36min total length

Solution of Equations
54m
Introduction to Optimization
54m
Multivariate Optimization
55m
Constrained Optimization: Optimality Criteria
55m
Constrained Optimization: Further Issues
56m

Module V. Selected Topics in Numerical Analysis

| 04h 39min total length

Interpolation
58m
Numerical Integration
53m
Numerical Solution of ODE's as IVP
53m
Boundary Value Problems, Question of Stability in IVP Solution?
55m
Stiff Differential Equations, Existence and Uniqueness Theory
58m

Module VI. Ordinary Differential Equations

| 04h 50min total length

Theory of First-Order ODE's
53m
Linear Second Order ODE's
1h 61 min
Methods of Linear ODE's
1h 61 min
ODE Systems
53m
Stability of Dynamic Systems
1h 61 min

Module VII. Application of ODE\'s in Approximation Theory

| 03h 57min total length

Series Solutions and Special Functions
1h 61 min
Sturm-Liouville Theory
1h 60 min
Approximation Theory and Fourier Series
1h 60 min
Fourier Integral to Fourier Transform, Minimax Approximation
55m

Module VIII. Overviews: PDE\'s, Complex Analysis and Variational Calculus

| 05h 28min total length

Calculus of Variations
55m
Separation of Variables in PDE's, Hyperbolic Equations
54m
Parabolic and Elliptic Equations, Membrane Equation
51m
Analytic Functions
51m
Integration of Complex Functions
58m
Singularities and Residues
57m

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More Courses by Dr Bhaskar Dasgupta

Module I. Solution of Linear Systems

Module II. The Algebraic Eigenvalue Problem

Module III. Selected Topics in Linear Algebra and Calculus

Module IV. An Introductory Outline of Optimization Techniques

Module V. Selected Topics in Numerical Analysis

Module VI. Ordinary Differential Equations

Module VII. Application of ODE\'s in Approximation Theory

Module VIII. Overviews: PDE\'s, Complex Analysis and Variational Calculus

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