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Numerical Methods with MATLAB Theory, Code & Applications
Published 9/2026
Created by Muhammad Sarmad Arshad
MP4 | Video: h264, 1920x1080 | Audio: AAC, 44.1 KHz, 2 Ch
Level: All Levels | Genre: eLearning | Language: English | Duration: 12 Lectures ( 3h 0m ) | Size: 5.1 GB
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 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 MATLABRequirements
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 analysis2. 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 implementation3. 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 implementation4. Numerical Differentiation
Learn to approximate derivatives using
Forward Difference Backward Difference Central Difference Error and accuracy MATLAB implementation5. Numerical Integration
Learn to approximate definite integrals using
Trapezoidal Rule Simpson's Rule Accuracy and approximation errors MATLAB implementation and practical examples6. 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 solutions7. 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 solutionsIt'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 memorizationWho Is This Course For?
This course is suitable for
BS Mathematics studentsMS/MPhil Mathematics studentsEngineering studentsComputer Science studentsData Science studentsArtificial Intelligence studentsScientific Computing studentsStudents learning MATLABResearchers beginning numerical computingStudents preparing for university examinationsAnyone interested in numerical analysis and computational mathematicsWhether 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 problemsStart 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
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