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 → ApplicationsFirst, 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 Learn1.

Root-Finding MethodsLearn to find approximate roots of nonlinear equations using:Bisection MethodRegula Falsi MethodNewton-Raphson MethodSecant MethodError, stopping criteria, and convergenceMATLAB implementation and graphical analysis2. Systems of Linear EquationsLearn both direct and iterative methods for solving linear systems:Gaussian EliminationLU DecompositionGauss-Jacobi MethodGauss-Seidel MethodConvergence conceptsMATLAB implementation3. Interpolation MethodsLearn how to estimate unknown values from tabulated data using:Lagrange InterpolationNewton's Divided Difference FormulaInterpolation polynomial constructionNumerical examples and MATLAB implementation4.

Numerical DifferentiationLearn to approximate derivatives using:Forward DifferenceBackward DifferenceCentral DifferenceError and accuracyMATLAB implementation5. Numerical IntegrationLearn to approximate definite integrals using:Trapezoidal RuleSimpson's RuleAccuracy and approximation errorsMATLAB implementation and practical examples6. Numerical Solution of ODEsLearn to solve initial-value problems using:Euler MethodRunge-Kutta Method of Order 2 (RK2)Runge-Kutta Method of Order 4 (RK4)Error and accuracyMATLAB implementationGraphical visualization of numerical solutions7.

MATLAB Implementation in DetailThe 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 filesVariables and arraysLoops and if-statementsUser-defined functionsNumerical operationsIterative algorithmsTabulation of numerical valuesGraphsComparison 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 + MATLABOne 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 it2. The derivation of its numerical formulation3. Performing a hand calculation of one problem4.

Understanding the numerical algorithm5. Writing the program for the technique using MATLAB6. Analysis of the results obtained7.

Visualization of the results where possibleWhat 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 instructor15+ years of university teaching experienceUniversity-level mathematical explanationsComplete theory for the numerical methodsStep-by-step hand-worked examplesMATLAB implementation for every major methodClear algorithmic explanationsGraphical visualizationEnglish subtitles for all lecturesUrdu/English explanationsPractical computational examplesFocus 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 CourseBy completing the course, you will be able to:Understand the fundamental concepts of numerical methodsSelect appropriate numerical techniques for different problemsPerform numerical calculations by handUnderstand iterative numerical algorithmsAnalyze approximation and numerical errorsSolve nonlinear equations numericallySolve systems of linear equationsConstruct interpolation polynomialsApproximate derivatives numericallyEvaluate definite integrals numericallySolve ordinary differential equations numericallyWrite MATLAB programs for numerical methodsInterpret and visualize numerical resultsApply numerical techniques to practical mathematical and engineering problemsStart Your Journey into Numerical ComputingNumerical 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.