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 (s 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 mean (proof of theorems not expected).
Population & Samples: Sampling distribution of mean (s 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 mean (proof of theorems not expected).
References
B.S. Grewal, Higher Engineering Mathematics, Khanna Publishers.
M.K. Venkataraman, Engineering Mathematics Vol. II -3rd year Part A & B, National Publishing Company.
Ian N.Sneddon, Elements of Partial Differential Equations,Mc Graw Hill International Edn.
Richard A Johnson, Miller and Fread’s Probability and statistics for engineers, Pearson Education Asia / PHI.
Bali and Iyengar, A text book of Engineering Mathematics (Volume II), Laxmi Publications Ltd.
Erwin Kreyszig, Advanced Engg. Mathematics, Wiley Eastern Ltd.
Hogg and Tanis, Probability and statistical inferences, Pearson Education Asia.
M.K. Venkataraman, Engineering Mathematics Vol. II -3rd year Part A & B, National Publishing Company.
Ian N.Sneddon, Elements of Partial Differential Equations,Mc Graw Hill International Edn.
Richard A Johnson, Miller and Fread’s Probability and statistics for engineers, Pearson Education Asia / PHI.
Bali and Iyengar, A text book of Engineering Mathematics (Volume II), Laxmi Publications Ltd.
Erwin Kreyszig, Advanced Engg. Mathematics, Wiley Eastern Ltd.
Hogg and Tanis, Probability and statistical inferences, Pearson Education Asia.
mg university b.tech syllabus S4 Civil