Mathematical Methods in Engineering and Science. Instructor: Dr. Bhaskar Dasgupta, Department of Mechanical Engineering, IIT Kanpur.
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September 25, 2023
English
English [CC]
Description
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
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- Lecture 01 – Introduction 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
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- 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 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 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
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