Course10310611871 lectures
Matlab Programming for Numerical Computation
Prof. Niket Kaisare · IIT Madras
Lectures
Module 1: Introduction to MATLAB
- Week-01 Plan
- Basics of Programming using MATLAB
- Array Operations in MATLAB
- Tutorial: Using Arrays
- For Loops and Array Indexing in MATLAB
- Cell Arrays and Structures in MATLAB
- Bonus - Mixed_Data_Types
- Plotting and Output
Module-2: Building Your Code with MATLAB
- Week-02 Plan
- Loops and Execution Control
- MATLAB Files -- Scripts and Functions
- Parameter struct in MATLAB
- Good Practices in MATLAB Functions
- Good Practices in MATLAB Functions (Part-2)
- Debugging MATLAB Code
Module 3: Errors and Approximations
- Errors in Numerical Computation
- Truncation Errors and Taylors Series
- Round-Off Errors; and Iterative Methods
- Step-wise Methods and Error Propagation
Module 4: Linear Equations
- Basics of Linear Algebra
- Gauss Elimination and Back-Substitution
- LU Decomposition and Partial Pivoting
- Gauss Siedel Method
- (Tutorial)
- Tri-Diagonal Matrix Algorithm
Module 5: Solving Nonlinear Equations
- Nonlinear Equations in Single Variable
- Using MATLAB command fzero
- Fixed Point Iteration in Single Variable
- Newton-Raphson (single variable)
- Using MATLAB command fsolve (multi-variable)
- Newton-Raphson (multi Variable)
Module 6: Numerical Differentiation and Integration
- Week-06 Plan
- Differentiation in Single Variable
- Higher Order Differentiation Formulae
- Partial Differentials (Bonus)
- Numerical Integration
- Multiple Applications of Integration Formulae
- In-Build MATLAB Integration Functions
Module 7: Ordinary Differential Equations (single variable)
- Introduction and Euler's Method
- Runge-Kutta (RK-2) method
- MATLAB ode45 algorithm
- Higher order Runge-Kutta Methods
- Error Analysis
Module 8: ODE-IVP - Practical Aspects
- Multi-Variable ODE
- Stiff Systems & Solution using ode15s
- ODE-IVP - Practical Aspects
- A Final Example for ODE-IVP
Module 9: Regression and Interpolation
- Week-09 Plan
- Introduction
- Linear Least Squares Regression
- Nonlinear and Functional Regression
- Interpolation Functions in MATLAB
- Tutorial: How to do linear and nonlinear regression
Week 10: Ordinary Differential Equations – Boundary Value Problems
- ODE-BVP: Introduction and Solution using MATLAB Solver
- ODE-BVP: Solution using Finite Difference
- ODE-BVP: Shooting Method
- Extensions to ODE-BVP
week-11
- Partial Differential Equations (PDEs)
- PDE Solution Approaches
- Method of Lines for transient PDEs
- Method of Lines for Hyperbolic PDEs
- Bonus: Finite Differences for Solving Transient PDEs
- Bonus: Solving Elliptic PDEs
week-12
- Practical Applications and Course Wrap-Up
- Revisiting Examples from this Course
- Solve Nonlinear Equations (with numerical derivative)
- Regression and Differentiation: Practical Issues
- Transient PDEs in Multiple Variables
Live Session
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.
- Who can watch
- NPTEL gives no rating. Invisible Network shows it to Tweens profiles and older, judged from what the source says about it. How courses are placed
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