Mathematics - Advanced Engineering Mathematics (IIT Kharagpur)

# playlist of the 42 videos (click the up-left corner of the video)

source: nptelhrd     2013年4月29日
Mathematics - Advanced Engineering Mathematics by Prof. P. D. Srivastava, Dr. P. Panigrahi, Prof. Somesh Kumar, Prof. J. Kumar, Department of Mathematics, IIT Kharagpur. For more details on NPTEL visit http://nptel.iitm.ac.in

01 Review Groups, Fields and Matrices 58:15
02 Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors 1:03:30
03 Basis, Dimension, Rank and Matrix Inverse 1:02:09
04 Linear Transformation, Isomorphism and Matrix Representation 51:33
05 System of Linear Equations, Eigenvalues and Eigenvectors 58:34
06 Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices 56:16
07 Jordan Canonical Form, Cayley Hamilton Theorem 1:00:01
08 Inner Product Spaces, Cauchy-Schwarz Inequality 56:16
09 Orthogonality, Gram-Schmidt Orthogonalization Process 59:22
10 Spectrum of special matrices,positive/negative definite matrices 53:48
11 Concept of Domain, Limit, Continuity and Differentiability 53:10
12 Analytic Functions, C-R Equations 54:08
13 Harmonic Functions 55:19
14 Line Integral in the Complex 54:24
15 Cauchy Integral Theorem 52:54
16 Cauchy Integral Theorem (Contd.) 52:48
17 Cauchy Integral Formula 54:03
18 Power and Taylor's Series of Complex Numbers 54:11
19 Power and Taylor's Series of Complex Numbers (Contd.) 55:01
20 Taylor's, Laurent Series of f(z) and Singularities 55:12
21 Classification of Singularities, Residue and Residue Theorem 55:56
22 Laplace Transform and its Existence 59:05
23 Properties of Laplace Transform 57:40
24 Evaluation of Laplace and Inverse Laplace Transform 58:02
25 Applications of Laplace Transform to Integral Equations and ODEs 57:43
26 Applications of Laplace Transform to PDEs 57:26
27 Fourier Series 57:24
28 Fourier Series (Contd.) 58:00
29 Fourier Integral Representation of a Function 57:56
30 Introduction to Fourier Transform 57:57
31 Applications of Fourier Transform to PDEs 57:53
32 Laws of Probability - I 57:10
33 Laws of Probability - II 57:20
34 Problems in Probability 59:25
35 Random Variables 59:26
36 Special Discrete Distributions 58:01
37 Special Continuous Distributions 58:06
38 Joint Distributions and Sampling Distributions 58:29
39 Point Estimation 55:38
40 Interval Estimation 57:22
41 Basic Concepts of Testing of Hypothesis 54:48
42 Tests for Normal Populations 59:50