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MACM 204: Computing with Calculus

Fall 2016

Lecture: Tuesdays 3:30pm in AQ 5018
Lab D101: Wednesdays 2:30pm AQ 3148.1
Lab D103: 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 2016 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 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.

Least Squares class notes from Tuesday October 18th: Lecture notes (.pdf)

Linear Algebra examples from Tuesday October 18th: Worksheet (.pdf)

Least squares approximation from Tuesday October 18th: Worksheet (.pdf)

Lead accumulation in the bones model from Wednesday November 9th: Lead.pdf Lead.mw

House heating model from Wednesday November 9th: House.pdf House.mw

Lotka Votera model from Wednesday November 16th: Lotka.pdf Lotka.mw

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
  • p. (778) 782-4279 · f. (778) 782-4947 · Shrum Science K 10501 · Department of Mathematics · 8888 University Drive · Burnaby · BC · V5A 1S6 · Canada