1. Programming 3
hours
1.1
Overview
of programming.
1.2
Programming
languages.
1.3
Programming
techniques.
2. Overview of C
language 9
hours
1.1
Data
types, variables, constants, arithmetic expressions and assignment statements.
1.2
Program
control statements, console I/O.
1.3
Arrays,
functions and pointers. Structures,
unions, enumerated data types.
1.4
File
handling.
1.5
The
C-preprocessor, C standard Lib and header files.
3. Errors in Numerical Computation 3
hours
3.1
Sources
of errors in numerical computation.
3.2
Round-off
error.
3.3
Truncation
error.
3.4
Inherent
error.
3.5
Stability
of numerical algorithms.
4. Transcendental and
Polynomial Equations 9
hours
4.1
Bisection
method.
4.2
Secant
method.
4.3
Regula-Falsi
method.
4.4
Newton-Raphson
method.
4.5
Rate
of convergence of iterative methods.
4.6
System
of nonlinear equations.
5. Systems of Linear Equations and Inverse of a Matrix 9 hours
5.1
Gauss-elimination
method.
5.2
Gauss-Jordan
method.
5.3
LU
decomposition method.
5.4
Cholesky
method for symmetric and positive definite systems.
5.5
Gauss-Jacobi
iteration method.
5.6
Gauss-Seidel
iteration method.
5.7
Rate
of convergence of iterative methods.
6. Interpolation and Approximation 9
hours
6.1
Lagrange
interpolation.
6.2
Errors
of interpolation.
6.3
Divided
differences.
6.4
Newton’s
divided difference interpolation.
6.5
Finite
differences.
6.6
Newton’s
forward and backward differences interpolation.
6.7
Least
squares approximation.
7. Numerical Differentiation 6
hours
7.1
Methods
based on interpolation.
7.2
Methods
based on finite differences.
7.3
Methods
based on undetermined coefficients.
7.4
Choice
of optimal step size.
7.5
Richardson
extrapolation methods.
8. Numerical Integration 9
hours
8.1
Newton
Cotes methods (Trapezoidal rule, Simpson’s rule).
8.2
Composite
integration methods.
8.3
Derivation
of methods using the method of undetermined parameters.
8.4
Romberg
integration.
8.5
Gaussian
methods (Gauss-Legendre methods, Gauss-Chebyshev methods, Gauss-Laguerre
methods, Gauss-Hermite methods).
9. Numerical Solution of
First Order Ordinary Differential Equations 3 hours
9.1
Taylor’s
series method.
9.2
Euler
method.
9.3
Runge-Kutta
methods (Second and fourth order).
I.
E.Balagurusamy, “Programming in ANSI C”, Tata Mc Graw Hill, 1992.
II.
M.K. Jain, S.R.K. Iyengar and R.K. Jain, “Numerical Methods for
Scientific and Engineering Computation”, Fourth Edition, New Age
International Publishers, 2003.
1.
M.K.
Jain, S.R.K. Iyengar and R.K. Jain, “Numerical Methods : Problems and Solutions”,
New Age International Publishers, 1994.
2.
A.
Ralston and P. Rabinowitz “A First Course in Numerical Analysis”, McGraw-Hill,
2nd edition, 1978.