This course aims at providing the student with the concepts of Matrices, Numerical
Techniques and Curve fitting.
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
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.
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
All Units Material(PDF) : Download
Note: To Cover the 2 mark's question for M-III, note down all the Formula's and implementation.Formula's are IMP.......