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Advanced Engineering Mathematics. Instructors: Dr. Pratima Panigrahi, Prof. P.D. Srivastava, Prof. Somesh Kumar, and Prof. Jitendra Kumar, Department of Mathematics, IIT Kharagpur
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English
English [CC]
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Description
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. (from nptel.ac.in)
Course content
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- Lecture 01 – Review Groups, Fields, and Matrices Unlimited
- Lecture 02 – Vector Spaces, Subspaces, Linearly Dependent/Independent of Vectors Unlimited
- Lecture 03 – Basis, Dimension, Rank and Matrix Inverse Unlimited
- Lecture 04 – Linear Transformation, Isomorphism and Matrix Representation Unlimited
- Lecture 05 – System of Linear Equations, Eigenvalues and Eigenvectors Unlimited
- Lecture 06 – Method to Find Eigenvalues and Eigenvectors, Diagonalization of Matrices Unlimited
- Lecture 07 – Jordan Canonical Form, Cayley Hamilton Theorem Unlimited
- Lecture 08 – Inner Product Spaces, Cauchy-Schwarz Inequality Unlimited
- Lecture 09 – Orthogonality, Gram-Schmidt Orthogonalization Process Unlimited
- Lecture 10 – Spectrum of Special Matrices, Positive/Negative Definite Matrices Unlimited
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- Lecture 11 – Concept of Domain, Limit, Continuity and Differentiability Unlimited
- Lecture 12 – Analytic Functions, C-R Equations Unlimited
- Lecture 13 – Harmonic Functions Unlimited
- Lecture 14 – Line Integral in the Complex Unlimited
- Lecture 15 – Cauchy Integral Theorem Unlimited
- Lecture 16 – Cauchy Integral Theorem (cont.) Unlimited
- Lecture 17 – Cauchy Integral Formula Unlimited
- Lecture 18 – Power and Taylor’s Series of Complex Numbers Unlimited
- Lecture 19 – Power and Taylor’s Series of Complex Numbers (cont.) Unlimited
- Lecture 20 – Taylor’s, Laurent Series of f(z) and Singularities Unlimited
- Lecture 21 – Classification of Singularities, Residue and Residue Theorem Unlimited
- Lecture 22 – Laplace Transform and its Existence Unlimited
- Lecture 23 – Properties of Laplace Transform Unlimited
- Lecture 24 – Evaluation of Laplace and Inverse Laplace Transform Unlimited
- Lecture 25 – Applications of Laplace Transform to Integral Equations and ODEs Unlimited
- Lecture 26 – Applications of Laplace Transform to PDEs Unlimited
- Lecture 27 – Fourier Series Unlimited
- Lecture 28 – Fourier Series (cont.) Unlimited
- Lecture 29 – Fourier Integral Representation of a Function Unlimited
- Lecture 30 – Introduction to Fourier Transform Unlimited
- Lecture 31 – Applications of Fourier Transform to PDEs Unlimited
Instructor
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