# InfoCoBuild

## Mathematical Methods in Engineering and Science

Mathematical Methods in Engineering and Science. Instructor: Dr. Bhaskar Dasgupta, Department of Mechanical Engineering, IIT Kanpur. The aim of this course is to develop a firm mathematical background necessary for advanced studies and research in the fields of engineering and science. Solution of linear systems. The algebraic eigenvalue problem. Selected topics in linear algebra and calculus. An introductory outline of optimization techniques. Selected topics in numerical analysis. Ordinary differential equations. Application of ODEs in approximation theory. Partial differential equations. Complex analysis and variational calculus. (from nptel.ac.in)

 Introduction

 Module I. Solution of Linear Systems Lecture 01 - Introduction Lecture 02 - Basic Ideas of Applied Linear Algebra Lecture 03 - Systems of Linear Equations Lecture 04 - Square Non-singular Systems Lecture 05 - Ill-conditioned and Ill-posed Systems Module II. The Algebraic Eigenvalue Problem Lecture 06 - The Algebraic Eigenvalue Problem Lecture 07 - Canonical Forms, Symmetric Matrices Lecture 08 - Methods of Plane Rotations Lecture 09 - Householder Method, Tridiagonal Matrices Lecture 10 - QR Decomposition, General Matrices Module III. Selected Topics in Linear Algebra and Calculus Lecture 11 - Singular Value Decomposition Lecture 12 - Vector Space: Concepts Lecture 13 - Multivariate Calculus Lecture 14 - Vector Calculus in Geometry Lecture 15 - Vector Calculus in Physics Module IV. An Introductory Outline of Optimization Techniques Lecture 16 - Solution of Equations Lecture 17 - Introduction to Optimization Lecture 18 - Multivariate Optimization Lecture 19 - Constrained Optimization: Optimality Criteria Lecture 20 - Constrained Optimization: Further Issues Module V. Selected Topics in Numerical Analysis Lecture 21 - Interpolation Lecture 22 - Numerical Integration Lecture 23 - Numerical Solution of ODEs as IVP Lecture 24 - Boundary Value Problems, Question of Stability in IVP Solution Lecture 25 - Stiff Differential Equations, Existence and Uniqueness Theory Module VI. Ordinary Differential Equations Lecture 26 - Theory of First Order ODEs Lecture 27 - Linear Second Order ODEs Lecture 28 - Methods of Linear ODEs Lecture 29 - ODE Systems Lecture 30 - Stability of Dynamic Systems Module VII. Application of ODEs in Approximation Theory Lecture 31 - Series Solutions and Special Functions Lecture 32 - Sturm-Liouville Theory Lecture 33 - Approximation Theory and Fourier Series Lecture 34 - Fourier Integral to Fourier Transform, Minimax Approximation Module VIII. Overviews: PDEs, Complex Analysis and Variational Calculus Lecture 35 - Separation of Variables in PDEs, Hyperbolic Equations Lecture 36 - Parabolic and Elliptic Equations, Membrane Equation Lecture 37 - Analytic Functions Lecture 38 - Integration of Complex Functions Lecture 39 - Singularities and Residues Lecture 40 - Calculus Variations

 References Mathematical Methods in Engineering and Science Instructor: Dr. Bhaskar Dasgupta, Department of Mechanical Engineering, IIT Kanpur. The aim of this course is to develop a firm mathematical background necessary for advanced studies and research in the fields of engineering and science.