NPTEL : NOC:Tools in Scientific Computing (Mechanical Engineering)

Co-ordinators : Prof. Aditya Bandopadhyay


Lecture 1 - Preliminaries and Data types

Lecture 2 - Loops and Conditionals Implementation of bubble sort

Lecture 3 - Commonly used Functions

Lecture 4 - Matrix Manipulations Mohr's circle

Lecture 5 - Nonlinear algebraic equations - Visualizing convergence

Lecture 6 - Nonlinear algebraic equations - system of equation and Newton's basin of attraction

Lecture 7 - Overview of Jupyterlab, Octave GUI, Spyder GUI

Lecture 8 - Interactivity with Python - Ipywidgets

Lecture 9 - Geometric Interpretations of ODEs

Lecture 10 - Bifurcation: Saddle node bifurcation

Lecture 11 - Bifurcation: Transcritical bifurcation

Lecture 12 - Bifurcation: Pitchfork bifurcation

Lecture 13 - Imperfect bifurcations and catastrophies

Lecture 14 - 2D flows - linear systems

Lecture 15 - 2D flows - Trajectories: spirals, star and degeneracy

Lecture 16 - Phase portraits - nonlinear systems

Lecture 17 - 2D phase portraits - limit cycles

Lecture 18 - Bifurcations and 3D flows

Lecture 19 - 1D Maps

Lecture 20 - Probability density functions and sampling

Lecture 21 - Monte-carlo simulations: Darts and Buffon's needle

Lecture 22 - 1D Random walks

Lecture 23 - 2D Random walks

Lecture 24 - Boundary Value Problems - Part 1

Lecture 25 - Boundary Value Problems - Part 2

Lecture 26 - Regular Perturbation for ODE

Lecture 27 - Singular Perturbation for ODE

Lecture 28 - 2D Boundary Values Problems

Lecture 29 - PETSc and MPI basics

Lecture 30 - PETSc - Creating Vectors and Matrices

Lecture 31 - KSP object and solving a system

Lecture 32 - Poisson equation in PETSc

Lecture 33 - Nonlinear Solver of PETSc

Lecture 34 - Nonlinear solver with Jacobian in PETSc

Lecture 35 - Reaction-diffusion system in PETSc

Lecture 36 - Time stepping in PETSc

Lecture 37 - Heat transport using PETSc

Lecture 38 - Solving nonlinear PDE on a periodic domain yielding different patterns

Lecture 39 - Audio analysis - Determine motor RPM

Lecture 40 - Spectrogram and Doppler shift

Lecture 41 - Image processing - Preliminaries

Lecture 42 - Balloon problem and viscous fingers

Lecture 43 - Analyzing data files and 2D interpolation