Learn · Mathematical Methods in Engineering and Science
Lecture 18 of 40Module IV. An Introductory Outline of Optimization Techniques
Multivariate Optimization
Prof. Bhaskar Dasgupta · IIT Kanpur
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- Mathematical Methods in Engineering and Science, IIT Kanpur (at NPTEL)
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All the lectures
- Introduction
- Basic Ideas of Applied Linear Algebra
- Systems of Linear Equations
- Square Non-Singular Systems
- Ill-Conditioned and Ill-Posed Systems
- The Algebraic Eigenvalue Problem
- Canonical Forms, Symmetric Matrices
- Methods of Plane Rotations
- Householder Method, Tridiagonal Matrices
- QR Decomposition, General Matrices
- Singular Value Decomposition
- Vector Space: Concepts
- Multivariate Calculus
- Vector Calculus in Geometry
- Vector Calculus in Physics
- Solution of Equations
- Introdcution to Optimization
- Multivariate Optimization
- Constrained Optimization: Optimality Criteria
- Constrained Optimization: Further Issues
- 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
- Theory of First Order ODE's
- Linear Second Order ODE's
- Methods of Linear ODE's
- ODE Systems
- Stability of Dynamic Systems
- Series Solutions and Special Functions
- Sturm-Liouville Theory
- Approximation Theory and Fourier Series
- Fourier Integral to Fourier Transform, Minimax Approximation
- 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