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Indian Institute of Science Education and Research Bhopal
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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