Module 1
Ordinary Differential Equations: Linear Differential equations with constant coefficents – Finding P.I. by the method of variation of parameters – Cauchys equations- Linear Simultaneous eqns- simple applications in engineering problems.
Ordinary Differential Equations: Linear Differential equations with constant coefficents – Finding P.I. by the method of variation of parameters – Cauchys equations- Linear Simultaneous eqns- simple applications in engineering problems.
Module 2
Partial Differential Equations – formation by eliminating arbitrary constants and arbitrary Functions – solution of Lagrange Linear Equations –Charpits Method – solution of homogeneous linear partial differential 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.
Partial Differential Equations – formation by eliminating arbitrary constants and arbitrary Functions – solution of Lagrange Linear Equations –Charpits Method – solution of homogeneous linear partial differential 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 & Cosine transforms – inverse transforms – transforms of derivatives – Convolution Theorem (no proof) – Parsevals Identity – simple problems.
Fourier Transforms: – Statement of Fourier Integral Theorems – Fourier Transforms – Fourier Sine & Cosine transforms – inverse transforms – transforms of derivatives – Convolution Theorem (no proof) – Parsevals 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 & poisson distributions – normal distribution – properties of normal curve – standard normal curve – simple problems in binomial, poisson and normal distributions.
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 & poisson distributions – normal distribution – properties of normal curve – standard normal curve – simple problems in binomial, poisson and normal distributions.
Module 5
Population & 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 of proportions, single mean and difference of means (proof of theorems not expected).
Population & 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 of proportions, single mean and difference of means (proof of theorems not expected).
References
1. Higher Engineering Mathematics – B.S. Grewal, Khanna Publishers.
2. Engineering Mathematics Vol.II -3rd year Part A & B – M.K. Venkataraman, National Publishing Company
3. Elements of Partial Differential Equations – Ian N.Sneddon.,McGraw Hill.
4. Miller and Fread’s Probability and statistics for engineers – Richard A Johnson, Pearson Education Asia / PHI.
5. A text book of Engineering Mathematics (Volume II) – Bali and Iyengar, Laxmi Publications Ltd.
6. Advanced Engg. Mathematics Erwin Kreyszig, Wiley Eastern Ltd.
7. Probability and statistical inferences – Hogg and Tanis, Pearson Education Asia.
1. Higher Engineering Mathematics – B.S. Grewal, Khanna Publishers.
2. Engineering Mathematics Vol.II -3rd year Part A & B – M.K. Venkataraman, National Publishing Company
3. Elements of Partial Differential Equations – Ian N.Sneddon.,McGraw Hill.
4. Miller and Fread’s Probability and statistics for engineers – Richard A Johnson, Pearson Education Asia / PHI.
5. A text book of Engineering Mathematics (Volume II) – Bali and Iyengar, Laxmi Publications Ltd.
6. Advanced Engg. Mathematics Erwin Kreyszig, Wiley Eastern Ltd.
7. Probability and statistical inferences – Hogg and Tanis, Pearson Education Asia.