Syllabus:
MODULE 1 Fourier series ( 12 hours)
Dirichlet conditions – Fourier series with period 2 π and 2l – Half range sine and cosine series –
Harmonic Analysis – r.m.s Value
MODULE 2 Fourier Transform ( 12 hours)
Statement of Fourier integral theorem – Fourier transforms – derivative of transforms- convolution
theorem (no proof) – Parsevals identity
MODULE 3 Partial differential equations ( 12 hours)
Formation by eliminating arbitrary constants and arbitrary functions – solution of Lagrange’s equation –
Charpits method –solution of Homogeneous partical differential equations with constant coefficients.
MODULE 4 Probability distribution ( 12 hours)
Concept of random variable , probability distribution – Bernoulli’s trial – Discrete distribution – Binomial
distribution – its mean and variance- fitting of Binominal distribution – Poisson distribution as a limiting
case of Binominal distribution – its mean and variance – fitting of Poisson distribution – continuous
distribution- Uniform distribution – exponential distribution – its mean and variance – Normal
distribution – Standard normal curve- its properties.
MODULE 5 Testing of hypothesis ( 12 hours)
Populations and Samples – Hypothesis – level of significance – type I and type II error – Large samples
tests – test of significance for single proportion, difference of proportion, single mean, difference of mean
– chi –square test for variance- F test for equality of variances for small samples.
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Study Materials:
MODULE 1 :-
TEXT 1
TEXT 2
TEXT 3
MODULE 2 :-
TEXT 1
Mathematical equations
Integral Equations
