# Numerical Computations in MATLAB: Video Course

URL: https://yarpiz.com/numerical-computations-in-matlab-video-tutorial-572
Author: Mostapha Kalami Heris
Published: 2019-07-06
Updated: 2026-10-30
Topics: Courses

> A guided MATLAB course covering equations, matrices, interpolation, integration, polynomials, differential equations and optimization, with links to all seven chapters.

Learn to solve equations, work with matrices, fit data, integrate functions and simulate differential equations with MATLAB. This course connects the mathematical ideas to short examples using MATLAB's numerical functions. Mostapha Kalami Heris teaches the course on the Yarpiz YouTube channel.

The course has 22 videos, about 4 hours and 27 minutes in total, grouped into seven chapters. Each video takes one MATLAB function or group of functions, explains the math behind it briefly, and then solves small examples live in MATLAB. Each chapter also has its own page on Yarpiz with a detailed summary of its videos.

## Watch online

The 22 sections of this course are available on YouTube and are embedded here as a playlist.

::: video {playlist="PLgH3sgdvgO4SFXpbgu5OwQV7rFaJl1j9U" youtube="yCJ73SDvzwk" count="22" title="Numerical Computations in MATLAB: Video Course"}
:::

## What the course covers

### 1. Root finding and equation solving

The first chapter solves equations of the form $f(x) = 0$. It finds all roots of a polynomial with `roots`, one root of a nonlinear equation with `fzero` (and shows why the starting point matters), a system of nonlinear equations with `fsolve`, and a system of linear equations $Ax = b$ with `linsolve` and the backslash operator. Chapter page: [Root Finding in MATLAB](https://yarpiz.com/root-finding-yptnm190520s01).

1. Finding roots of polynomials using roots ([YouTube](https://youtu.be/yCJ73SDvzwk))
2. Finding roots of nonlinear functions using fzero ([YouTube](https://youtu.be/UKa7rxPpzqw))
3. Solving systems of nonlinear equations using fsolve ([YouTube](https://youtu.be/hfUrZ3F8b2A))
4. Solving systems of linear equations using linsolve ([YouTube](https://youtu.be/E7RUl6ll9oE))

### 2. Eigenvalues, eigenvectors and SVD

This chapter computes eigenvalues and eigenvectors with `eig`, checks that the eigenvalues' product equals the determinant and their sum equals the trace, and diagonalizes a matrix with independent eigenvectors as $A = VDV^{-1}$. It then computes the singular value decomposition $A = USV^{T}$ for real matrices with `svd` and uses a low rank approximation to compress an image. Chapter page: [Eigenvalues and Eigenvectors in MATLAB](https://yarpiz.com/eigenvalues-and-eigenvectors-video-tutorial-yptnm190520s05).

5. Eigenvalues and Eigenvectors ([YouTube](https://youtu.be/aEjeuj5jfLU))
6. Singular Value Decomposition ([YouTube](https://youtu.be/eVUXOagTiL8))

### 3. Interpolation and curve fitting

This chapter fits polynomials to noisy data with `polyfit` and `polyval`, interpolates data in one or more dimensions with `interp1` to `interpn`, interpolates periodic data in the frequency domain with `interpft`, builds smooth paths with cubic splines, and interpolates scattered data in 2D and 3D with `griddata`. Chapter page: [Interpolation and Curve Fitting in MATLAB](https://yarpiz.com/interpolation-video-tutorial-yptnm190520s07).

7. Polynomial Fitting using polyfit ([YouTube](https://youtu.be/9Dui-ExAEEc))
8. Interpolation using interp1 to interpn ([YouTube](https://youtu.be/9n5acUZRl34))
9. Interpolation using interpft ([YouTube](https://youtu.be/Rzc-8QgjawQ))
10. Interpolation using Cubic Splines ([YouTube](https://youtu.be/QdAcdStzsh4))
11. Interpolation using griddata in 2D and 3D Spaces ([YouTube](https://youtu.be/ELudRu1UZAg))

### 4. Numerical integration and differentiation

This chapter computes integrals of functions with `integral` and `quadgk`, including improper integrals, error tolerances and contour integrals in the complex plane. It continues with double and triple integrals (`integral2`, `quad2d`, `integral3`), then integrates sampled data with `sum`, `cumsum`, `trapz` and `cumtrapz`. It ends with derivatives of sampled data using `diff`, `gradient` and `del2`. Chapter page: [Integration and Differentiation in MATLAB](https://yarpiz.com/integration-and-differentiation-video-tutorial-yptnm190520s12).

