MATLAB-tutorial-2021.pdf

Dynamics and Vibrations

MATLAB tutorial

School of Engineering

Brown University

To prepare for HW1, do sections 1-11.6 – you can do the rest later as needed

6. MATLAB ‘Live Scripts’ (for algebra, plotting, calculus, and solving differential equations exactly)

6.1Solving Equations

6.2 Functions and Plotting

6.3 Calculus

6.4Vectors

6.5 Matrices

6.6 Solving differential equations (with symbols)

7. Working with M-files

8. MATLAB Functions in M files

9. Basic Programming Concepts

9.7 Using plots to display curves and surfaces stored in vectors and matrices

9.8 Conditional statements

10. Organizing complex calculations as functions in an M-file

11. Solving ordinary differential equations (ODEs) using MATLAB

11.1 Solving a basic differential equation

11.2 Solving a basic differential equation in an M-file

11.3 Solving a differential equation with adjustable parameters

11.4 Common errors

11.5 Solving simultaneous differential equations

11.6 Controlling the accuracy of solutions to differential equations

12.3 Optimizing with constraints

13. Reading and writing data to/from files

14. Movies and animation

You can think of MATLAB as a sort of graphing calculator on steroids – it is designed to help you

manipulate very large sets of numbers quickly and with minimal programming. MATLAB is particularly

good at doing matrix operations (this is the origin of its name). It is also capable of doing symbolic

computations, and has huge numbers of built-in packages that will do things like image processing,

design control systems, machine learning, bioinformatics, and so on. It is also capable of communicating

https://www.brown.edu/information-technology/software/catalog/matlab

The instructions tell you to

wait for an email from mathworks, but they don’t always send one. Just check your account – if the

download button for MATLAB appears you are all set. If you have previously registered, you can

download upgraded versions of MATLAB whenever you like. The latest release is 2019b, but if you are

using 2019a that should work fine.

3. Basic MATLAB windows

4. Using the MATLAB command window

You can use the MATLAB command window as a simple calculator. Try this for yourself, by typing the

following into the command window. Press ‘enter’ at the end of each line.

>>x=4

>>y=x^2

>>sin(pi)

MATLAB will display the solution to each step of the calculation just below the command. Do you notice

anything strange about the solution given to the last step?

We almost never use MATLAB like this, however – the format of the output is difficult to read, and it’s

hard to keep track of complicated calculations. Instead, we write a script to do the calculations, and then

have MATLAB execute the script. There are two general types of MATLAB script:

calculus, plotting functions, and so on;

5. MATLAB help

Help is available through the online manual – Click on the question-mark in the strip near the top right of

the window). The matlab manuals are also online, and will come up in google search.

If you already know the name of the MATLAB function you want to use the help manual is quite good –

you can just enter the name of the function in the search, and a page with a good number of examples

6. MATLAB ‘Live Scripts’

If you would like to use MATLAB to do math calculations, algebra, or to plot

graphs, you can write a MATLAB ‘Live Script.’ This will organize your

calculations for you, and will also display the results in a nice clean format.

You should see a menu like the one below.

In the next few sections we will work through some useful things you can do with a ‘Live Script.’

6.1 Solving Equations

get used to it.

the first equation. The object can be used in future calculations. If you want to create an

equality inside an equation you have to use = =

Now try (just edit your script; you don’t have to type it all in again)