"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).
