## MA2264 NUMERICAL METHODS Lecture Notes Common to Civil, Aero & EEE Departments

MA2264 Lecture Notes

Syllabus :

UNIT I SOLUTION OF EQUATIONS AND EIGENVALUE PROBLEMS
Solution of equation - Fixed point iteration: x=g(x) method – Newton’s method – Solution of linear
system by Gaussian elimination and Gauss-Jordon methods - Iterative methods - Gauss-Seidel
methods - Inverse of a matrix by Gauss Jordon method – Eigen value of a matrix by power method
and by Jacobi method for symmetric matrix.

UNIT II INTERPOLATION AND APPROXIMATION
Lagrangian Polynomials – Divided differences – Interpolating with a cubic spline – Newton’s forward
and backward difference formulas.

UNIT III NUMERICAL DIFFERENTIATION AND INTEGRATION
Differentiation using interpolation formulae –Numerical integration by trapezoidal and Simpson’s 1/3
and 3/8 rules – Romberg’s method – Two and Three point Gaussian quadrature formulas – Double
integrals using trapezoidal and Simpsons’s rules.

UNIT IV INITIAL VALUE PROBLEMS FOR ORDINARY DIFFERENTIAL
EQUATIONS
Single step methods: Taylor series method – Euler methods for First order Runge – Kutta method for
solving first and second order equations – Multistep methods: Milne’s and Adam’s predictor and
corrector methods.

UNIT V BOUNDARY VALUE PROBLEMS IN ORDINARY AND PARTIAL
DIFFERENTIAL EQUATIONS
Finite difference solution of second order ordinary differential equation – Finite difference solution of
one dimensional heat equation by explicit and implicit methods – One dimensional wave equation
and two dimensional Laplace and Poisson equations.