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nm2021

License: MIT Python3

Contains Jupyter notebooks and other materials prepared for the course Numerical Methods offered at TIFR Hyderabad (https://www.tifrh.res.in/~ramakrishnan/index.php/teaching/)

Interactive notebooks

Access interactive notebooks at https://mybinder.org/v2/gh/raghurama123/nm2021/HEAD

Syllabus:

  1. Python: Writing/running codes, Jupyter notebooks, modules

  2. Linear Equations: Direct methods: Cramer's rule, row-reduction, forward/backward substitution, Gaussian elimination; LU factorization: Cholesky's method

  3. Data Modeling: Approximations: least squares fitting; Interpolation: polynomial interpolation, scipy.interpolate.interp1d

  4. Root finding: The problem, fixed-point iteration, bisection method, Newton-Raphson method (1-D and n-D), Jacobian matrix, pseudo-inverse, quasi-Newton method (1-D: secant method, n-D: Broyden), scipy.optimize

  5. Optimization/Minimization: 1-D problems, n-D problems, scipy.optimize.minimize(method=’L-BFGS-B’), Simplex method

  6. Numerical Differentiation: Finite difference; Error analysis

  7. Numerical Integration: Newton-Cotes formulae, Romberg/Gaussian integration, Multiple integrals

  8. Initial Value Problems: Euler/Runge-Kutta methods; Stability and Stiffness

  9. Boundary Value Problems: Shooting Method

  10. Symmetric Matrix Eigenvalue Problems: Jacobi rotations, Power/inverse power method, Tridiagonal form

  11. Application to Chemical Physics: Molecular thermodynamics (Ideal gas, harmonic oscillator, rigid rotor partition functions), Equation of states, Schroedinger equation of Hydrogen molecule cation, Hartree-Fock for He atom, Linear variational problems in Quantum mechanics (1D potentials, Tunneling problems), Potential energy surface fitting, Time-dependent Schroedinger equation.

  12. Optional Topics: Krylov Subspace Techniques, Lanczos iteration, Iterative linear solvers, Non-linear regression, Matrices: Rank and condition numbers

Contact

For comments, questions, suggestions or requests please write to ramakrishnan@tifrh.res.in

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Contains Jupyter notebooks and other materials prepared for the course Numerical Methods offered at TIFR Hyderabad (https://www.tifrh.res.in/~ramakrishnan/index.php/teaching)

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