MACM 204: Computing with Calculus

Fall 2017

Lecture: Tuesdays 4:30pm in BLU 10921
Lab D101: Wednesdays 2:30pm AQ 3148.1
Lab D102: Wednesdays 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 a lot of simple programs involving loops, functions, arrays, lists and sets.

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 may purchase Maple 2017 for Students for $75 + taxes from Maplesoft using the course promotion code.

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

Maple Worksheets and Class Notes

I will put various Maple worksheets here as we go through the course. Some will be from the lectures, some from the labs, and some with additional examples for help with assignments.

Course Outline

Maple and single variable calculus (2 weeks)

Using Maple as a scientific calculator

Maple's worksheet user interface

graphing functions and curves in the plane

solving equations exactly and numerically

factoring polynomials

calculating integrals exactly and numerically

application to measuring river flow

Programming in Maple and Maple library packages (4 weeks)

loops and procedures

lists, sets and arrays

efficiency: quadratic verses linear algorithms

graphics programming tools

the LinearAlgebra package

simulating a web surfer

simulating mortgage payments

Multivariate calculus (3 weeks)

graphing curves and surfaces in 3D

partial derivatives

Taylor series and tangent planes

finding, classifying and visualizing critical points

solving systems of equations

Least squares approximation and visualization

Differential equations and modelling (4 weeks)

initial value problems

algebraic and numerical methods

Newton's law of cooling

modeling a mortgage

compartment models

visualizing vector fields and solutions of differential equations

numerical tools for solving non-linear systems