1st Edition

Advanced Problem Solving with Maple A First Course

By William P. Fox, William C. Bauldry Copyright 2020
    346 Pages 107 B/W Illustrations
    by CRC Press

    358 Pages 107 B/W Illustrations
    by Chapman & Hall

    358 Pages 107 B/W Illustrations
    by Chapman & Hall

    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

    Biography

    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).