Module 1
Ordinary Differential Equations: Linear Differential Equations with constant
coefficients – Finding P.I by the method of variation of parameters – Cauchy’s
equations – Linear Simultaneous equations – simple applications in engineering
problems.
Module 2
Partial Differential Equations: Formation by eliminating arbitrary constants and
arbitrary functions – solution of Lagrange’s Linear equations – Charpit’s method –
solution of homogeneous linear partial differential equation – equation with
constant coefficients - solution of one dimensional wave equation and heat
equation using method of separation of variables – Fourier solution of one
dimensional wave equation.
Module 3
Fourier Transforms: Statement of Fourier Integral Theorems – Fourier transforms –
Fourier sine and cosine transforms – inverse transforms – transforms of
derivatives – Convolution Theorem (no proof) – Parseval’s identity – simple
problems.
Module 4
Probability and Statistics: Binomial law of probability – The binomial distribution,
its mean and variance – Poisson distribution as a limiting case of binomial
distribution – its mean and variance – fitting of binomial and Poisson distributions
http://mgusyllabus.blogspot.com/
– normal distribution – properties of normal curve – standard normal curve –
simple problems in binomial, Poisson and normal distributions.
Module 5
Population and samples: Sampling distribution of mean ( known) – sampling
distribution of variance, F and Chi square test – Level of significance – Type 1 and
Type 2 errors – Test of hypothesis – Test of significance for large samples – test of
significance for single proportion, difference proportion, single mean and
difference of mean (proof of theorems not expected).
References
1. Higher Engg. Mathematics: Grawal B. S, Khanna Publ.
2. Engineering Mathematics Vol.2: M. K Venkataraman, National Publishing
Co.
3. Elements of Partial Differential Equations: Ian N. Sneddon, Mc Graw Hill Intl’
4. Miller and Fread’s Probability and Statistics for Engineers: Richard A.
Johnson, Pearson education/ PHI.
5. A Text Book of Engg. Mathematics, Vol.2: Bali and Iyengar, Lakshmi Publ. Ltd.
6. Advanced Engg. Mathematics: Erwin Kreyszig, Wiley Eastern.
7. Probability and Statistical Inferences: Hogg and Tam’s, Pearson Education Asia.
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