Other university all, Electrical & Electronics Engineering , Mathematics-IV Syllabus

Subject Code KAS302/KAS402

Mathematics-IV

( PDE, Probability and Statistics )

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
1. Erwin Kreyszig, Advanced Engineering Mathematics, 9thEdition, John Wiley &
Sons, 2006.
2. P. G. Hoel, S. C. Port and C. J. Stone, Introduction to Probability Theory,
Universal Book Stall, 2003(Reprint).
3. S. Ross: A First Course in Probability, 6th Ed., Pearson Education India, 2002.
4. W. Feller, An Introduction to Probability Theory and its Applications, Vol. 1, 3rd
Ed., Wiley, 1968.

Reference Books
1. B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers, 35th Edition, 2000.
2.T.Veerarajan : Engineering Mathematics (for semester III), Tata McGraw-Hill, New
Delhi.
3. R.K. Jain and S.R.K. Iyenger: Advance Engineering Mathematics; Narosa Publishing
House, New Delhi.
4. J.N. Kapur: Mathematical Statistics; S. Chand & Sons Company Limited, New Delhi.
5. D.N.Elhance,V. Elhance & B.M. Aggarwal: Fundamentals of Statistics; Kitab Mahal
Distributers, New Delhi