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

Autor William P. Fox, William C. Bauldry
en Limba Engleză Paperback – 21 ian 2023
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.


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Specificații

ISBN-13: 9781032475547
ISBN-10: 1032475544
Pagini: 346
Ilustrații: 107
Dimensiuni: 156 x 234 x 21 mm
Greutate: 0.5 kg
Ediția:1
Editura: CRC Press
Colecția CRC Press
Seria Textbooks in Mathematics


Cuprins



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

Notă biografică

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).

Descriere

The text presents modeling topics using Maple as the computer algebra system for solving mathematical equations as well as obtaining plots that help us perform our analyses. It presents cogent applications of applied mathematics, provides discussions of the results obtained, and stimulate thought and analysis of additional applications.