# Math 473 Intermediate Differential Equations

### Course Info

Almost everything is on the course canvas page.

### MATLAB Info

I put a little bit of MATLAB stuff here, but it is also mainly on Canvas.

#### MATLAB startup file

I use a file startup.m to replace the default MATLAB graphing settings with something a little bit nicer. In particular, I include $\LaTeX$ formatting in my axis labels. $\LaTeX$ is a markup language that mathematicians use to typeset math. If any of my MATLAB programs give you errors, run these lines first:

set(groot,'DefaultAxesFontSize',14)
set(groot,'DefaultLineLineWidth',2)
set(groot,'DefaultFunctionLineLineWidth',2)
set(groot,'DefaultTextInterpreter','latex')
set(groot,'DefaultAxesTickLabelInterpreter','latex')
set(groot,'DefaultLegendInterpreter','latex');


In Part 1 of Strogatz it will be helpful to use software to draw direction fields. In Part 2, it will be useful to use software to draw phase planes. This is not built into MATLAB in a simple way, so you’ll have to install some additional software. The site provides complete documentation and how-to videos.

### Here are some HTML files exported from MATLAB

I have created a few tutorials that we will be using over the course of the semester. They will be linked from Canvas, but I am collecting them here for reference:

#### Basic MATLAB Usage

• First MATLAB assignment: Quantitative Comparison of Euler, Improved Euler, & Runge-Kutta Methods $\bullet$

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  * Solution: $\circ$


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• MATLAB Basics: Function Handles and Anonymous Functions $\bullet$

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  * Solution: $\circ$


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• MATLAB Basics: Using ode45 $\bullet$

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  * Problem 1 solution: $\circ$


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  * Problem 2 solution: $\circ$


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### Companion to the textbook

• A Simple Bifurcation Diagram: A MATLAB based solution to Strogatz problem 4.3.3. $\bullet$

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• The Lorenz system: Companion to Chapter 9 $\bullet$

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• Iterated Map Demonstration: Companion to Strogatz 10.1–10.4

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• The Rössler system: Companion to Strogatz 10.6 $\bullet$

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• Box-counting dimension for the Hénon attractor: Companion to Strogatz 11.4 $\bullet$

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• Attractor reconstruction for the Lorenz System (similar to Strogatz 12.4) $\bullet$

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• Attractor reconstruction for a chemistry experiment: Companion to Strogatz 12.4 $\bullet$

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📄 Data File

• Strange attractor for the chaotic forced-damped double well oscillator: Companion to Strogatz 12.5, following Moon & Holmes 1979 $\bullet$

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• Forced-damped pendulum example: Shows period-doubling in a Poincaré map of the forced damped pendulum $\bullet$

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