Syllabus
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Course Code: EI-OE-301 Course Name: Open Elective- III - (iii) Mathematics-III |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Bessel functions: series solution of Bessel differential equation, Bessel function of first kind Jn(x), recurrence relations. Legendre Polynomials: Legendre differential equation, Legendre polynomials Pn(x) as solution of Legendre differential equation for (n>0), recurrence relations. |
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| 2 | Fourier Series: Euler’s formulae, conditions for Fourier expansions, Fourier expansion of functions having points of discontinuity, change of interval, odd & even functions, half range series. Fourier Transforms: Fourier Integrals, Fourier transforms, Fourier cosine and sine transforms, Properties of Fourier Transforms: convolution theorem, Parseval’s identity, relation between Fourier and Laplace transforms |
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| 3 | Function of a complex variables: Cauchy-Riemann equations, necessary and sufficient conditions for a function to be analytic, harmonic functions, Taylor and Laurent series, singular points, residues, evaluation of residues at poles, and poles of mth order, Cauchy’s residue theorem, the Cauchy’s principle value, evaluation of definite integrals. | |
| 4 | Probability Distributions: Probability, Bayes theorem, Discrete & Continuous probability distributions, discrete random variable, probability function, distribution function, Mathematical expectation, expectation of a sum of random variables, expectation of product of independent variables, covariance, Moment generating function, probability generating function. | |
