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MACM 204: Computing with Calculus

Fall 2022

Lecture: Tuesdays 2:30pm in AQ 3005
Lab D101: Wednesdays 2:30pm in AQ 3148.1
Lab D102: Wednesdays 3:30pm in AQ 3148.2

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.

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. First save it on your desktop then open from inside 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 MapleNotes (.pdf) file so you can look at it from your browser.

This file will help you learn to 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 Maple Programming (.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
  • Taylor polynomials
  • Application: measuring river flow (discharge)
  • 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 polynomials 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
  • The SIR virus model
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