Applied Mathematics - III

Unit I : Numerical Methods [8 Hours]

Solution of algebraic and transcendental equations: Newton-Raphson method, Method of false position and their convergence, Solution of simultaneous linear equations using Gauss-Seidal method and Crout's method (LU decomposition).

Numerical solution of ordinary differential equations: Taylor's series method, Euler's modified method, Runge-Kutta fourth order method, Milne's predictor-corrector method.

Unit II: Matrices [7 Hours]

Linear dependence of vectors, Eigen values and Eigen vectors, Reduction to diagonal form, Singular value decomposition, Sylvester's theorem (Statement only), Largest Eigen value and its corresponding Eigen vector by iteration method.

Unit III: Mathematical Expectation and Probability Distributions [8 Hours]

Discrete Random Variables: Review of discrete random variable, Probability function and Distribution function, Mathematical expectation, Variance and Standard deviation, Moments, Moments generating function.

Probability Distributions: Binomial distribution, Poisson distribution, Exponential distribution.

Unit IV: Statistical Techniques [ 6 Hours]

Statistics: Introduction to correlation and regression, Multiple correlation and its properties, Multiple regression analysis, Regression equation of three variables.

Measures of central tendency and dispersion: Mean, Median, Quartile, Decile, Percentile, Mode, Mean deviation, Standard deviation.

Skewness: Test and uses of skewness and types of distributions, Measures of skewness, Karl Pearson's coefficient of skewness, Measure of skewness based on moments.

Unit V: Stochastic Process and Sampling Techniques [7 Hours]

Stochastic Process: Introduction of stochastic process, Classification of random process, Stationary and non-stationary random process, Stochastic matrix.

Markov Chain: Classification of states, Classification of chairs, Random walk and Gambler ruin.

Sampling: Population(Universe), Sampling types and distribution, Sampling of mean and variance, Testing a hypothesis, Null and Alternative Hypothesis, One-tail and two-tails tests (Only introduction), t test and F test (Only introduction), Chi-square test.

Text/Reference Books:

1. Advanced Engineering Mathematics (Wiley), Erwin Kreyzig.

2. Higher Engineering Mathematics (Khanna Publishers) B.S. Grewal.

3. Advanced Engineering Mathematics (S. Chand), H. K. Dass.

4. Probability and Statistics (Schaum;s Outline Series), Murray Spiegel, John Schiller, R. A. Srinivasan.

5. Advanced Mathematics for Engineers, Chandrika Prasad.

6. Probability, Statistics and Random Processes(TMH), T. Veerajan.