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ADDITIONAL MATHEMATICS – II

Semester :  IV

Course Code : 18MATDIP41

CIE Marks : 40                       SEE Marks : 60

ADDITIONAL MATHEMATICS-II

SYLLABUS

Module-1

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. 

Module-2

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 

Module-3

Higher order ODE’s: Linear differential equations of second and higher order equations with constant coefficients. Homogeneous /non-homogeneous equations. Inverse differential operators.

Module-4

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. 

Module-5

Probability: Introduction. Sample space and events. Axioms of probability. Addition & multiplication theorems. Conditional probability, Bayes’s theorem, problems.