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A Step-by-Step Guide for Engineering, Computing, Data Science, AI and Mathematics Students
What you'll learn

Implement complete MATLAB codes for all Numerical Methods with visualizations, plots and real engineering problem solutions

Analyze and compare convergence, accuracy and efficiency of Numerical Methods to choose the best method for any engineering problem

Solve Systems of Equations, apply Numerical Integration and Differentiation, and solve ODEs using Euler and Runge Kutta RK4 in MATLAB
Requirements

Basic knowledge of Calculus and Linear Algebra. MATLAB or free GNU Octave installed. No programming experience needed.
Description
Welcome to Numerical Methods with MATLAB: Theory, Codes & Applications. A practical and thorough course that will guide you step-by-step into understanding, implementing, and applying the most important numerical methods in mathematics, engineering, computer science, and computational science.
Numerical Methods with MATLAB: Theory, Codes & Applications is instructed by Dr. Muhammad Sarmad Arshad Khan, PhD in Computational Mathematics, Associate Professor, with more than 15 years of experience in teaching at universities level and also rich in experience in numerical analysis, computational mathematics, and mathematical modeling.
In contrast to just giving codes in MATLAB, this course takes you through the entire learning process
Mathematical Theory → Hand Calculation → Algorithm → MATLAB Code → Solution → Visualization → Applications
First, you will learn why and how the method works mathematically, then how to do it by hand, and then finally code it in MATLAB.
What You Will Learn
1. Root-Finding Methods
Learn to find approximate roots of nonlinear equations using

Bisection Method

Regula Falsi Method

Newton-Raphson Method

Secant Method

Error, stopping criteria, and convergence

MATLAB implementation and graphical analysis
2. Systems of Linear Equations
Learn both direct and iterative methods for solving linear systems

Gaussian Elimination

LU Decomposition

Gauss-Jacobi Method

Gauss-Seidel Method

Convergence concepts

MATLAB implementation
3. Interpolation Methods
Learn how to estimate unknown values from tabulated data using

Lagrange Interpolation

Newton's Divided Difference Formula

Interpolation polynomial construction

Numerical examples and MATLAB implementation
4. Numerical Differentiation
Learn to approximate derivatives using

Forward Difference

Backward Difference

Central Difference

Error and accuracy

MATLAB implementation
5. Numerical Integration
Learn to approximate definite integrals using

Trapezoidal Rule

Simpson's Rule

Accuracy and approximation errors

MATLAB implementation and practical examples
6. Numerical Solution of ODEs
Learn to solve initial-value problems using

Euler Method

Runge-Kutta Method of Order 2 (RK2)

Runge-Kutta Method of Order 4 (RK4)

Error and accuracy

MATLAB implementation

Graphical visualization of numerical solutions
7. MATLAB Implementation in Detail
The implementation of programs using MATLAB is a major aspect of this course.
With respect to each numerical method, you will learn how to implement it in terms of MATLAB code.
You will use

MATLAB script files

Variables and arrays

Loops and if-statements

User-defined functions

Numerical operations

Iterative algorithms

Tabulation of numerical values

Graphs

Comparison of numerical solutions
It's not just about copying and running code. The MATLAB implementation of the algorithm will be done step-by-step so that you can understand how the mathematical algorithm is implemented in MATLAB.
Theory + Hand Calculation + MATLAB
One of the important aspects of this class is the combination of mathematical theory and numerical computation.
For every major technique, the process of learning includes
1. The knowledge of the mathematics behind it
2. The derivation of its numerical formulation
3. Performing a hand calculation of one problem
4. Understanding the numerical algorithm
5. Writing the program for the technique using MATLAB
6. Analysis of the results obtained
7. Visualization of the results where possible
What Makes This Course Different?
Many numerical-methods courses focus either on mathematical theory or on programming.
This course combines both.
You will learnthe mathematics behind the method andthe MATLAB implementation of the method.
You will get

PhD-qualified university instructor

15+ years of university teaching experience

University-level mathematical explanations

Complete theory for the numerical methods

Step-by-step hand-worked examples

MATLAB implementation for every major method

Clear algorithmic explanations

Graphical visualization

English subtitles for all lectures

Urdu/English explanations

Practical computational examples

Focus on understanding rather than memorization
Who Is This Course For?
This course is suitable for

BS Mathematics students

MS/MPhil Mathematics students

Engineering students

Computer Science students

Data Science students

Artificial Intelligence students

Scientific Computing students

Students learning MATLAB

Researchers beginning numerical computing

Students preparing for university examinations

Anyone interested in numerical analysis and computational mathematics
Whether you are studying numerical methods for an academic course or want to develop practical MATLAB skills, this course provides a structured path from fundamental concepts to implementation.
By the End of This Course
By completing the course, you will be able to

Understand the fundamental concepts of numerical methods

Select appropriate numerical techniques for different problems

Perform numerical calculations by hand

Understand iterative numerical algorithms

Analyze approximation and numerical errors

Solve nonlinear equations numerically

Solve systems of linear equations

Construct interpolation polynomials

Approximate derivatives numerically

Evaluate definite integrals numerically

Solve ordinary differential equations numerically

Write MATLAB programs for numerical methods

Interpret and visualize numerical results

Apply numerical techniques to practical mathematical and engineering problems
Start Your Journey into Numerical Computing
Numerical methods are at the heart of modern scientific and engineering computation. From solving nonlinear equations and systems of equations to interpolation, integration, and differential equations, these techniques provide powerful tools for problems where exact analytical solutions may be difficult or unavailable.
WithMATLAB, these methods become even more powerful because mathematical algorithms can be implemented, tested, visualized, and applied to larger problems efficiently.
So, if you want to move beyond simply learning formulas and actually understandhow numerical methods work and how to implement them in MATLAB, this course is for you.
Enroll now and start learning Numerical Methods with MATLAB - from theory and hand calculations to complete computational implementation and applications.
Who this course is for

Engineering, Mathematics, Computer Science, IT, Software Engineering, Data Science and AI students at BS MS PhD level, researchers and anyone wanting to solve real-world problems computationally using MATLAB.
Homepage

Code:

https://www.udemy.com/course/numerical-methods-with-matlab-theory-code-applications

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Numerical Methods with MATLAB Theory, Code & Applications

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