Advanced Engineering Mathematics
Advanced Engineering Mathematics. Instructors: Dr. Pratima Panigrahi, Prof. P.D. Srivastava, Prof. Somesh Kumar, and Prof. Jitendra Kumar, Department of Mathematics, IIT Kharagpur. This is a course suitable for B.Tech / M.Tech students of various discipline. It deals with some advanced topics in Engineering Mathematics usually covered in a degree course: linear algebra, theory of complex variables, Laplace transform, Fourier series and transform, probability and statistics.
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Lecture 35 - Random Variables
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Linear Algebra
Lecture 01 - Review Groups, Fields, and Matrices
Lecture 02 - Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors
Lecture 03 - Basis, Dimension, Rank and Matrix Inverse
Lecture 04 - Linear Transformation, Isomorphism and Matrix Representation
Lecture 05 - System of Linear Equations, Eigenvalues and Eigenvectors
Lecture 06 - Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices
Lecture 07 - Jordan Canonical Form, Cayley Hamilton Theorem
Lecture 08 - Inner Product Spaces, Cauchy-Schwarz Inequality
Lecture 09 - Orthogonality, Gram-Schmidt Orthogonalization Process
Lecture 10 - Spectrum of Special Matrices, Positive/Negative Definite Matrices
Theory of Complex Variables
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 (cont.)
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 (cont.)
Lecture 20 - Taylor's, Laurent Series of f(z) and Singularities
Lecture 21 - Classification of Singularities, Residue and Residue Theorem
Transform Calculus
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 (cont.)
Lecture 29 - Fourier Integral Representation of a Function
Lecture 30 - Introduction to Fourier Transform
Lecture 31 - Applications of Fourier Transform to PDEs
Probability and Statistics
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