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 learn the mathematics behind the method and the 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.

With MATLAB, 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 understand how 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.