Syllabus
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Course Code: B-PHY-501 Course Name: (II) Mathematical Physics |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | FOURIER SERIES Periodic functions, Orthogonality of sine and cosine functions, Dirichlet Conditions (Statement only), Expansion of periodic functions in a series of sine and cosine functions and determination of Fourier coefficients, Complex representation of Fourier series, Expansion of functions with arbitrary period, Expansion of non-periodic functions over an interval, Even and odd functions and their Fourier expansions, Application, Summing of Infinite Series. SOME SPECIAL INTEGRALS Beta and Gamma FunctionS, Relation between them.Expression of Integrals in terms of Gamma Functions, Error Function (Probability Integral). |
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| 2 | CALCULUS OF FUNCTIONS OF MORE THAN ONE VARIABLE Partial derivatives,exact and inexact differentials,Integrating factor, with simple illustration, Constrained Maximization using Lagrange Multipliers. PARTIAL DIFFERENTIAL EQUATIONS Solutions to partial differential equations, using separation of variables: Laplace's Equation in problems of rectangular, cylindrical and spherical symmetry. |
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| 3 | FROBENIUS METHOD AND SPECIAL FUNCTIONS Singular Points of Second Order Linear Differential Equations and their importance,Frobenius method and its applications to differential equations, Legendre, Bessel, Hermite and Laguerre Differential Equations, Properties of Legendre Polynomials: Rodrigues Formula, Orthogonality, Simple recurrence relations. |
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| 4 | COMPLEX ANALYSIS Brief Revision of Complex Numbers and their Graphical Representation, Euler's formula, De Moivre's theorem, Roots of Complex Numbers, Functions of Complex Variables, Analyticity and Cauchy-Riemann Conditions, Examples of analytic functions, Singular functions: poles and branch points, order of singularity, branch cuts, Integration of a function of a complex variable, Cauchy's Inequality, Cauchy’s Integral formula. |
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