# 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