Mathematical Methods in Engineering and Science

IIT Kanpur Course , Prof. Bhaskar Dasgupta

165 students enrolled

Overview

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

Lecture 1: Introduction

Up Next
You can skip ad in
SKIP AD >
Advertisement
      • 2x
      • 1.5x
      • 1x
      • 0.5x
      • 0.25x
        EMBED LINK
        COPY
        DIRECT LINK
        PRIVATE CONTENT
        OK
        Enter password to view
        Please enter valid password!
        0:00
        2.9 (47 Ratings)

        Lecture Details

        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

        LECTURES



        Review


        2.9

        47 Rates
        5
        30%
        14
        4
        13%
        6
        3
        11%
        5
        2
        13%
        6
        1
        34%
        16

        Comments Added Successfully!
        Please Enter Comments
        Please Enter CAPTCHA
        Invalid CAPTCHA
        Please Login and Submit Your Comment