M3 syllabus (Mathematics-III) for JNTUH B.Tech I year II sem is covered here. This gives the details about credits, number of hours and other details along with reference books for the course.
M3 Syllabus (Mathematics-III) JNTUH R16
B.Tech. I Year II Sem. L T/P/D C
Course Code: PH103BS 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 – 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 two-tail tests, Tests concerning one mean and proportion, two means-proportions and their differences-ANOVA for one-way classified data.
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.
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