Introduction to MATLAB

Overview

This session will cover the basics of programming in a high level language such as MATLAB. We do not assume that you have any programming experience. The session includes a brief introduction to the MATLAB environment, and will familiarize the participant with basic commands that are useful for analyzing data and developing simple models. Most of the time you will work at your own pace, with individual help from the faculty as needed.

Units

• MATLAB basics: Read and work through the MATLAB Primer.
  • If you type commands from the Primer into the MATLAB window, you do not need to type the percent sign "%" nor the text to the right of the percent sign on each line. These are comments for the reader, not for MATLAB.
  • You can also copy-and-paste commands from the PDF copy of the Primer into the MATLAB window.
  Work through the parts of the Primer that are new to you, try some of the exercises at the end of the Primer, and please ask questions when you have them! For the last exercise, here is a sample image.
• Advanced (Particle Tracking): Acquiring and analyzing data from digital video. You can download the video here. Start with the brief instructions for importing video, which shows you how to read in and isolate some frames of a video of a double pendulum with some colored stickers attached. Then work on the following tasks.
  • Write MATLAB code that identifies the pixels corresponding to (at least) the red and blue stickers in a given frame.
  • Write a MATLAB function that, given the pixels you have identified, estimates the location of the center of each sticker.
  • Write a MATLAB script that estimates a state vector (angles and velocities) for each of a sequence of frames.
  • Graph the estimated trajectories in various ways; animate and compare with the motion of a model for the double pendulum.
  For the model, read the description of double pendulum model (based on a more detailed model by Carl Akerlof) and use the associated M-files pendrhs.m and pendanim.m.

MATLAB Resources

• Physical Modeling in MATLAB by Allen Downey. This book provides an introduction to programming in the MATLAB environment and is meant for students with little to no programming background.
• Product Documentation from the Mathworks.
• MATLAB Guide by Higham & Higham. Example m-files are freely available.
• Numerical computing with MATLAB, by Cleve Moler.
• A Guide to MATLAB, by B. Hunt, R. Lipsman, J. Rosenberg with K. Coombes, J. Osborn, G. Stuck.

MATLAB computing examples

• Plotting and visualizing data.
  • plotting_1d.m An example of plotting 1d data.
  • plotting_2d.m An example of plotting 2d data.
• Matrix operations, eigenvalues, linear systems of equations
  • linalg.m A variety of linear algebra and matrix/vector manipulations
• Numerical integration
  • integration.m An example of numerical integration by the trapezoidal rule.
• Ordinary differential equations (ODEs)
  • ode_msd.m An exmaple of solving ODEs. This example is the spring equation solved with three different methods including matlabs ode45.
  • Ordinary Differential Equations in MATLAB More extensive notes on using MATLAB to solve ODEs.
• Boundary value problems
  • Notes on PB equations An example of solving the Poisson-Boltzmann equations for the distribution of ions near a wall with an applied voltage. Brief notes to state the equations.
  • pb.m A MATLAB example of solving the Poisson-Boltzmann equations.