This tutorial deals with variable I/O, matrix manipulation and plotting. The following files should be downloaded to your directory and the tutorial1.m file should be run.
This tutorial illustrates why using the matrix inverse is both inefficient and error prone in solving very large systems of equations. For such problems it is much faster to use the \ operator. The tutorial is given here. Run the tutorial using the "publish" command to get it to display properly - and to show you how to publish your assignments!
This tutorial looks at how you can use SVD to do facial recognition. It takes the face pictures of all the CBE graduate students off the department web page from a couple of years ago, calculates an "average" face, and then determines how each individual face compares to the principal components of the average. Thus, an individual face is described by a unique (and very small!) vector of singular values. Download the zip file below containing the analysis program and the pictures.
This week's tutorial is last year's project 2: the use of auto and cross-correlations to determine time constants and front velocities for weather patterns. The project and its solution are given in the zip file:
This tutorial looks at the error propagation formula, and applies it to the calculation of an equilibrium constant. The error is pretty large, so we also look at whether the formula yields the correct values (e.g., whether the equilibrium constant follows the normal distribution). Download and run the following script and function, and run through it before tutorial.
This tutorial looks at the model linearization and error propagation in the study of Michaelis-Menten Kinetics. Download and run the following script and run through it before tutorial. This is a useful review of the things we have been talking about in class the past week, and it is material that will be covered on the mid-term.
This tutorial uses the Margules model to examine activity coefficient data and plot up confidence intervals for the fitted parameters. It also shows the danger of not plotting up your residuals... Download and run the following script and run through it before tutorial.
This tutorial deals with non-linear regression and analyzes the senior lab methane oxidation experiment. The lecture notes are given here and the links to the example codes are below. Please read through the lecture notes and run the example before tutorial. This is something that you are going to want to keep track of in a year and a half...
This tutorial demonstrates how Newton's method behaves for functions which have repeated roots (e.g., linear rate of convergence rather than quadratic) and shows how a modified version of the method can regain the quadratic convergence. Note that it only works if you -know- a priori the multiplicity of the root, though! Download and run the following script and run through it before tutorial.
This tutorial shows how you can use Lagrange multipliers to look for critical points (maxima or minima - it doesn't care!) for a constrained optimization problem. Download and run the following script and function and run through it before tutorial.
This tutorial shows you how you can use Brownian Dynamics to solve a time-dependent PDE in a complicated geometry. Here we look at the average temperature of a triangular rod being quenched (e.g., where we suddenly drop the surface temperature to some lower constant value). Download and read (and run) the following file.
This tutorial shows how you can use the shooting method to solve a high order ODE with an unknown initial condition. The example we use is the classic third order non-linear ODE, the Blasius Equation for flow past a flat plate. Download and run the following files