Tools in Scientific Computing

Overview Rapid advancements in computer hardware and high quality software libraries have enabled one to undertake works requiring high precision scientific computing with relative ease. The course involves exploration of various tools available for scientific computing with an emphasis on hands-on implementation. The course will deal briefly with the theory and the associated implementation for practical problems that an engineer may encounter. Undergraduates, postgraduates, and PhD students may find this course immensely useful for their project or research work. The course will make use of Python, GNU Octave, and PETSC (C based) as the medium of coding.

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Last updated Wed, 08-Jun-2022
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Course overview
Lecture Details

Prof. Aditya Bandopadhyay
Mechanical Engineering
IIT Kharagpur

Curriculum for this course
44 Lessons 34:30:27 Hours
Lecture
44 Lessons 34:30:27 Hours
  • Tools in Scientific Computing- Introduction
    Preview 00:03:11
  • Preliminaries and Data types
    00:48:41
  • Loops and Conditionals Implementation of bubble sort
    00:38:20
  • Commonly used functions
    00:51:36
  • Matrix Manipulations Mohr's circle
    01:13:37
  • Nonlinear algebraic equations - Visualizing convergence
    00:50:20
  • Nonlinear algebraic equations - system of equation and Newton's basin of attraction
    01:16:42
  • Overview of Jupyter Lab, Octave GUI, Spyder GUI
    00:42:55
  • Interactivity with Python - Ipywidgets
    00:19:40
  • Geometric Interpretations of ODEs
    00:55:02
  • Bifurcations: Saddle node bifurcation
    00:46:06
  • Bifurcation: Transcritical bifurcation
    00:37:16
  • Bifurcation: Pitchfork bifurcation
    00:54:27
  • Imperfect bifurcations and catastrophies
    01:01:00
  • 2D flows - linear systems
    01:05:55
  • 2D flows - Trajectories: spirals, star and degeneracy
    00:49:27
  • Phase portraits - nonlinear systems
    00:59:25
  • 2D phase portraits - limit cycles
    01:09:36
  • Bifurcations and 3D flows
    01:27:57
  • 1D Maps
    00:58:25
  • Probability density functions and sampling
    00:47:27
  • Monte-carlo simulations: Darts and Buffon's needle
    00:32:13
  • 1D Random walks
    00:56:44
  • 2D Random walks
    00:42:21
  • Boundary Value Problems
    00:45:07
  • Boundary Value Problems - p2
    00:25:36
  • Regular Perturbation for ODE
    00:36:40
  • Singular Perturbation for ODE
    00:42:43
  • 2D Boundary Values Problems
    00:43:38
  • PETSc and MPI basics
    00:46:12
  • PETSc - Creating Vectors and Matrices
    00:37:03
  • KSP object and solving a system
    01:00:13
  • Poisson equation in PETSc
    01:10:52
  • Nonlinear Solver of PETSc
    00:28:52
  • Nonlinear solver with Jacobian in PETSc
    00:34:06
  • Reaction-diffusion system in PETSc
    00:51:32
  • Time stepping in PETSc
    00:54:18
  • Heat transport using PETSc
    01:03:30
  • PETSc - Turing patterns
    00:44:49
  • Audio analysis - Determine motor RPM
    00:38:55
  • Spectrogram and Doppler shift
    00:25:42
  • Image processing - Preliminaries
    00:33:00
  • Balloon problem and viscous fingers
    00:23:41
  • Analyzing data files and 2D interpolation
    00:35:35
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