Advanced Engineering Mathematics


Lecture 1 - Review Groups, Fields and Matrices


Lecture 2 - Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors


Lecture 3 - Basis, Dimension, Rank and Matrix Inverse


Lecture 4 - Linear Transformation, Isomorphism and Matrix Representation


Lecture 5 - System of Linear Equations, Eigenvalues and Eigenvectors


Lecture 6 - Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices


Lecture 7 - Jordan Canonical Form, Cayley Hamilton Theorem


Lecture 8 - Inner Product Spaces, Cauchy-Schwarz Inequality


Lecture 9 - Orthogonality, Gram-Schmidt Orthogonalization Process


Lecture 10 - Spectrum of special matrices,positive/negative definite matrices


Lecture 11 - Concept of Domain, Limit, Continuity and Differentiability


Lecture 12 - Analytic Functions, C-R Equations


Lecture 13 - Harmonic Functions


Lecture 14 - Line Integral in the Complex


Lecture 15 - Cauchy Integral Theorem


Lecture 16 - Cauchy Integral Theorem (Continued.)


Lecture 17 - Cauchy Integral Formula


Lecture 18 - Power and Taylor's Series of Complex Numbers


Lecture 19 - Power and Taylor's Series of Complex Numbers (Continued.)


Lecture 20 - Taylor's, Laurent Series of f(z) and Singularities


Lecture 21 - Classification of Singularities, Residue and Residue Theorem


Lecture 22 - Laplace Transform and its Existence


Lecture 23 - Properties of Laplace Transform


Lecture 24 - Evaluation of Laplace and Inverse Laplace Transform


Lecture 25 - Applications of Laplace Transform to Integral Equations and ODEs


Lecture 26 - Applications of Laplace Transform to PDEs


Lecture 27 - Fourier Series


Lecture 28 - Fourier Series (Continued.)


Lecture 29 - Fourier Integral Representation of a Function


Lecture 30 - Introduction to Fourier Transform


Lecture 31 - Applications of Fourier Transform to PDEs


Lecture 32 - Laws of Probability - I


Lecture 33 - Laws of Probability - II


Lecture 34 - Problems in Probability


Lecture 35 - Random Variables


Lecture 36 - Special Discrete Distributions


Lecture 37 - Special Continuous Distributions


Lecture 38 - Joint Distributions and Sampling Distributions


Lecture 39 - Point Estimation


Lecture 40 - Interval Estimation


Lecture 41 - Basic Concepts of Testing of Hypothesis


Lecture 42 - Tests for Normal Populations