Some jupyter notebooks for PH755
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A Quick Introduction to Python : Basics, control statements, lists and arrays, for loop, user-defined functions, graphics and visualization, error and speed. (8 hours)
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Integrals and Derivatives : Trapezoidal rule, Simpson’s rule, Romberg method, Gaussian quadrature, Errors and steps, Integrals over infinite ranges, Forward and backward differences, Central differences, Interpolation - linear and cubic spline methods. (8 hours)
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Solution of Linear and Non-Linear Equations : Gaussian elimination, back-substitution, LU decomposition, relaxation method, bisection method, secant method, Gauss-Newton method and gradient descent. (8 hours)
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Ordinary Differential Equations : Euler’s method, Runge-Kutta method, Adaptive step-size. (6 hours)
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Partial Differential Equations : Laplace equation - boundary value problem and relaxation method, Initial value problem – Diffusion equation. ( 6 hours)
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Random Processes and Monte Carlo Methods : Random numbers, Gaussian random numbers, Monte Carlo integration, importance sampling, Markov chain method. (4 hours)
Text Books :
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Computational Physics, Mark Newman (2012).
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Introductory methods of numerical analysis, S. S. Sastry, PHI Learning Pvt. Ltd (2012).