Introduction to Computational Physics, Jul-Nov 2025
Credits 9 credits
Instructor Sivaram Ambikasaran,
Classroom NNAC \(631\)
Timings 'E' slot
Mailing list
You can find on google groups when you login via smail. Search for "2025_cp" or "2025_cp-group@smail.iitm.ac.in". Click on it and request to be added to the group.
All assignments need to be submitted before Sunday midnight.
Students need to submit their solution in Jupyter/Python notebook through the dropbox link provided.
The name of the Jupyter notebook should be as follows: da02b034_5.ipynb, where da02b034 is your roll number and 5 implies that you are submitting your fifth assignment.
Any copying on assignments will result in a zero on the assignment.
We will be using JPlag to detect similarities among multiple sets of source code files.
The grader will expect you to express your ideas clearly, legibly, and completely, often requiring complete English sentences rather than merely just a long string of equations or unconnected mathematical expressions. This means you could lose points for poorly written proofs or answers. Clear exposition is a crucial ingredient of technical communication. Clarity of thought and presentation is more important in mathematics, sciences & technology than any other field. The only way to master exposition is by repeated practicing.
Short Syllabus
Dominant part of the course will focus on computationally solving ordinary and partial differential equations arising out of physics; Lectures around 40.
Ordinary differential equations:
First order differential equations with applications in Newton’s law, Radioactive decay, non-linear differential equations like population growth, etc.
Second order differential equations like free fall, effects of air drag, projectile motion, etc; Oscillatory motion, Simple Harmonic oscillator, Damped harmonic oscillator, Damped harmonic oscillator with external forcing.
Solution construction for ODEs: Construction of solution of homogeneous, constant coefficient, linear ODE; Linear independence of solutions and Wronskian; Method of variation of parameters; Green’s function.
Numerical differentiation; Accuracy of Finite differences; Pade approximations
Numerical Integration; Trapezoidal and Simpson’s Rules; Euler Maclaurin summation and higher order trapezoidal rules; Romberg Integration and Richardson Extrapolation; Adaptive Quadrature; Gauss Quadrature
Numerical Methods for solving ODEs; Implicit and Explicit methods; Accuracy of numerical schemes; Consistency, Stability and convergence of numerical schemes; Analysis of various numerical methods Euler, trapezoidal, Runge-Kutta, Multi-step methods like leapfrog, Adams Bashforth etc.
Partial Differential Equations:
Classification of PDEs: parabolic, hyperbolic and elliptic
Parabolic PDEs; Examples, Diffusion/Heat equation with applications;
Hyperbolic PDEs; Examples, Wave equation with applications;
Analytic solution for above PDEs; Separation of variables; Green’s function
Numerical solution for above PDE; Finite difference methods, finite volume methods, finite element methods, boundary element methods; Accuracy and stability of different algorithms;
Textbooks
Computational Physics: Problem Solving With Python by Rubin H. Landau, Manuel J. P ́aez, Cristian C. Bordeianu; Publisher: Wiley; 4th edition
Computational Physics: With Worked Out Examples in FORTRAN and MATLAB by Michael Bestehorn; Publisher: De Gruyter; 2nd edition
Fundamentals of Engineering Numerical Analysis, by Parviz Moin; Publisher: Cambridge University Press; Edition: 2nd edition