12. Numerical Integration using integral and quadgk ([YouTube](https://youtu.be/wiYeBfBBEys))
13. Double and triple integrals ([YouTube](https://youtu.be/e1zyt26NBZ4))
14. Discrete integrals and summations ([YouTube](https://youtu.be/Fak-n-SETpU))
15. Numerical Differentiation ([YouTube](https://youtu.be/g93udhjFFFw))

### 5. Working with polynomials

A single video reviews the polynomial functions of MATLAB, using the coefficient vector form: evaluation with `polyval`, `roots` and `poly`, fitting with `polyfit`, multiplication and division with `conv` and `deconv`, and exact derivatives and integrals with `polyder` and `polyint`. Chapter page: [Working with Polynomials in MATLAB](https://yarpiz.com/working-with-polynomials-video-tutorial-yptnm190520s16).

16. Working with Polynomials ([YouTube](https://youtu.be/HPsRYJKnAMA))

### 6. Differential equations

This chapter solves initial value problems with `ode45` and the other nonstiff and stiff solvers, using the van der Pol oscillator and the Lorenz system as examples. It then solves boundary value problems with `bvp4c` and `bvpinit`, and delay differential equations with `dde23`, `ddesd` and `ddensd`. Chapter page: [Numerical Solution of Differential Equations in MATLAB](https://yarpiz.com/numerical-solution-of-differential-equations-video-tutorial-yptnm190520s17).

17. Solving Ordinary Differential Equations ([YouTube](https://youtu.be/U1H08ph4Y0I))
18. Solving Boundary Value Problems ([YouTube](https://youtu.be/RngJAKnFARs))
19. Solving Delayed Differential Equations ([YouTube](https://youtu.be/TCWrD3cZG9s))

### 7. Optimization

The last chapter solves linear and mixed integer linear programs with `linprog` and `intlinprog`, a quadratic program with `quadprog`, and nonlinear problems with `fminbnd`, `fminsearch`, `fminunc` and `fmincon`. The examples include the Rosenbrock function and the design of a box with the largest volume for a given surface area. Chapter page: [Optimization in MATLAB](https://yarpiz.com/optimization-video-tutorial-yptnm190520s20).

20. Linear Programming and Mixed-Integer LP ([YouTube](https://youtu.be/kRv7QMUH7gA))
21. Quadratic Programming ([YouTube](https://youtu.be/XBA_VemmaxY))
22. Constrained and Unconstrained Nonlinear Optimization ([YouTube](https://youtu.be/7nCgLN00yqk))

## Who it is for

The course suits applied math, science and engineering students, and anyone who needs numerical methods in MATLAB. It assumes basic math and calculus, some background in numerical methods, and basic MATLAB programming. Some functions, such as `fsolve`, `linprog`, `quadprog` and `fmincon`, need Optimization Toolbox.

## How to study the course

Start with the root finding chapter if you are new to the numerical tools. Follow the chapter order above, or choose the chapter that matches your problem. The chapter list is a study guide, and the master YouTube playlist may use a different order for its first two videos.

Run each small example before changing its inputs. Check a solver's result against the original equations, inspect the shape of matrix outputs and compare numerical approximations at more than one tolerance or step size. The videos use an older MATLAB release, so function options and plots may differ in your installation.

## Related tutorials on Yarpiz

- [Numerical Root Finding Methods in Python and MATLAB](https://yarpiz.com/numerical-root-finding-methods-in-python-and-matlab-yprf191221): the bisection, secant and Newton-Raphson methods.
- [Runge-Kutta Method in Python and MATLAB](https://yarpiz.com/runge-kutta-rk4-in-python-and-matlab-yptdeq190515).
- [Linear Programming in MATLAB](https://yarpiz.com/linear-programmin-in-matlab-linprog-yptlp190516), with the transportation problem.
- [Least Squares in Python, JavaScript and MATLAB](https://yarpiz.com/least-squares-in-python-javascript-and-matlab-yptls190514).

## How to cite

Mostapha Kalami Heris, Numerical Computations in MATLAB: Video Course (572), Yarpiz, 2019. https://yarpiz.com/numerical-computations-in-matlab-video-tutorial-572