**PHY ****312: Numerical Methods and Programming**** ****(4)**

*Approximation Methods and Errors: *Truncation and round-o errors. Accuracy and precision

*Roots of Equations:* Bracketing Methods (false position. bisection) Iteration Methods (Newton- Raphson and secant). Systems of linear algebraic equations inversion and LU decompositon methods. Gauss elimination, matrix

*Curve fitting:* Least squares regression. Linear, multiple linear and nonlinear regressions. Cubic spline.

*Interpolation Methods:* interpolating polynomials. Newton's divided diff erence and Lagr'ange

*Fourier approximation:* Curve fitting with oscillatory functions Frequency and time domains. Discrete
Fourier and Fast Fourier transforms

*Numerical differentiation and integration:* Divided difference method for differentiation. Newton-Cotes formula. Trapezoidal and Simpson's rules. Romberg and Gauss quadrature methods.

*Ordinary differential equations:* Euler's method and its modications Runge-Kutta methods. Boundary
value and Eigenvalue problems. Partial differential equations. Finite difference equations. Elliptic equations. Laplace's equation and solutions. Parabolic equations. Solution of the heat conduction equation. Finite element method: General approach. Application to 1-dimensional and 2-dimensional problems.

*Programming: *Case studies in the form of problems on the topics covered in the course to be introduced as programs in suitable computer languages.

*Suggested Books*:

- Numerical Methods for Engineering, S.C. Chapra and R.C. Canale, McGraw-Hill (1989).
- Introductory Methods of Numerical Analysis, S.S. Sastry, Prentice Hall of India (1983).
- Numerical Mathematical Analysis, J.B. Scarborough, John Hopkins (1966).
- Computer Oriented Numerical Methods, V. Rajaraman, PHI Learning Private Limited (1993)
- M.K. Jain, S.R.K. Iyengar and R.K. Jain, Numerical Methods for Scientic and Engineering Computation, Wiley Eastern (1992).

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