# MACM 204: Computing with Calculus

### Fall 2013

Lecture: Tuesdays 4:30pm in AQ 5016
Lab: Thursdays 3:30pm AQ 3148.1

## Content

The course teaches you how to use mathematical software (we will use Maple) to explore calculus and study mathematical models. We will use Maple for calculus in one variable and two variables, and for graphing functions, curves and surfaces. We will learn how to model physical systems with differential equations and use Maple to solve them and visualize their solutions. The course will also strengthen your programming skills. We will write some simple programs, simple recursive programs and also write not so simple recursive programs for drawing fractals.

## Software

We will use Maple extensively for calculations and programming in this course. The university has a site license. Maple is installed on the PCs and MACs in the assignment lab, university open labs and the library. You can purchase your own copy of Maple for \$99 from Maplesoft.

The following file will below help you get started. It shows you how to use Maple to do calculus. It is a Maple worksheet (.mws file) which you can open in Maple: Getting Started with Maple. After you've opened it you need to execute the commands by pressing the enter key. The worksheet is also available as an Adobe Acrobat (.pdf) file so you can look at it from your browser.

This file help you program in Maple: Maple Programming (.mws). It shows you how to write loops and write Maple procedures. It also shows you how to use Maple lists and sets. The worksheet is also available as an Adobe Acrobat (.pdf) file.

## Maple Worksheets

Examples of 3d plots, partial derivatives and Taylor series for f(x,y) from September 24 and 26 Worksheet (.mw) and (.pdf)

Broccoli fractal worksheet (.mw) and (.pdf) from Tuesday October 8.

Serpinski's gasket fractal worksheet (.mw) and (.pdf) from Thursday October 10.

Vectors, Matrices and Linear Algebra commands Worksheet (.mw) and (.pdf) from Thursday October 17.

Examples for using dsolve and DEplot worksheet (.mw) and (.pdf) from Thursday October 24 and 31.

Mortgage simulation worksheet (.mw) and (.pdf) from Thursday November 7.

Random walk simulation worksheet (.mw) and (.pdf) from Thursday November 7.

Lead model and House warming model worksheet (.mw) and (.pdf) from November 14.

Lokta-Voltera model and SIR virus model worksheet (.mw) and (.pdf) from November 21.

## Course Outline

Maple basics (2 weeks)

• Using Maple as a scientific calculator
• Graphing functions and curves in the plane
• Solving equations in one variable
• Maple's worksheet user interface
• Simple programming in Maple
• Caculus (3 weeks)

• Calculus in one variable
• Calculus in two variables
• Graphing curves and surfaces in 3D
• Visualizing partial derivatives and tangent planes
• Solving systems of linear and non-linear equations
• Fractals and recursion (2 weeks)

• Recursive programs
• Constructing fractals
• Differential equations (4 weeks)

• Modeling with differential equations
• Newton's law of cooling, growth models, disease spread models
• Solving (systems of) differential equations
• Visualizing vector fields and solutions of differential equations