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Last updated:

September 23, 2023

Duration:

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FREE

This course includes:

Unlimited Duration

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Description

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)

Course Curriculum

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

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