Periodic functions, Euler’s formulae. Fourier series of odd and even functions and functions
with arbitrary period. Half range expansions. Fourier sine and cosine transforms. Fourier integrals.
Application of Fourier series to forced vibration problems.
Partial differential equations:
Basic concepts, solutions of equations involving derivatives with respect to
one variable only. Solutions by indicated transformations and separation of variables. Derivation of onedimensional
wave equation (vibrating string) and its solution by using the method of separation of
variables. Simple problems. D’Alembert’s solution of wave equation. Derivation of one dimensional heat
equation using Gauss divergence theorem and its solution by separation of variables. Solutions of 2-D
Laplace equations.
Introduction to probability:
Finite sample space, conditional probability and independence. Bayes’ theorem,
one-dimensional random variables. Two and higher dimensional random variables: mean, variance,
correlation coefficient and regression. Chebyshev inequality.
Distribution:
Binomial, Poisson, Uniform, Normal, Gamma, Chi-square and Exponential. Simple problems.
Text Books:
1. Murray R.Spiegel: Vector Analysis. Edn.1959, Schaum Publishing Co.
2. Erwin Kreyszig: Advanced Engineering Mathematics-Fifth edn.1985, Wiley Eastern.
3. P.L.Meyer: Introduction to probability and Statistical Applications, second Edn. 979, Amerind
Publishing Co.
Reference Books:
1. Bengamine A.R. and Cornell C.A : Probability and Statistics second edn. 1970, McGraw Hill.
2. Ang. A.H.,S. and Tang V.H. : probability concepts in Engineering, Planning and design, Vols. I and II,
John Wiley.
3. Hogg and Craig: Introduction of Mathematical Statistics, fourth edn. 195 Mac Millan International.
4. B.S.Grewal: Higher Engineering Mathematics edn. 1989, Khanna publishers.