MATH3 (B-TECH Civil Engineering 3rd)

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 cosine 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, Trigonometric and

Hyperbolic functions, Logarithmic functions. Limit and Continuity of a function,

Differentiability 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 probles. Integration of complex functions. Cauchy-Integral theorem and formula.

Section-Cm

Power series, radius and circle of convergence, Taylor's Maclaurin's and Ls aurent’

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