# Mathematical Methods in Engineering and Science

IIT Kanpur, , Prof. Bhaskar Dasgupta

Updated On 02 Feb, 19

IIT Kanpur, , Prof. Bhaskar Dasgupta

Updated On 02 Feb, 19

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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4.1 ( 11 )

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

Sam

Sep 12, 2018

Excellent course helped me understand topic that i couldn't while attendinfg my college.

Dembe

March 29, 2019

Great course. Thank you very much.