2K6 ALL 501: ENGINEERING MATHEMATICS –IV
Module I Probability distributions (13 hours)
Random variables-Probability distributions – binomial distribution –Poisson distribution-normal distribution –Mean, variance and Moment generating function -Poisson process – Chebyshev’s theorem- Geometric Distribution-Uniform Distribution, Gamma distribution, Beta Distribution, Exponential Distribution and Hyper-Geometric Distributions.
Module II Statistical inference (13hours)
Population and Sample-Sampling Distributions of Mean and Variance-Point Estimation-Interval Estimation -Null Hypotheses and Significance tests-Hypotheses concerning one mean- Confidence Intervals of mean and variance – Estimation of Variances-Hypotheses concerning one variance-Hypotheses concerning two variance- Chi square test as test of goodness of fit.
Module III (Series solutions of differential equations (13hours)
Power series method of solving ordinary differential equations – series solution of Bessel’s equation – Recurrence formula for Jn(x)-expansions for J0 and J1 – value of J1/2- generating function for Jn(x)- Orthogonality of Bessel functions – Legendre’s equation – series solution of Legendre’s differential equation -Rodrigues formula-Legendre Polynomials – Generating function for Pn(x)- Recurrence formulae for Pn(x) -Orthogonality of Legendre polynomials
Module IV Quadratic forms and Fourier Transforms (13 hours)
Quadratic forms – Matrix associated with a quadratic form – Technique of Diagonalization using row and column transformations on the matrix – Definite, Semidefinite and Indefinite forms – their identification using the Eigen values of the matrix of the quadratic form. Fourier Transform-Properties of Fourier Transforms-Linearity property-Change of scale property-shifting properties – Modulation property-Transform of the Derivative-simple problems- Fourier Cosine transform-Fourier Sine Transform.
Text book
Johnson RA, Miller & Freund’s Probability and Statistics for Engineers, Prentice Hall of India (For Module I and II only)
Reference Books
1. Wylie C R & Barrett L. C., Advanced Engineering Mathematics, Mc Graw Hill
2. Kreyszig E., Advanced Engineering Mathematics, John Wiley.
3. Bali N. P. & Manish Goyal, A Text book of Engineering Mathematics, Laxmi Publications
4. Grewal B. S, Higher Engineering Mathematics, Khanna Publishers