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Maths 3 Mdu Btech
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QUESTION PAPER

SYLLABUS:-

Section-A
Fourier Series and Fourier Transforms : Euler’s formulae, conditions for a Fourier expansion,
change of interval, Fourier expansion of odd and even functions, Fourier expansion of square
wave, rectangular wave, saw-toothed wave, half and full rectified wave, half range sine and
consine series.
Fourier integrals, Fourier transforms, Shifting theorem (both on time and frequency axes),
Fourier transforms of derivatives, Fourier transforms of integrals, Convolution theorem,
Fourier transform of Dirac-delta function.

Section-B
Functions of Complex Variable : Definition, Exponential function, Trignometric and
Hyperbolic functions, Logrithmic functions. Limit and Continuity of a function,
Differnetiability and Analyticity.
Cauchy-Riemann equations, necessary and sufficient conditions for a function to be
analytic, polar form of the Cauchy-Riemann equations. Harmonic functions, application
to flow problems. Integration of complex functions. Cauchy-Integral theorem and
fourmula.

Section-C
Power series, radius and circle of convergence, Taylor's Maclaurin's and Laurent's series.
Zeroes and singularities of complex functions, Residues. Evaluation of real integrals using
residues (around unit and semi circle only).
Probability Distributions and Hypothesis Testing : Conditional probability, Bayes theorem
and its applications, expected value of a random variable. Properties and application of
Binomial, Poisson and Normal distributions.

Section-D
Testing of a hypothesis, tests of significance for large samples, Student’s t-distribution
(applications only), Chi-square test of goodness of fit.
Linear Programming: Linear programming problems formulation, Solving linear
programming problems using (i) Graphical method (ii) Simplex method (iii) Dual simplex
method.

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