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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:

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