Syllabus
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Course Code: EP- 701 Course Name: Mathematical Tools for Physicists & Engineers |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Vector spaces and Matrices Definition of a linear vector space, Linear independence, basis and dimension, scalar Product, Orthonormal basis, Gram-Schmidt Orthogonalization process, Linear operators, Matrices: Orthogonal, Unitary and Hermitian matrices, Eigenvalues and eigenvectors of matrices, Matrix diagonalization. |
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| 2 | Differential equations Second order linear differential equation with variable coefficients, Solution of Bessel's, Legendre’s, Laguerre’s and Hermite's equations. Complex Variables Function of a complex variable, Cauchy Riemann conditions, Cauchy’s integral theorem, Cauchy's integral formula, Taylor's and Laurent series, Cauchy's Residue theorem, Singular points and evaluation of residues, Jordan's Lemma. |
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| 3 | Special Functions Definition of special functions, Generating functions for Bessel function of integral order Jn(x) , Recurrence relations, Integral representation; Legendre polynomials Pn(x) , Generating functions for Pn(x) , Recurrence relations; Hermite Polynomials, Generating functions, Rodrigue's formula for Hermite polynomials; Laguerre polynomials, Generating function and Recurrence relations. |
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| 4 | Integral Transforms Integral transform, Laplace transform, some simple properties of Laplace transforms such as first and second shifting property, Inverse Laplace Transform by partial fractions method, Laplace transform of derivatives, Laplace Transform of integrals, Fourier series, Evaluation of coefficients of Fourier series Cosine and Sine series, Fourier Transforms, Fourier sine Transforms, Fourier cosine Transforms. |
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