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Course10310611871 lectures

Matlab Programming for Numerical Computation

Prof. Niket Kaisare · IIT Madras

Start with lecture 1 At NPTEL

Lectures

Module 1: Introduction to MATLAB

  1. Week-01 Plan Video
  2. Basics of Programming using MATLAB Video
  3. Array Operations in MATLAB Video
  4. Tutorial: Using Arrays Video
  5. For Loops and Array Indexing in MATLAB Video
  6. Cell Arrays and Structures in MATLAB Video
  7. Bonus - Mixed_Data_Types Video
  8. Plotting and Output Video

Module-2: Building Your Code with MATLAB

  1. Week-02 Plan Video
  2. Loops and Execution Control Video
  3. MATLAB Files -- Scripts and Functions Video
  4. Parameter struct in MATLAB Video
  5. Good Practices in MATLAB Functions Video
  6. Good Practices in MATLAB Functions (Part-2) Video
  7. Debugging MATLAB Code Video

Module 3: Errors and Approximations

  1. Errors in Numerical Computation Video
  2. Truncation Errors and Taylors Series Video
  3. Round-Off Errors; and Iterative Methods Video
  4. Step-wise Methods and Error Propagation Video

Module 4: Linear Equations

  1. Basics of Linear Algebra Video
  2. Gauss Elimination and Back-Substitution Video
  3. LU Decomposition and Partial Pivoting Video
  4. Gauss Siedel Method Video
  5. (Tutorial) Video
  6. Tri-Diagonal Matrix Algorithm Video

Module 5: Solving Nonlinear Equations

  1. Nonlinear Equations in Single Variable Video
  2. Using MATLAB command fzero Video
  3. Fixed Point Iteration in Single Variable Video
  4. Newton-Raphson (single variable) Video
  5. Using MATLAB command fsolve (multi-variable) Video
  6. Newton-Raphson (multi Variable) Video

Module 6: Numerical Differentiation and Integration

  1. Week-06 Plan Video
  2. Differentiation in Single Variable Video
  3. Higher Order Differentiation Formulae Video
  4. Partial Differentials (Bonus) Video
  5. Numerical Integration Video
  6. Multiple Applications of Integration Formulae Video
  7. In-Build MATLAB Integration Functions Video

Module 7: Ordinary Differential Equations (single variable)

  1. Introduction and Euler's Method Video
  2. Runge-Kutta (RK-2) method Video
  3. MATLAB ode45 algorithm Video
  4. Higher order Runge-Kutta Methods Video
  5. Error Analysis Video

Module 8: ODE-IVP - Practical Aspects

  1. Multi-Variable ODE Video
  2. Stiff Systems & Solution using ode15s Video
  3. ODE-IVP - Practical Aspects Video
  4. A Final Example for ODE-IVP Video

Module 9: Regression and Interpolation

  1. Week-09 Plan Video
  2. Introduction Video
  3. Linear Least Squares Regression Video
  4. Nonlinear and Functional Regression Video
  5. Interpolation Functions in MATLAB Video
  6. Tutorial: How to do linear and nonlinear regression Video

Week 10: Ordinary Differential Equations – Boundary Value Problems

  1. ODE-BVP: Introduction and Solution using MATLAB Solver Video
  2. ODE-BVP: Solution using Finite Difference Video
  3. ODE-BVP: Shooting Method Video
  4. Extensions to ODE-BVP Video

week-11

  1. Partial Differential Equations (PDEs) Video
  2. PDE Solution Approaches Video
  3. Method of Lines for transient PDEs Video
  4. Method of Lines for Hyperbolic PDEs Video
  5. Bonus: Finite Differences for Solving Transient PDEs Video
  6. Bonus: Solving Elliptic PDEs Video

week-12

  1. Practical Applications and Course Wrap-Up Video
  2. Revisiting Examples from this Course Video
  3. Solve Nonlinear Equations (with numerical derivative) Video
  4. Regression and Differentiation: Practical Issues Video
  5. Transient PDEs in Multiple Variables Video

Live Session

  1. Live Session 04-02-2021 Video
  2. Live Session 18-02-2021 Video
  3. Live Session 04-03-2021 Video

Syllabus and materials

At NPTEL, as the course publishes them.

Credits and licence

Institution
IIT Madras
Department
Chemical Engineering
Teacher
Prof. Niket Kaisare
Level
Undergraduate
Language
English
Subjects
Chemistry, Engineering
Source
NPTEL
Licence
CC BY-NC-SA, as NPTEL states it. Non-commercial use only. NPTEL's terms
Attribution
NPTEL states: "Distributed under Creative Commons Attribution-ShareAlike / CC BY - NC - SA", beside a BY-NC-SA badge.
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