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, tdistribution, Sampling distribution of means ( unknown)  Sampling distribution of variances – X^{2} 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 twotail tests, Tests concerning one mean and proportion, two meansproportions and their differencesANOVA for oneway 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 GaussJacobi and GaussSeidal 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, RungeKutta method (second and fourth order)
Text Books:
 Probability and Statistics for Engineers by Richard Arnold Johnson, Irwin Miller and John E. Freund, New Delhi, Prentice Hall.
 Probability and Statistics for Engineers and Sciences by Jay L. Devore, Cengage Learning.
 Numerical Methods for Scientific and Engineering Computation by M. K. Jain, S. R. K. Iyengar and R. K. Jain, New Age International Publishers
References:
 Fundamentals of Mathematical Statistics by S. C. Guptha & V. K. Kapoor, S. Chand.
 Introductory Methods of Numerical Analysis by S. S. Sastry, PHI Learning Pvt. Ltd.
 Mathematics for engineers and scientists by Alan Jeffrey, 6th edition, CRC press.

CreatedDec 15, 2016

UpdatedDec 15, 2016

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