# Mathematical Methods in Engineering and Science

IIT Kanpur Course , Prof. Bhaskar Dasgupta

### Lecture 1: Introduction

##### Lecture Details :

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

##### Course Description :

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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