| Lectures: 4 Periods/Week | Sessional Marks: 30 |
| University Exam: 3 Hours | University Examination Marks: 70 |
UNIT-I
Functions:
Beta, Gamma and Error Functions
Integral Transforms:
Introduction, Definition, Fourier integrals-Fourier sine and cosine integrals, Complex form of Fourier integrals, Fourier transforms, Fourier
sine and cosine transforms, Properties of Fourier transforms.
UNIT-II
Probability and Distributions:
Probability and problems related to probability- addition theorem, multiplication theorem, Bayes theorem and its applications. Normal
distribution, Normal approximation to binomial distribution, Some other distribution.
Sampling and Inference:
Sampling, Testing a Hypothesis, Simple sampling of attributes, Sampling of variables-large & small samples, Chi-square test.
UNIT-III
Complex Analysis:
Introduction, Continuity. Cauchy-Riemann's equation, Analytic functions. Harmonic functions, Orthogonal system.
Complex Integration:
Cauchy integral theorem, Cauchy's integral formula.
UNIT-IV
Series:
Taylor's series, Laurent's series, Zeroes and singularities.
Calculation of residues:
Calculation of residues, Residue theorem, Evaluation of real definite integrals (by applying the residue theorem).
Text Books