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Course11110503542 lectures

Advanced Engineering Mathematics

Prof. J. Kumar and others · IIT Kharagpur

Start with lecture 1 At NPTEL

Lectures

Linear Algebra

  1. Review Groups, Fields and Matrices Video
  2. Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors Video
  3. Basis, Dimension, Rank and Matrix Inverse Video
  4. Linear Transformation, Isomorphism and Matrix Representation Video
  5. System of Linear Equations, Eigenvalues and Eigenvectors Video
  6. Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices Video
  7. Jordan Canonical Form, Cayley Hamilton Theorem Video
  8. Inner Product Spaces, Cauchy-Schwarz Inequality Video
  9. Orthogonality, Gram-Schmidt Orthogonalization Process Video
  10. Spectrum of special matrices,positive/negative definite matrices Video

Theory of Complex Variables

  1. Concept of Domain, Limit, Continuity and Differentiability Video
  2. Analytic Functions, C-R Equations Video
  3. Harmonic Functions Video
  4. Line Integral in the Complex Video
  5. Cauchy Integral Theorem Video
  6. Cauchy Integral Theorem (Contd.) Video
  7. Cauchy Integral Formula Video
  8. Power and Taylor's Series of Complex Numbers Video
  9. Power and Taylor's Series of Complex Numbers (Contd.) Video
  10. Taylor's, Laurent Series of f(z) and Singularities Video
  11. Classification of Singularities, Residue and Residue Theorem Video

Transform Calculus

  1. Laplace Transform and its Existence Video
  2. Properties of Laplace Transform Video
  3. Evaluation of Laplace and Inverse Laplace Transform Video
  4. Applications of Laplace Transform to Integral Equations and ODEs Video
  5. Applications of Laplace Transform to PDEs Video
  6. Fourier Series Video
  7. Fourier Series (Contd.) Video
  8. Fourier Integral Representation of a Function Video
  9. Introduction to Fourier Transform Video
  10. Applications of Fourier Transform to PDEs Video

Probability and Statistics

  1. Laws of Probability - I Video
  2. Laws of Probability - II Video
  3. Problems in Probability Video
  4. Random Variables Video
  5. Special Discrete Distributions Video
  6. Special Continuous Distributions Video
  7. Joint Distributions and Sampling Distributions Video
  8. Point Estimation Video
  9. Interval Estimation Video
  10. Basic Concepts of Testing of Hypothesis Video
  11. Tests for Normal Populations Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Kharagpur
Department
Mathematics
Taught by
Prof. J. Kumar, Prof. P.D. Srivastava, Dr. P. Panigrahi, Prof. Somesh Kumar
Level
Undergraduate
Language
English
Subjects
Mathematics
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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