Advanced Engineering Mathematics Video Lectures

Advanced Engineering Mathematics
'Advanced Engineering Mathematics' Video Lectures by Dr. P. Panigrahi, Prof. J. Kumar, Prof. P.D. Srivastava, Prof. Somesh Kumar from IIT Kharagpur
"Advanced Engineering Mathematics" - Video Lectures
1. Review Groups, Fields and Matrices
2. Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors
3. Basis, Dimension, Rank and Matrix Inverse
4. Linear Transformation, Isomorphism and Matrix Representation
5. System of Linear Equations, Eigenvalues and Eigenvectors
6. Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices
7. Jordan Canonical Form, Cayley Hamilton Theorem
8. Inner Product Spaces, Cauchy-Schwarz Inequality
9. Orthogonality, Gram-Schmidt Orthogonalization Process
10. Spectrum of special matrices,positive/negative definite matrices
11. Concept of Domain, Limit, Continuity and Differentiability
12. Analytic Functions, C-R Equations
13. Harmonic Functions
14. Line Integral in the Complex
15. Cauchy Integral Theorem
16. Cauchy Integral Theorem (Contd.)
17. Cauchy Integral Formula
18. Power and Taylor's Series of Complex Numbers
19. Power and Taylor's Series of Complex Numbers (Contd.)
20. Taylor's, Laurent Series of f(z) and Singularities
21. Classification of Singularities, Residue and Residue Theorem
22. Laplace Transform and its Existence
23. Properties of Laplace Transform
24. Evaluation of Laplace and Inverse Laplace Transform
25. Applications of Laplace Transform to Integral Equations and ODEs
26. Applications of Laplace Transform to PDEs
27. Fourier Series
28. Fourier Series (Contd.)
29. Fourier Integral Representation of a Function
30. Introduction to Fourier Transform
31. Applications of Fourier Transform to PDEs
32. Laws of Probability - I
33. Laws of Probability - II
34. Problems in Probability
35. Random Variables
36. Special Discrete Distributions
37. Special Continuous Distributions
38. Joint Distributions and Sampling Distributions
39. Point Estimation
40. Interval Estimation
41. Basic Concepts of Testing of Hypothesis
42. Tests for Normal Populations
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