COMPLEX ANALYSIS, PROBABILITY AND STATISTICAL METHODS | 18MAT41

Module-1

Calculus of complex functions: Review of function of a complex variable, limits, continuity, and differentiability. Analytic functions: Cauchy-Riemann equations in Cartesian and polar forms and consequences. 

Construction of analytic functions: Milne-Thomson method-Problems. 

Module-2 

Conformal transformations: Introduction. Discussion of transformations:𝑤 = 𝑍 2 , 𝑤 = 𝑒 𝑧 , 𝑤 = 𝑧 + 1 𝑧 , 𝑧 ≠ 0 .Bilinear transformations- Problems. 

Complex integration: Line integral of a complex function-Cauchy‟s theorem and Cauchy‟s integral formula and problems. 

Module-3 

Probability Distributions: Review of basic probability theory. Random variables (discrete and continuous), probability mass/density functions. Binomial, Poisson, exponential and normal distributions- problems (No derivation for mean and standard deviation)-Illustrative examples. 

Module-4 

Statistical Methods: Correlation and regression-Karl Pearson‟s coefficient of correlation and rank correlation -problems. Regression analysis- lines of regression –problems. Curve Fitting: Curve fitting by the method of least squares- fitting the curves of the form- 𝑦 = 𝑎𝑥 + 𝑏, 𝑦 = 𝑎𝑥 𝑏𝑎𝑛𝑑𝑦 = 𝑎𝑥 2 + 𝑏𝑥 + 𝑐. 

Module-5 

Joint probability distribution: Joint Probability distribution for two discrete random variables, expectation and covariance. Sampling Theory: Introduction to sampling distributions, standard error, Type-I and Type-II errors. Test of hypothesis for means, student‟s t-distribution, Chi-square distribution as a test of goodness of fit.

For any queries  message us on:

 

Course Outcomes:

At the end of the course the student will be able to: 

 Use the concepts of analytic function and complex potentials to solve the problems arising in electromagnetic field theory. 

 Utilize conformal transformation and complex integral arising in aerofoil theory, fluid flow visualization and image processing. 

 Apply discrete and continuous probability distributions in analyzing the probability models arising in engineering field. 

 Make use of the correlation and regression analysis to fit a suitable mathematical model for the statistical data. 

 Construct joint probability distributions and demonstrate the validity of testing the hypothesis

Question paper pattern: 

 The question paper will have ten full questions carrying equal marks. 

 Each full question will be for 20 marks. 

 There will be two full questions (with a maximum of four sub- questions) from each module.