Eberhart C. Maple Problem Solving Handbook

Department of Mathematics, University of Kentucky, 2009. - 133 p.Raison d’Maple
Four Properties of Maple
The Worksheet: A handy place to solve problems
Get to know the language
Experiment!
A short introduction to the Maple languages
Arithmetic
Expressions, Names, Statements, and Assignments
Functions
Built in Maple functions and Operations with Functions
Using Maple as a fancy graphing calculator
Data types, Expression Sequences, Lists, Sets, Arrays, Tables, Matrices:
Maple control statements
A Brief Vocabulary of Maple Words
Trouble Shooting Notes
Setting Up and Solving Problems
What is a problem?
Setup – Solve – Interpret
A Swimming Pool Problem:
Four methods of solving equationsMore About Plotting
Putting in a parameterDefining your own Maple wordsMore worked Problems
A billiard ball problem
A Variation on the Billiard Ball Problem
Water tank problem
A ladder problem
Another Ladder Problem
Variation on the last ladder problem
Differentiation and its uses
Defining Derivatives
The student packageNewton’s Method
Use of the derivatives in plotting
Implicit Differentiation
Max-min Problems
A Paper folding problem:
More Max-min Problems
Stumbling onto max-min ProblemsSolutions
Early Integration.
Learning to use the Maple words Sum and sum
Riemann Sums with the student package
Learning to use Int and int
Average value
Modeling the flow of air in lungs:
Two Area problems
Moments and Center of Mass
Center of mass of a Wire
Center of mass of a solid of revolution
Definitions and Theorems of Calculus I
Inverse Functions
A Useful Function – The natural logarithm
The inverse of the natural log
Inverse Functions: The inverse trig functions
Integration Techniques and Applications
Symbolic Integration Problems
Numerical Integration Problems
Taylor’s Theorem
Taylor polynomials
Taylor remainder theoremSequences and Series
Sequences
Series
Two interesting curves
Differential equations
Terminology
Problems leading to first order equations
Logistic Growth