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MACM 204: Computing with Calculus

Fall 2014

Lecture: Tuesdays 4:30pm in AQ 5016
Lab D101: Thursdays 2:30pm AQ 3148.1
Lab D103: 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 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 18 for Students 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

I will put here various Maple worksheets 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 info sheet (.txt)

Linear Algebra and Graph examples from Tuesday October 14th: Worksheet (.mw) and Adobe (.pdf) .

Course Outline

Maple and single variable calculus (2 weeks)

  • using Maple as a scientific calculator
  • Maple's worksheet user interface
  • graphing functions and derivatives
  • graphing 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
  • graphics programming tools
  • the LinearAlgebra package
  • the GraphTheory package
  • simulating a web surfer
  • simulating mortgage payments
  • Multivariate calculus (2 weeks)

  • graphing curves and surfaces in 3D
  • partial derivatives and critical points
  • solving systems of equations
  • Taylor series, tangent planes
  • Differential equations and modelling (4 weeks)

  • initial value problems
  • algebraic and numerical methods
  • Newton's law of cooling
  • modeling a mortgage
  • compartment models
  • visualization tools
  • visualizing vector fields and solutions of differential equations
  • p. (778) 782-4279 · f. (778) 782-4947 · Shrum Science K 10501 · Department of Mathematics · 8888 University Drive · Burnaby · BC · V5A 1S6 · Canada