GEOS 597e: Spatiotemporal Data Analysis Workshop

Homework 1: Practice programming in MATLAB

Last updated 8/30/06. To be completed prior to class session Weds., Sept. 7th, with results handed in as hard copy.  

Introduction.  Now that we're set up to compute in MATLAB, let's take a session to perform some simple problem-solving exercises in the environment.  The following exercises are either verbatim or modified from Pratap (2002),  Getting Started with MATLAB: A quick introduction for scientists and engineers, Chapter 2.  Reporting your results to three decimal places should be sufficient. Alhtough you needn't script anything until problem 6, you may find it helpful to script your answers, naming results as variables q1a, q1b, q1c, q2a, q2b, ... or some other convention.
  1. Arithmetic operations.  Compute the following quantities:
    1. 25/(25-1) and compare with (1-2-5)-1.
    2. 3(51/2-1)/(51/2+1)2 - 1.  The square root x0.5 can be calculated with the command sqrt(x) or x^0.5.
    3. Area = pi*r2, with r=pi1/3-1.  (pi=3.14159265358979... in MATLAB).
  2. Exponential and logarithms.  The mathematical quantities ex, ln x and log x are calculated with exp(x), log(x), and log10(x), respectively. Calculate the following quantities:
    1. e3, ln(e3), log10(e3), and log10(105).
    2. Solve 3x = 17 for x and check the result.
  3. Complex numbers.  MATLAB recognizes the letters i and j as the imaginary number -11/2.  A complex number 2+5i may be input as 2+5i or 2+5*i in MATLAB.  The former case is always interpreted as a complex number whereas the latter case is taken as complex only if i has not been assigned any local value.  The same is true for j.  This kind of context dependence, for better or worse, pervades MATLAB.  Compute the following quantities:
    1. e(i*pi/4).  Check Euler's formula eix = cosx + i sinx by computing right and left hand sides of the equation with x=pi/4.
    2. Execute the commands exp(pi/2*i) and exp(pi/2i).  Can you explain the difference between the two results?
  4. Multiply, divide and exponentiate vectors. Create a vector t with 3 elements: 1,2,3.  Now compute the following quantities: 
    1. x=tsin(t).
    2. y=(t-1)/(t+1).
    3. z=sin(t2)/t2.
  5. Matrices, vectors, and plotting. Create a vector and a matrix as follows: v=0:0.2:12; and M=[sin(v); cos(v)].
    1. Find the dimensions of v and M using the size command.
    2. Extract the first 10 elements of each row of the matrix, and plot them as a scatter plot.  Label the x and y axes, and give your plot a title.
    3. Use the command plot3(x,y,z) to plot the circular helix x(t)=sint, y(t)=cost, z(t)=t, 0<=t<=20.  Label axes and give your plot a title.
    4. Plot y=cosx and z=1-x2/2+x4/24 for 0<=x<=pi on the same plot.  (Hint: you can use plot(x,y,'-o',x,z,'--') or you can plot the first curve, use the hold on command, then plot the second curve, and then use hold off.)
  6. Scripting. Write a simple script called circle.m to draw a circle with radius input at a prompt.  Here's an outline of the script in comments:
% circle - a script file to draw a circle of radius input by the user
% after file written by Rudra Pratap (6/28/98);  last modified DD/MM/YY by MNE.
                                      % get radius r from data input
                                      % create vector theta with 100 elements from 0 to 2*pi
                                      % generate x coordinate; x=rcos(theta)
                                      % generate y coordinate: y=rsin(theta)
                                      % plot the circle
                                      % set an equal scale on both x and y axes
title(['radius=', num2str(r)])        % give the graph a title with the value of r
% end of script -----------------------------------------------------------------------------------

Commands you may use in your script are:  input, linspace, cos, sin, plot, axis, title, num2str, help.
  1. Check in.  Send me an email telling me whether this introduction to MATLAB programming was
    1. old hat; not too useful
    2. somewhat unfamiliar territory; somewhat useful
    3. very unfamiliar and new; very useful.
Please add to your email any outstanding questions we didn't answer in class.

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