Numerical Methods and Programming

1
Numerical Methods and Programming

• P. B. Sunil Kumar
• Department of Physics
• IIT Mdras
• Sunil_at_iitm.ac.in

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Basic structure
Class room

• (1) C Programing for beginners
• (2) How accurate and precise are your numerical
  answers ?
• (3) Modeling data Interpolation and fitting
• (4) Linear algebra
• (5) Solutions of nonlinear equations and
  minimization of functions
• (6) Numerical differentiation and Integration
• (7) Solutions of ordinary differential equations
• (8) Solutions of partial differential equations
• (9) Discrete and Fast Fourier Transforms

Books

1. Numerical Methods for Engineers - S. C.
   Chapra and R. P. Canale. McGraw-Hill College
   (2001)
2. Applied Numerical Analysis - C. F. Gerald and
   P. O. Wheatley Addison Wesley, Boston, 2004.
   (2004)
3. Computer Oriented Numerical Methods. V. Rajaraman
   . Prentice-Hall of India Pvt.Ltd (15 Aug 2004)
4. Elementary Numerical Analysis. S. D. Conte and C.
   de Boor McGraw-Hill College (1972)

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C Programming for beginners
Basic structure of C program. Different types
of variables. Arrays and Pointers , use of
functions and pointers to functions, elementary
examples using pointers, arrays and functions
Accuracy and precision
Representation of numbers, numerical arithmetic,
condition number and propagation of errors
Modeling data
Lagrange and Newton interpolation methods,
divided difference table. Piece wise polynomial
interpolation. Error in polynomial interpolation.
Least squares regression. Linear, multiple linear
and nonlinear regressions
Linear algebra coupled linear equations,
eigenvalues and eigenvectors
Elimination method and Pivoting, LU
decomposition, Fadeev Leverrier method for
characteristic polynomials, power method for
eigenvalues. Bairstow's method.
Solutions of nonlinear equations and
minimization of functions
Methods of successive bisection. False position
and mid point methods. Secant method.
Newton-Raphson scheme.
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Numerical differentiation and Integration
Divided difference method for differentiation.
Newton-Cotes formula. Higher order derivatives.
Comparison of errors. Midpoint, Trapezoidal ,
rectangular and Simpsons rules. Quadrature
methods
Solutions of ordinary differential equations
Euler and predictor corrector methods. Runge
Kutta method. Adaptive step size selection.
Solutions of partial differential equations
Examples of partial differential equations.
Implicit and explicit methods. Alternate
direction Crank-Nicolson scheme.
Discrete and Fast Fourier Transforms
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Computer Laboratory
Part- A Basic C Programming
Part- B Familiarizing with the codes
corresponding to the topics  covered in class
room lectures.
Part-C Problem solving.

1. Curve fitting 
2. Interpolation
3. Numerical Integration calculation total
   scattering cross section
4. Differential equationsCoupled harmonic
   oscillators, heat conduction through a rod and a
   two dimensional sheet, double pendulum.
5. Eigenvalues and Eigenvectors
6. Fourier Transforms Diffraction of light, power
   spectrum.