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E-raamat: Advanced Problem Solving with Maple: A First Course

(U.S. Naval Post Graduate School),
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Advanced Problem Solving with Maple: A First CourseSuurem pilt
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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 books 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 COMAPs 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.
Preface vii
1 Introduction to Problem Solving and Maple
1(32)
1.1 Problem Solving
1(2)
1.2 Introduction to Maple
3(2)
1.3 The Structure of Maple
5(2)
1.4 General Introduction to Maple
7(23)
1.5 Maple Training
30(1)
1.6 Maple Applications Center
30(3)
2 Introduction, Basic Concepts, and Techniques in Problem Solving with First-Order, Ordinary Differential Equations
33(50)
2.1 Introduction
33(3)
2.2 Applied First-Order Differential Equations and Solution Methods
36(2)
2.3 Slope Fields and Qualitative Assessments
38(6)
2.4 Analytical Solution of First-Order Ordinary Differential Equations
44(10)
2.5 First-Order Ordinary Differential Equations and Maple
54(3)
2.6 Numerical Methods for First-Order Ordinary Differential Equations
57(26)
3 Introduction, Basic Concepts, and Techniques in Problem Solving with Systems of Ordinary Differential Equations
83(56)
3.1 Systems of Differential Equations
83(1)
3.2 Applied Systems of Differential Equations
84(5)
3.3 Phase Portraits and Qualitative Assessment
89(5)
3.4 Solving Homogeneous and Nonhomogeneous Systems of ODEs
94(17)
3.5 Numerical Solutions to Systems of Ordinary Differential Equations
111(28)
4 Problem Solving with Linear, Integer, and Mixed Integer Programming
139(68)
4.1 Formulating Linear Programming Problems
142(9)
4.2 Understanding Two-Variable Linear Programming: A Graphical Simplex
151(12)
4.3 Solving the Linear Program: The Simplex Method and Maple
163(18)
4.4 Linear Programming with Maple's Commands
181(3)
4.5 Sensitivity Analysis with Maple
184(5)
4.6 Integer and Mixed Integer Problems with Maple
189(18)
5 Model Fitting and Linear Regression
207(26)
5.1 Introduction
207(3)
5.2 The Different Curve Fitting Criterion
210(11)
5.3 Plotting the Residuals for a Least-Squares Fit
221(6)
5.4 Case Studies
227(6)
6 Statistical and Probabilistic Problem Solving with Maple
233(64)
6.1 Introduction
233(1)
6.2 Basic Statistics: Univariate Data
234(18)
6.3 Introduction to Classical Probability
252(6)
6.4 Reliability in Engineering and Business
258(10)
6.5 Case Study: Airlines Overbooking Model
268(6)
6.6 Continuous Probability Models
274(9)
6.7 The Normal Distribution
283(4)
6.8 Confidence Intervals and Hypothesis Testing
287(10)
7 Problem Solving with Simulation
297(34)
7.1 Introduction
297(2)
7.2 Monte Carlo Simulation
299(6)
7.3 Probability and Monte Carlo Simulation Using Deterministic Behavior
305(7)
7.4 Probability and Monte Carlo Simulation Using Probabilistic Behavior
312(3)
7.5 Case Studies: Applied Simulation Models
315(16)
Index 331
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 COMAPs Math Contest in Modeling (MCM).
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