MALAVIYANATIONALINSTITUTEOFTECHNOLOGY, JAIPUR.
DEPARTMENT OF MATHEMATICS
Syllabus (M.Tech. CIVIL)
MAT-602 Advanced Course in Mathematics
2L-1T
3credits
Statistics and Probability: Probability theory , Baye’s theorem, Binomial, Poisson and normal
distributions, correlation and regression, coefficient of correlation, rank correlation ,lines of
regression.
Numerical Methods: Solution of linear system of equations- Gauss elimination method,
Gauss Jordan method, Gauss-seidel method, Method of Factorisation, Solution of other
equations: Newton- Raphson method, Regula- Falsi method.
Numerical Analysis: Interpolation, finite differences-forward, backward and central
differences, Newton’s formulae for forward differences and backward differences; Stirling’s
formula for central differences, Numerical differentiation and integration- Simpsons onethird, Simpsons three- eighth and trapezoidal rules, Numerical solution of ODE of I order:
Euler’s ,modified Euler’s and Runga Kutta 4th order, Milne’s methods.
Numerical solution of PDE:
Laplace equation in two dimensions, heat equation in one
dimension, wave equation in one dimension, using finite difference methods.
Matrices: Rank of a matrix, solution of linear simultaneous equations, inverse of a matrix
by elementary transformations, eigen values, eigen vectors, Cayley-Hamilton Theorem
(without proof).
Text Books:
1. B.V.Ramana, Higher Engineering Mathematics, McGraw – Hill.
2. R.K.Jain & S. R. K. Iyengar, Advanced Engineering Mathematics, Narosa