Note: This syllabus is common for EEE, ECE, CSE, EIE, BME, IT, ETE, ECM, ICE. Also common for Civil, ME, AE, ME (M), MME, AU, Mining, Petroleum, CEE, ME (Nanotech).

MA203BS: Mathematics - III
(Statistical and Numerical Methods)
B.Tech. I Year II Sem. L T/P/D C
4 1/0/0 4

---

Prerequisites: Foundation course (No prerequisites).

Course Objectives: To learn

• random variables that describe randomness or an uncertainty in certain realistic situation
• binomial geometric and normal distributions
• sampling distribution of mean, variance, point estimation and interval estimation
• the testing of hypothesis and ANOVA
• the topics those deals with methods to find roots of an equation
• to fit a desired curve by the method of least squares for the given data
• solving ordinary differential equations using numerical techniques

Course Outcomes: After learning the contents of this course the student must be able to

• differentiate among random variables involved in the probability models which are useful for all branches of engineering
• calculate mean, proportions and variances of sampling distributions and to make important decisions s for few samples which are taken from a large data
• solve the tests of ANOVA for classified data
• find the root of a given equation and solution of a system of equations
• fit a curve for a given data
• find the numerical solutions for a given first order initial value problem

UNIT – I

Random variables and Distributions:
Introduction, Random variables, Discrete random variable, Continuous random variable, Probability distribution function, Probability density function, Expectation, Moment generating function, Moments and properties. Discrete distributions: Binomial and geometric distributions. Continuous distribution: Normal distributions.

UNIT – II

Sampling Theory: Introduction, Population and samples, Sampling distribution of means ( Known)-Central limit theorem, t-distribution, Sampling distribution of means ( unknown) - Sampling distribution of variances – X² and F- distributions, Point estimation, Maximum error of estimate, Interval estimation.

UNIT – III

Tests of Hypothesis: Introduction, Hypothesis, Null and Alternative Hypothesis, Type I and Type II errors, Level of significance, One tail and two-tail tests, Tests concerning one mean and proportion, two means-proportions and their differences-ANOVA for one-way classified data.

UNIT – IV

Algebraic and Transcendental Equations & Curve Fitting: Introduction, Bisection Method, Method of False position, Iteration methods: fixed point iteration and Newton Raphson methods. Solving linear system of equations by Gauss-Jacobi and Gauss-Seidal Methods.

Curve Fitting: Fitting a linear, second degree, exponential, power curve by method of least squares.

UNIT – V

Numerical Integration and solution of Ordinary Differential equations: Trapezoidal rule - Simpson’s 1/3^rd and 3/8^th rule- Solution of ordinary differential equations by Taylor’s series, Picard’s method of successive approximations, Euler’s method, Runge-Kutta method (second and fourth order)

Text Books:

1. Probability and Statistics for Engineers by Richard Arnold Johnson, Irwin Miller and John E. Freund, New Delhi, Prentice Hall.
2. Probability and Statistics for Engineers and Sciences by Jay L. Devore, Cengage Learning.
3. Numerical Methods for Scientific and Engineering Computation by M. K. Jain, S. R. K. Iyengar and R. K. Jain, New Age International Publishers

References:

1. Fundamentals of Mathematical Statistics by S. C. Guptha & V. K. Kapoor, S. Chand.
2. Introductory Methods of Numerical Analysis by S. S. Sastry, PHI Learning Pvt. Ltd.
3. Mathematics for engineers and scientists by Alan Jeffrey, 6th edition, CRC press.