# 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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