Engineering Tutorials

MAT-201-F MATHEMATICS-III

(Common to CSE, ME, ECE, BME, EE, EEE, E&I, I&C, IT, CE)

NOTE: Examiner will set 9 questions in total, with two questions from each section and one question covering all sections which will be Q.1. This Q.1 is compulsory and of short answers type. Each question carries equal mark (20 marks). Students have to attempt 5 questions in total at least one question from each section.

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 problems. Integration of complex functions. Cauchy-Integral theorem and formula.

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.

TEXT BOOKS:

1. Engineering Mathematics by Babu Ram (Pearson media Publication)

2. Advanced Engg. Mathematics: F Kreyszig.

3. Higher Engg. Mathematics: B.S. Grewal.

REFERENCE BOOKS :

1. Advance Engg. Mathematics: R.K. Jain, S.R.K.Iyenger.

2. Advanced Engg. Mathematics: Michael D. Greenberg.

3. Operation Research: H.A. Taha.

4. Probability and statistics for Engineers: Johnson. PHI.

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