School of Scientific Computing & Informatics · Computational physics & chemistry
Computational Physics & Numerical Methods
Most physical and biological systems are too complex to solve on paper. This course teaches the numerical methods used to simulate them, with the error analysis that tells you whether to believe the result.
Course overview
Computational Physics & Numerical Methods covers the workhorse algorithms of computational science: root finding, numerical linear algebra, ordinary and partial differential equations, Fourier transforms and stochastic simulation.
Examples are drawn from physics and biophysics: oscillators and orbits, diffusion and heat flow, random walks and polymer models, and the Monte Carlo and molecular-dynamics ideas that underpin molecular simulation.
Learning outcomes
By the end of the course you will be able to:
- Implement and analyse root finding, interpolation and integration
- Solve ODEs with explicit, implicit and symplectic integrators
- Solve diffusion and wave equations with finite differences
- Run Monte Carlo simulations including the Metropolis algorithm
- Quantify numerical error, stability and convergence
Skills you will practise
Eligibility and prerequisites
Who can apply
- Students and graduates in any science, engineering, pharmacy, medicine, agriculture, geography or computing programme (B.Sc., B.Tech., B.E., BCA, M.Sc., M.Tech., MCA, PhD)
- Researchers, faculty and working professionals in research, healthcare, biotech, pharma or IT who want to apply computing to science
- Final-year students may apply before their results are declared
Prerequisites
- Scientific Computing with Python or equivalent
- Calculus and basic linear algebra
Best suited to
- Physics, engineering and chemistry students
- Biophysicists and computational biologists
- Learners preparing for molecular simulation or quantum chemistry
Module-wise syllabus
6 modules. Each pairs instructor-led sessions with a hands-on lab on public data.
Topics
- Floating point and error
- Root finding and interpolation
- Numerical integration
Topics
- Euler and Runge–Kutta
- Stiff systems
- Symplectic integrators
Topics
- Finite differences
- Diffusion and heat equations
- Stability conditions
Topics
- Random numbers
- Monte Carlo integration
- Metropolis sampling and the Ising model
Topics
- Eigenvalue problems
- The FFT
- Signal analysis
Topics
- Model
- Numerical method
- Error analysis
Practical sessions and projects
Capstone project
Simulate and verify
Simulate a physical or biophysical system and show, with convergence tests, that the numerical result can be trusted.
Assessed on the correctness of the analysis, the quality of the code and the reasoning in the write-up. A pass is required for the certificate.
- Numerical foundations
Compare integration schemes on a known integral and measure their convergence.
- Ordinary differential equations
Simulate a pendulum and a planetary orbit and show why energy drifts with the wrong integrator.
- Partial differential equations
Model diffusion of a molecule in tissue and find the stable time step.
- Stochastic methods
Simulate the Ising model and estimate its phase transition.
- Linear algebra and Fourier methods
Find normal modes of a molecule-like spring network and analyse a noisy signal with the FFT.
- Project: simulate a system
Simulate a physical or biophysical system and justify the method with an error and convergence analysis.
Software, tools and datasets
Software and tools
All software is free and open source or free for academic use. Recommended computer: 8 GB RAM, 30 GB free disk, Linux, macOS or Windows with WSL2.
Datasets
- Simulated physical systems: Methods with analytical answers.Generated in class
Core reading
- Newman M. Computational Physics. CreateSpace, 2013.
- Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical Recipes, 3rd edition. Cambridge University Press, 2007.
Duration, format and fees
- Next cohort
- Dates are sent with your admission offer
- Timetable
- Three evening or weekend sessions a week (IST), plus a lab clinic; intensive and weekend-only schedules on request
- Payment
- Secure online payment link with your admission offer (UPI, cards, net banking). Instalments on request for fees above ₹15,000.
- Refunds
- See the refund and cancellation policy.
Instructor
The instructor for each cohort is named in your admission offer and on this page when the cohort is announced. Vedicgen instructors are selected for hands-on research or industry experience in the subject they teach, and every course is reviewed by a second subject expert.
Questions about who teaches a cohort? [email protected]
Certificate
Learners who complete the course and pass its capstone receive a Vedicgen certificate of completion for Computational Physics & Numerical Methods, issued by Vivofold, stating the guided hours and skills assessed. Each certificate has a unique ID and QR code that anyone can check.
Apply for Computational Physics & Numerical Methods
Apply
Send the form below. It takes about five minutes.
Review
An adviser confirms your fit and format within two working days.
Offer
You receive dates, timetable and a secure payment link.
Onboard
Set-up guide, pre-reading and joining links.
Frequently asked questions
In the live cohort, modules are taught in instructor-led sessions with a weekly lab clinic where you work on real public data with help at hand; every session is recorded. The self-paced format uses the same lessons, labs and datasets with mentor review of your capstone. Both formats end with an assessed project reviewed for the code and the science.
A laptop with at least 8 GB of RAM and about 30 GB of free disk space, running Linux, macOS, or Windows with WSL2. Installation instructions are sent before the first session, and lab clinics help with any set-up problems.
Yes. Learners who complete the course and pass its assessment receive a Vedicgen certificate of completion, issued by Vivofold. Every certificate carries a unique ID and a QR code that anyone, including an employer or admissions office, can check on the certificate verification page.
Apply with the form on this page. Live and in-person cohorts run through the year; the dates, timetable and joining details of the next cohort are sent with your admission offer and listed on this page once announced. Self-paced enrolment opens as soon as your application is accepted.
Yes. No course runs longer than four weeks, and the length is customisable: choose the standard schedule, an intensive one- to two-week schedule, weekends only, or a custom timetable. Pick your preference on the application form; colleges and teams can book their own dates.
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