Course Co-ordinated by IIT Kanpur
 Coordinators IIT Kanpur

Untitled Document

• Applied Linear Algebra

• Nonlinear Optimization

• Numerical Methods

• Vector and Complex Analysis

• Differential Equations and Applications

• Approximation Techniques

 Sl. No Topic Lectures 1. Solution of Systems of Linear Equations. Introduction Basic Ideas of Applied Linear Algebra Systems of Linear Equations Square Non-Singular Systems Ill-Conditioned and Ill-Posed Systems 1-5 2. The Algebraic Eigenvalue Problem. The Algebraic Eigenvalue Problem  Canonical Forms, Symmetric Matrices  Methods of Plane Rotations  Householder Method, Tridiagonal Matrices  QR Decomposition, General Matrices 6-10 3. Selected Topics in Linear Algebra and Calculus Singular Value Decomposition  Vector Space: Concepts  Multivariate Calculus  Vector Calculus in Geometry  Vector Calculus in Physics 11-15 4. An Introductory Outline of Optimization Techniques. Solution of Equations  Introdcution to Optimization  Multivariate Optimization  Constrained Optimization: Optimality Criteria  Constrained Optimization: Further Issues 16-20 5. Selected Topics in Numerical Analysis Interpolation Numerical Integration  Numerical Solution of ODE's as IVP  Boundary Value Problems, Question of Stability in IVP Solution  Stiff Differential Equations, Existence and Uniqueness Theory 21-25 6. Ordinary Differential Equations Theory of First Order ODE's Linear Second Order ODE's Methods of Linear ODE's ODE Systems  Stability of Dynamic Systems 26-30 7. Application of ODE's in Approximation Theory Series Solutions and Special Functions  Sturm-Liouville Theory  Approximation Theory and Fourier Series Fourier Integral to Fourier Transform, Minimax Approximation 30-34 8. Overviews: PDE's, Complex Analysis and Variational Calculus Separation of Variables in PDE's, Hyperbolic Equations Parabolic and Elliptic Equations, Membrane Equation  Analytic Functions  Integration of Complex Functions  Singularities and Residues  Calculus of Variations 35-40