Numerical Methods with MATLAB: Theory, Code & Applications

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.