IIT Kanpur Course , Prof. Bhaskar Dasgupta

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IIT Kanpur Course , Prof. Bhaskar Dasgupta

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;The Algebraic Eigenvalue Problem:The Algebraic Eigenvalue Problem - Canonical Forms, Symmetric Matrices - Methods of Plane Rotations - Householder Method, Tridiagonal Matrices - QR Decomposition, General Matrices;Selected Topics in Linear Algebra and Calculus:Singular Value Decomposition - Vector Space: Concepts - Multivariate Calculus - Vector Calculus in Geometry - Vector Calculus in Physics;An Introductory Outline of Optimization Techniques:Solution of Equations - Introdcution to Optimization - Multivariate Optimization - Constrained Optimization: Optimality Criteria - Constrained Optimization: Further Issues;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: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;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;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

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2.9 (47 Ratings)

Mathematical Methods in Engineering and Science by Dr. Bhaskar Dasgupta,Department of Mechanical Engineering,IIT Kanpur.For more details on NPTEL visit httpnptel.ac.in

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- 1.Introduction
- 2.Basic Ideas of Applied Linear Algebra
- 3.Systems of Linear Equations
- 4.Square Non-Singular Systems
- 5.Ill-Conditioned and Ill-Posed Systems
- 6.The Algebraic Eigenvalue Problem
- 7.Canonical Forms, Symmetric Matrices
- 8.Methods of Plane Rotations
- 9.Householder Method, Tridiagonal Matrices
- 10.QR Decomposition, General Matrices
- 11.Singular Value Decomposition
- 12.Vector Space Concepts
- 13.Multivariate Calculus
- 14.Vector Calculus in Geometry
- 15.Vector Calculus in Physics
- 16.Solution of Equations
- 17.Introdcution to Optimization
- 18.Multivariate Optimization
- 19.Constrained Optimization Optimality Criteria
- 20.Constrained Optimization Further Issues
- 21.Interpolation
- 22.Numerical Integration
- 23.Numerical Solution of ODEs as IVP
- 24.Boundary Value Problems, Question of Stability in IVP Solution
- 25.Stiff Differential Equations, Existence and Uniqueness Theory
- 26.Theory of First Order ODEs
- 27.Linear Second Order ODEs
- 28.Methods of Linear ODEs
- 29.ODE Systems
- 30.Stability of Dynamic Systems
- 31.Series Solutions and Special Functions
- 32.Sturm-Liouville Theory
- 33.Approximation Theory and Fourier Series
- 34.Fourier Integral to Fourier Transform, Minimax Approximation
- 35.Separation of Variables in PDEs, Hyperbolic Equations
- 36.Parabolic and Elliptic Equations, Membrane Equation
- 37.Analytic Functions
- 38.Integration of Complex Functions
- 39.Singularities and Residues
- 40.Calculus of Variations

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