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Course11210403540 lectures

Mathematical Methods in Engineering and Science

Prof. Bhaskar Dasgupta · IIT Kanpur

Start with lecture 1 At NPTEL

Lectures

Module I. Solution of Linear Systems

  1. Introduction Video
  2. Basic Ideas of Applied Linear Algebra Video
  3. Systems of Linear Equations Video
  4. Square Non-Singular Systems Video
  5. Ill-Conditioned and Ill-Posed Systems Video

Module II. The Algebraic Eigenvalue Problem

  1. The Algebraic Eigenvalue Problem Video
  2. Canonical Forms, Symmetric Matrices Video
  3. Methods of Plane Rotations Video
  4. Householder Method, Tridiagonal Matrices Video
  5. QR Decomposition, General Matrices Video

Module III. Selected Topics in Linear Algebra and Calculus

  1. Singular Value Decomposition Video
  2. Vector Space: Concepts Video
  3. Multivariate Calculus Video
  4. Vector Calculus in Geometry Video
  5. Vector Calculus in Physics Video

Module IV. An Introductory Outline of Optimization Techniques

  1. Solution of Equations Video
  2. Introdcution to Optimization Video
  3. Multivariate Optimization Video
  4. Constrained Optimization: Optimality Criteria Video
  5. Constrained Optimization: Further Issues Video

Module V. Selected Topics in Numerical Analysis

  1. Interpolation Video
  2. Numerical Integration Video
  3. Numerical Solution of ODE's as IVP Video
  4. Boundary Value Problems, Question of Stability in IVP Solution Video
  5. Stiff Differential Equations, Existence and Uniqueness Theory Video

Module VI. Ordinary Differential Equations

  1. Theory of First Order ODE's Video
  2. Linear Second Order ODE's Video
  3. Methods of Linear ODE's Video
  4. ODE Systems Video
  5. Stability of Dynamic Systems Video

Module VII. Application of ODE\'s in Approximation Theory

  1. Series Solutions and Special Functions Video
  2. Sturm-Liouville Theory Video
  3. Approximation Theory and Fourier Series Video
  4. Fourier Integral to Fourier Transform, Minimax Approximation Video

Module VIII. Overviews: PDE\'s, Complex Analysis and Variational Calculus

  1. Separation of Variables in PDE's, Hyperbolic Equations Video
  2. Parabolic and Elliptic Equations, Membrane Equation Video
  3. Analytic Functions Video
  4. Integration of Complex Functions Video
  5. Singularities and Residues Video
  6. Calculus of Variations Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kanpur
Department
Mechanical Engineering
Teacher
Prof. Bhaskar Dasgupta
Level
Undergraduate
Language
English
Subjects
Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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