Advanced Problem Solving with Maple
A First Course
Textbooks in Mathematics Series

Problem Solving is essential to solve real-world problems. Advanced Problem Solving with Maple: A First Course applies the mathematical modeling process by formulating, building, solving, analyzing, and criticizing mathematical models. It is intended for a course introducing students to mathematical topics they will revisit within their further studies.

The authors present mathematical modeling and problem-solving topics using Maple as the computer algebra system for mathematical explorations, as well as obtaining plots that help readers perform analyses. The book presents cogent applications that demonstrate an effective use of Maple, provide discussions of the results obtained using Maple, and stimulate thought and analysis of additional applications.

Highlights:

• The book?s real-world case studies prepare the student for modeling applications





• Bridges the study of topics and applications to various fields of mathematics, science, and engineering





• Features a flexible format and tiered approach offers courses for students at various levels





• The book can be used for students with only algebra or calculus behind them

About the authors:

Dr. William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his Ph.D. at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles.

William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. of Mathematics at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP?s Math Contest in Modeling (MCM).

*Please note that the Maple package, "PSM", is now on the public area of the Maple Cloud. To access it:

? From the web:

1. Go to the website https://maple.cloud

2. Click on "packages" in the left navigation pane

3. Click on "PSM" in the list of packages.

4. Click the "Download" button to capture the package.

? From Maple:

1. Click on the Maple Cloud icon (far right in the Maple window toolbar).

Or click on the Maple Cloud button on Maple's Start page to go to the website.

2. Click on the "packages" in the navigation pane

3. Click on "PSM" in the list of packages.

The package then downloads into Maple directly.

Introduction to Problem Solving and Maple

Problem Solving

Introduction to Maple

The Structure of Maple

General Introduction to Maple

Maple Training

Maple Applications Center

Introduction, Basic Concepts, and Techniques in Problem Solving with First Order, Ordinary Differential Equations

Introduction

Applied First Order Differential Equations and Solution Methods

Slope Fields and Qualitative Assessments

Analytical Solution of 1st Order ODEs

First Order ODEs and Maple

Numerical Methods for 1st Order ODEs

Introduction, Basic Concepts, and Techniques in Problem Solving with Systems of Ordinary Differential Equations

Systems of Differential Equations

Applied Systems of Differential Equations

Phase Portraits and Qualitative Assessment

Solving Homogeneous and Non-Homogeneous Systems of ODEs

Numerical Solutions to Systems of Ordinary Differential Equations

Problem Solving with Linear, Integer, and Mixed Integer Programming

Formulating Linear Programming Problems

Understanding Two-Variable Linear Programming: A Graphical Simplex

Solving the Linear Program: The Simplex Method and Maple

Linear Programming with Internal Maple Commands

Sensitivity Analysis with Maple

Integer and Mixed Integer Problems with Maple

Model Fitting and Linear Regression

Introduction
The Different Curve Fitting Criterion
Plotting the Residuals for a Least-Squares Fit
Case Studies

Statistical and Probabilistic Problem Solving with Maple
Introduction
Basic Statistics: Univariate Data
Introduction to Classical Probability
Reliability in Engineering and Business
Case Study: Airlines Overbooking Model
The Normal Distribution
Confidence Intervals and Hypothesis Testing

Problem Solving with Simulation

Introduction

Monte Carlo Simulation

Probability and Monte Carlo Simulation Using Deterministic Behavior

Probability and Monte Carlo Simulation: Using Probabilistic Behavior

Case Studies: Applied Simulation Models

Index

Dr. William P. Fox is an emeritus professor in the Department of Defense Analysis at the Naval Postgraduate School. Currently, he is an adjunct professor, Department of Mathematics, the College of William and Mary. He received his Ph.D. at Clemson University and has many publications and scholarly activities including twenty books and over one hundred and fifty journal articles.

William C. Bauldry, Prof. Emeritus and Adjunct Research Prof. at Appalachian State University, received his PhD in Approximation Theory from Ohio State. He has published many papers on pedagogy and technology, often using Maple, and has been the PI of several NSF-funded projects incorporating technology and modeling into math courses. He currently serves as Associate Director of COMAP’s Math Contest in Modeling (MCM).