17MAT41 Engineering Mathematics - IV syllabus for CS

Numerical Methods:

Numerical solution of ordinary differential equations of first order and first degree, Taylor’s series method, modified Euler’s method. Runge - Kutta method of fourth order, Milne’s and Adams-Bashforth predictor and corrector methods (No derivations of formulae-single step computation only).

Numerical Methods:

Numerical solution of second order ordinary differential equations, Runge-Kutta method and Milne’s method. (No derivations of formulae-single step computation only).

Special Functions:

Series solution of Bessel’s differential equation leading to Jn(x)-Bessel’s function of first kind. Basic properties and orthogonality. Series solution of Legendre’s differential equation leading to Pn(x)-Legendre polynomials. Rodrigue’s formula, problems

Complex Variables:

Review of a function of a complex variable, limits, continuity, differentiability. Analytic functions-Cauchy-Riemann equations in cartesian and polar forms. Properties and construction of analytic functions. Complex line integrals-Cauchy’s theorem and Cauchy’s integral formula, Residue, poles, Cauchy’s Residue theorem ( without proof) and problems.

Transformations:

Conformal transformations-Discussion of transformations: w=z², w=e^z, w = z + (1/z)(z ≠ 0). Bilinear transformations-problems

Probability Distributions:

Random variables (discrete and continuous), probability mass/density functions. Binomial distribution, Poisson distribution. Exponential and normal distributions, problems.

Joint probability distribution:

Joint Probability distribution for two discrete random variables, expectation, covariance, correlation coefficient.

Sampling Theory:

Sampling, Sampling distributions, standard error, test of hypothesis for means and proportions, confidence limits for means, student’s t-distribution, Chi-square distribution as a test of goodness of fit.

Stochastic process:

Stochastic processes, probability vector, stochastic matrices, fixed points, regular stochastic matrices, Markov chains, higher transition probabilitysimple problems.

Course Outcomes:

On completion of this course, students are able to:

1. Solve first and second order ordinary differential equation arising in flow problems using single step and multistep numerical methods.

2. Illustrate problems of potential theory, quantum mechanics and heat conduction by employing notions and properties of Bessel’s functions and Legendre’s polynomials.

3. Explain the concepts of analytic functions, residues, poles of complex potentials and describe conformal and Bilinear transformation arising in field theory and signal processing.

4. Develop probability distribution of discrete, continuous random variables and joint probability distribution occurring in digital signal processing, information theory and design engineering.

5. Demonstrate testing of hypothesis of sampling distributions and illustrate examples of Markov chains related to discrete parameter stochastic process.

Question Paper Pattern:

Note:- The SEE question paper will be set for 100 marks and the marks will be proportionately reduced to 60.

• The question paper will have ten full questions carrying equal marks.
• Each full question consisting of 20 marks.
• There will be two full questions (with a maximum of four sub questions) from each module.
• Each full question will have sub question covering all the topics under a module.
• The students will have to answer five full questions, selecting one full question from each module.

Text Books:

1. B.S. Grewal: Higher Engineering Mathematics, Khanna Publishers, 43rd Ed., 2015.

2. E. Kreyszig: Advanced Engineering Mathematics, John Wiley & Sons, 10th Ed., 2015.

Reference books:

1. N.P.Bali and Manish Goyal: A Text Book of Engineering Mathematics, Laxmi Publishers,7 th Ed., 2010.

2. B.V.Ramana: "Higher Engineering M athematics" Tata McGraw-Hill, 2006.

3. H. K. Dass and Er. RajnishVerma: "Higher Engineerig Mathematics", S. Chand publishing, 1st edition, 2011.