ADDITIONAL MATHEMATICS – II
Semester : IV
Course Code : 18MATDIP41
CIE Marks : 40 SEE Marks : 60
Linear Algebra: Introduction – rank of matrix by elementary row operations – Echelon form. Consistency of system of linear equations – Gauss elimination method. Eigen values and Eigen vectors of a square matrix. Problems.
Numerical Methods: Finite differences. Interpolation/extrapolation using Newton’s forward and backward difference formulae (Statements only)-problems. Solution of polynomial and transcendental equations – Newton-Raphson and Regula-Falsi methods (only formulae)- Illustrative examples. Numerical integration: Simpson’s one
Higher order ODE’s: Linear differential equations of second and higher order equations with constant coefficients. Homogeneous /non-homogeneous equations. Inverse differential operators.
Partial Differential Equations (PDE’s): Formation of PDE’s by elimination of arbitrary constants and functions. Solution of non-homogeneous PDE by direct integration. Homogeneous PDEs involving derivative with respect to one independent variable only.
Probability: Introduction. Sample space and events. Axioms of probability. Addition & multiplication theorems. Conditional probability, Bayes’s theorem, problems.