MATH 493 MATLAB Materials
Week 1
Simple activities
 Basic plotting
 Try also: On the same set of axes, create a plot of y = x, y = sin(x), and y = x^3. Make one graph blue, one red and one green.
 Create a plot of a bell curve, y = e^(x^2) for x=4..4. Hint: you'll need the exp function, and to be careful with the powers again.
 Creating matrices in different ways
 Try also: Create a 5x4 matrix; first 2 columns all ones, second two all zeros
 Create a 4x10 matrix; first row 1,2, ..., 10; second row 2, 4, ..., 20; third row 3, 6, ...30; fourth row 4, 8, ..., 40. Use colon notation, not explicit values.
 Syntax for matrix operations
 Try also: Use a search for 'arithmetic operator' to find the difference between x * x, and x .* x, or x^2 and x.^2.
 Which operations (+, , *, /, ^) have a 'dot' version as well as the 'regular' version?
 Loop structures
 Try also: Write a loop that displays all even numbers from 2 up to 10
 Write a loop that displays numbers counting by 5 from 0 to 100
 Find the sum of all even numbers between 0 and 40 (inclusive), once using a loop, and a second time using sum
More advanced activities

Heat equation  PDE solving example
 Download and run the script asis.
 Change the endpoint temperatures.
 Change the initial temperature profile in the beam to be a sine wave (which then cools towards a constant temperature).
 Reduce the time interval between steps to speed up the simulation.

Image loading and display
 Download the images zip file and unzip it in your MATLAB directory. You should now have a 'rotated' and 'newtest' subdirectories.
 Download and run the script asis.
 Change the directory where the script finds the images from
'rotated' to 'newtest'.
 Have the process skip over any file with more than 300 columns of pixels.
 Use the 'imresize' command to resize all images to the same size
before averaging, rather than finding the average only over the
smallest image region.
 Temperature DE  ODE solving example (single variable)
 Download tempScript.m and
tempDE.m
 Look at the code in tempDE.m and relate it to Newton's Law of Heating and Cooling (source DE).
 Run tempScript.m and see the text and graphical output.
 Change the initial temperature 20.
 Change the simulation time interval to t=0..40.
 Increase the cooling coefficient value and see the effect on the model.
 Try to create two plots on the same axes, showing the simulation
for two different cooling coefficient values.
 Spring DE  ODE solving example (2variable system)
 Download springScript.m and
springDE.m
 Look at the code in springDE.m and compare it to the DE x'' = k x.
 Run srpingScript.m and see the graphical output.
 Change the initial position and velocity.
 Change the spring coefficient to see the effect on the motion.
 Change the DE so it includes friction: x'' = kx cx'. Simulate and see how friction affects the motion.
 Change the DE so that is represents the motion of a pendulum: x'' = k sin(x). Increase the initial velocity until you see the 'going over the top' behaviour of a pendulum.
 MEX MATLABtoC Connection