Advanced Engineering Mathematics
IIT Kharagpur, , Prof. P. Panigrahi
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Updated On 02 Feb, 19
Linear Algebra : Review: Groups, Fields, & Matrices - Vector Spaces, Subspaces, Linearly dependent / independent of vectors - Basis, Dimension, Rank and Matrix Inverse - Linear Transformation, Isomorphism & Matrix Representation - System of Linear Equations, Eigenvalues and Eigenvectors - Method to find Eigenvalues and Eigenvectors, Diagonalization of Matrices - Jordan Canonical Form, Cayley Hamilton Theorem - Innerproduct Spaces, Cauchy-Schwarz Inequality - Orthogonality, Gram-Schmidt Orthogonalization Process - Spectrum of Special Matrices, Positive / Negative Definite Matrices.
Theory of Complex Variables : Concept of Domain, Limit, Continuity & Differentiability - Analytic Functions, C-R Equations - Harmonic Functions - Line Integral in the complex - Cauchy Integral Theorem - Cauchy Integral Formula - Power & Taylors Series of Complex Numbers - Power & Taylors Series of Complex Numbers (Contd.) - Taylors Laurent Series of f(z) & Singularities - Classification of Singularities , Residue and Residue Theorem.
Transform Calculus : Laplace Transform and its Existence - Properties of Laplace Transform - Evaluation of Laplace and Inverse Laplace Transform - Applications of Laplace Transform to Integral Equations and ODEs - Applications of Laplace Transform to PDEs - Fourier Series - Fourier Integral Representation of a Function - Introduction to Fourier Transform - Applications of Fourier Transform t PDEs.
Probability & Statistics : Laws of Probability - Problems in Probability - Random Variables - Special Discrete Distributions - Special Continuous Distributions - Joint Distributions and Sampling Distributions - Point Estimation - Interval Estimation - Basic Concepts of Testing of Hypothesis - Tests for Normal Populations.
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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 httpnptel.iitm.ac.in
Sep 12, 2018
Excellent course helped me understand topic that i couldn't while attendinfg my college.
March 29, 2019
Great course. Thank you very much.