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Mathematics-IV
( PDE, Probability and Statistics )
Computer/Electronics/Electrical & Allied Branches, CS/IT, EC/IC, EE/EN,
Mechanical& Allied Branches, (ME/AE/AU/MT/PE/MI/PL)
Textile/Chemical & Allied Branches, TT/TC/CT, CHE/FT
Subject Code KAS302/KAS
Category Basic Science Course
Subject Name MATHEMATICS-IV
Scheme and Credits L-T-P^
Theory Marks
Sessional Test Assig/Att. Total^ Credit 3 — 1 — 0 100 30 20 150 4 Pre- requisites (if any) Knowledge of Mathematics I and II of B. Tech or equivalent
Course Outcomes The objective of this course is to familiarize the students with partial differential equation, their application and statistical techniques. It aims to present the students with standard concepts and tools at an intermediate to superior level that will provide them well towards undertaking a variety of problems in the discipline.
The students will learn: The idea of partial differentiation and types of partial differential equations The idea of classification of second partial differential equations, wave , heat equation and transmission lines The basic ideas of statistics including measures of central tendency, correlation, regression and their properties. The idea s of probability and random variables and various discrete and continuous probability distributions and their properties. The statistical methods of studying data samples, hypothesis testing and statistical quality control, control charts and their properties.
Module I: Partial Differential Equations
Origin of Partial Differential Equations, Linear and Non Linear Partial Equations of first order, Lagrange’s Equations, Charpit’s method, Cauchy’s method of Characteristics, Solution of Linear Partial Differential Equation of Higher order with constant coefficients, Equations reducible to linear partial differential equations with constant coefficients.
Module II: Applications of Partial Differential Equations :
Classification of linear partial differential equation of second order, Method of separation of variables, Solution of wave and heat conduction equation up to two dimension, Laplace equation in two dimensions, Equations of Transmission lines.
Module III: Statistical Techniques I :
Introduction: Measures of central tendency, Moments, Moment generating function (MGF) , Skewness, Kurtosis, Curve Fitting , Method of least squares, Fitting of straight lines, Fitting of second degree parabola, Exponential curves ,Correlation and Rank correlation, Regression Analysis: Regression lines of y on x and x on y, regression coefficients, properties of regressions coefficients and non linear regression.
Module IV: Statistical Techniques II:
Probability and Distribution: Introduction, Addition and multiplication law of probability, Conditional probability, Baye’s theorem, Random variables (Discrete and Continuous Random variable) Probability mass function and Probability density function, Expectation and variance, Discrete and Continuous Probability distribution: Binomial, Poission and Normal distributions.
Module V: Statistical Techniques III:
Sampling, Testing of Hypothesis and Statistical Quality Control : Introduction , Sampling Theory (Small and Large) , Hypothesis, Null hypothesis, Alternative hypothesis, Testing a Hypothesis, Level of significance, Confidence limits, Test of significance of difference of means, T-test, F-test and Chi-square test, One way Analysis of Variance (ANOVA).Statistical Quality Control (SQC) , Control Charts , Control Charts for variables ( X and R Charts), Control Charts for Variables ( p, np and C charts).
Text Books
- Erwin Kreyszig, Advanced Engineering Mathematics, 9thEdition, John Wiley & Sons, 2006.
- P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory, Universal Book Stall, 2003(Reprint).
- S. Ross: A First Course in Probability, 6th Ed., Pearson Education India, 2002.
- W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd Ed., Wiley, 1968.
Reference Books
- B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition, 2000. 2.T.Veerarajan : Engineering Mathematics (for semester III), Tata McGraw-Hill, New Delhi.
- R.K. Jain and S.R.K. Iyenger: Advance Engineering Mathematics; Narosa Publishing House, New Delhi.
- J.N. Kapur: Mathematical Statistics; S. Chand & Sons Company Limited, New Delhi.
- D.N.Elhance,V. Elhance & B.M. Aggarwal: Fundamentals of Statistics; Kitab Mahal Distributers, New Delhi.
