### Mathematics III (CSE 2-1)

Objectives:
This course aims at providing the student with the concepts of Matrices, Numerical
Techniques and Curve fitting.

Syllabus:
Unit-I:
Elementary row transformations-Rank – Echelon form, normal form – Consistency of System
of Linear equations. Linear transformations. Hermitian, Skew-Hermitian and Unitary
matrices and their properties. Eigen Values, Eigen vectors for both real and complex
matrices. Cayley – Hamilton Theorem and its applications – Diagonolization of matrix.
Calculation of powers of matrix and inverse of a matrix. Quadratic forms – Reduction of
quadratic form to canonical form and their nature.

UNIT – II
Solution of Algebraic and Transcendental Equations: The Bisection Method – The Method of
False Position– Newton-Raphson Method, Solution of linear simultaneous equation: Crout’s
triangularisation method, Gauss - Seidal iteration method.

UNIT – III
Interpolation: Newton’s forward and backward interpolation formulae – Lagrange’s
formulae. Gauss forward and backward formula, Stirling’s formula, Bessel’s formula.

UNIT – IV
Curve fitting: Fitting of a straight line – Second degree curve – Exponentional curve-Power
curve by method of least squares. Numerical Differentiation for Newton’s interpolation
formula. Numerical Integration: Trapezoidal rule – Simpson’s 1/3 Rule – Simpson’s 3/8
Rule.

UNIT – V
Numerical solution of Ordinary Differential equations: Solution by Taylor’s series-Picard’s
Method of successive Approximations-Euler’s Method-Runge- Kutta Methods. Numerical
solutions of Laplace equation using finite difference approximation.

TEXT BOOKS:
1. Higher Engineering Mathematics, B.S.Grewal, Khanna publishers.
2. Introductory Methods of Numerical Analysis, S.S. Sastry, PHI publisher.

Material's for Mathematics-III

1. 