CS227-Scientific Computing

Lecture 1-Some MATLAB Basics

Contents of this lecture

•  Using MATLAB as a calculator.

•  MATLAB’s particular way of handling vectors and matrices.

•  Plotting parametrized curves and surfaces.

Using MATLAB as a calculator

Using MATLAB as a calculator

Variables Represent Matrices

Row vectors and column vectors

Row vectors and column vectors

Row vectors and column vectors

Creating Matrices

Arithmetic with matrices

Arithmetic with matrices

Arithmetic with matrices

Accessing Ranges of Matrix Elements

Built-in Functions are Applied Componentwise to Matrices

A more complicated example

User-Defined Functions

User-Defined Functions

Plotting

•  There are two flavors of plotting---the ‘ez’ version, where the source is a known mathematical function, and the ordinary version, where the source is discrete data.

•  Here we present just a few useful techniques.

Superimposed Graphs of two Functions

•  Suppose we want to superimpose the graphs of

and

in order to see where they cross. Note that there will be no solutions for x>1, and that both graphs are symmetric about the y-axis (they are even functions).

Superimposed Graphs of two Functions

You can use the menus in the Figure window to alter the appearance (e.g., scaling and range of axes, placement of legends and grid lines,…).

Parametrized Curve in Plane •  The curve is the set of points

for some functions x and y. (Think of this as giving the position of a point at time t.)

•  You get a nice ellipse from

Parametrized Curve in Plane

Curves in 3-Dimensional Space Use ezplot3(X,Y,Z) in exactly the way we

used ezplot(X,Y). Example: Helix of height 1, radius 1, with 5

turns, given by

Curves in 3-Dimensional Space

Surfaces in 3-Dimensional Space

•  In general, parametrized surface given by

•  Example: Sphere of radius 1 parametrized by spherical coordinates (essentially latitude and longitude):

Surfaces in 3-Dimensional Space

Using M-files

•  Instead of typing these 4 instructions on the command line, we can place them in a text file. (Use the Edit window in MATLAB to create it.)

•  Save the file with a name like “sphere.m” •  Type “sphere” and the command prompt

to execute.

plot

•  We can use plot if the data source is a vector. The syntax is

plot(x1,y1,x2,y2,….) where x1,y1 are vectors of the same size

giving x- and y- coordinates of one series of data, x2,y2 give x and y coordinates of the next series. You can supply additional arguments specifying how to draw each data series.

plot

•  The commands on the next page plot the first 19 Fibonacci numbers

1,1,2=1+1,3=2+1,5=3+2,8=5+3,13=8+5,… as red dots, and the graph of ((1+sqrt(5))/2)n/sqrt(5) as a black curve (in reality, though, a series

of line segments).

plot