Course Code:            MATH 1193

Course Title:              Introduction to Mathematical Software II - A Primer on Maple

Level:                         1

Semester:                   1, 2      

No. of Credits:             1

Pre-requisite(s):           Units 1 and 2 of CAPE Pure Mathematics or equivalent or

                                    Math 1125 or equivalent.

 

 

Course Rationale

Mathematics is a powerful tool used for solving practical problems and is a highly creative field of study, combining logic and precision with intuition and imagination.  The ability to employ mathematical reasoning is a fundamental skill for any well-educated individual in the pure and applied sciences. 

Recent improvements in computing technology and mathematical software have inevitably led to a marriage of mathematics and computers.  Specialized software can be used to solve problems in differential equations, numerical analysis, calculus, mathematical modelling, and so forth.  As such, knowledge of mathematical software is not only an asset but a necessity for contemporary mathematicians. 

This introductory level course is designed to introduce Maple software, which is a symbolic mathematical package that may be used in a wide range of mathematical applications.

 

Course Description

 

This course covers Maple software, which can be used to solve frequently encountered mathematics problems.  Maple is a symbolic mathematical package with a wide range of applications.  In this course, problem solving in algebra, calculus and differential equations will be covered.  Maple’s word processing features will be shown to students, who will be expected to produce scientific documents using the Maple word processor.  An introduction to the Maple programming language is also included in this module.

Teaching will take place entirely in weekly interactive lab sessions where the emphasis will be on active learning. Assessment will be based on coursework examinations and several lab assignments

 

Learning Outcomes

 

Upon successful completion of this module, students will be able to:

  • Create a professional looking scientific document using Maple.
  • Use built-in commands in Maple software to solve several types of mathematical problems.
  • Load and utilize packages embedded in Maple.
  • Utilize graphing tools in Maple, and export plots into various image formats. 
  • Write computer programs in Maple software to solve mathematical problems.

 

 

Course Content

  • The Maple environment.
  • Starting a Maple session in either Document or Worksheet mode.  Navigating through Maple.  Use Help files and symbol palettes.
  • Basic Maple syntax.  Troubleshooting syntax errors.
  • Simple mathematical computations.
  • Math versus Text mode. 
  • Algebra
  • Factoring a polynomial, expansion, simplification of expressions, radicals and rational functions.
  • Substitution.  Restoration of variable status.  Solutions of polynomial equations in one variable.  Exact solutions and approximate solutions.
  • Packages in Maple such as ‘numtheory’, ‘student’ and ‘plots’.  Initiating a package.
  • Calculus:
  • Define functions, perform composition of functions, derive limits.
  • Differentiate functions of one variable and perform partial differentiation of functions of several variables.
  • Integrate by substitution, by parts and using partial fractions.
  • Compute Taylor expansions.
  • Solution of trigonometric equations.
  • Conversion from degrees to radians and vice-versa.
  • Plotting in Maple:
  • Two-dimensional plotting
  • Restriction of domain and range in a plot.
  • Plots of Parametric and implicit functions.
  • Plotting of points and multiple plots.
  • Insertion of titles and text in a plot.
  • Use of Plotting options.
  • Saving and printing a plot.
  • Additional plot functions.
  • Three-dimensional plotting
  • Parametric and multiple plots.
  • Three-dimensional plotting options.
  • Additional three-dimensional plot functions.
  • Animation
  • Maple as a word processor:
  • Construction of professionally typeset scientific documents. 
  • Exporting to other file types such as .rtf and .pdf.
  • Differential Equations:
  • General solutions of Ordinary Differential Equations
  • Substitution of initial conditions.
  • Plots of solutions.
  • Programming in Maple:
  • Definition of a Maple procedure.
  • Construct simple procedures in Maple for computational purposes.

Teaching Methodology

Labs: One (1) computer lab session each week (2 hours).  These sessions will serve as an avenue for introducing various pieces of Mathematical software.

 

 

Assessment

 

Coursework – 100%

  • Two equally weighted 2-hour coursework examinations  –  60%

 

  • Six equally weighted  lab assignments – 40%

Students will be tested on principles learnt each week as delineated in the course calendar. 

 

 

Course Calendar

 

Week

Lecture subjects

Assignments/Exams

 

1

Course Overview/Introduction

Introduction to the Maple Interface: The Maple environment: Starting a Maple session in either Document or Worksheet mode.  Navigating through Maple.  Using Help files and symbol palettes.

None

2

Maple – Algebra:  Basic Maple syntax.  Troubleshooting syntax errors.  Simple mathematical computations.  Factoring a polynomial, expansion, simplification of expressions, radicals and rational functions.  Substitution.

Assignment 1 given

3

Maple – Algebra:  Restoration of variable status.  Solutions of polynomial equations in one variable.  Exact solutions and approximate solutions.

Assignment 1 due.

Assignment 2 given.

 

4

Maple – Calculus: Define functions, perform composition of functions.  Derive limits and one-sided limits.  Differentiate functions of one variable and perform partial differentiation of functions of several variables.  Integrate by substitution, by parts and using partial fractions. 

Assignment 2 due.

Assignment 3 given.

5

Maple – Calculus: Compute Taylor expansions.   Solution of trigonometric equations.  Conversion from degrees to radians and vice-versa. 

Assignment 3 due.

6

Maple – Word processing features:  Math versus Text mode.    Construction of professionally typeset scientific documents.  Exporting to other file types such as .rtf and .pdf.

 

7

First Coursework Examination.   

Assignment 4 given.

8

Maple – Use of Maple spreadsheets.

Assignment 4 due.

9

Maple – Two and three dimensional plotting: Restriction of domain and range in a plot.  Plots of Parametric and implicit functions.  Plotting of points and multiple plots.  Insertion of titles and text in a plot.  Use of Plotting options.  Saving and printing a plot.  Additional plot functions.  Animation.

Assignment 5 given.

10

Maple - Differential Equations:  General solutions of Ordinary Differential Equations.  Substitution of initial conditions.  Solution plots of Ordinary Differential Equations. 

Assignment 5 due.

 

11

Maple - Programming in Maple:  Construction of Maple procedures that produce single outputs. 

Assignment 6 given.

12

Maple - Programming in Maple:  Constructing procedures to perform complex mathematical computations.  Local and global variables.

Assignment 6 due.

13

Second Coursework Examination.   

 

 

 

Required Reading

Essential Text

  • D. Meade et al., Getting started with Maple, Wiley; 3rd edition