Advanced problem solving with Maple : a first course / William P. Fox and William C. Bauldry.

Format:

Book

Author/Creator:

Fox, William P., 1949- author.

Bauldry, William C., author.

Language:

English

Subjects (All):

Maple (Computer file).

Problem solving--Data processing.

Problem solving.

Quantitative research--Data processing.

Quantitative research.

Physical Description:

1 online resource (347 pages)

Edition:

1st ed.

Place of Publication:

Boca Raton : Taylor & Francis, CRC Press, 2020.

Summary:

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).

Contents:

Cover

Half Title

Title Page

Copyright Page

Table of Contents

Preface

1: Introduction to Problem Solving and Maple

1.1 Problem Solving

1.2 Introduction to Maple

1.3 The Structure of Maple

1.4 General Introduction to Maple

1.5 Maple Training

1.6 Maple Applications Center

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

2.1 Introduction

2.2 Applied First-Order Differential Equations and Solution Methods

2.3 Slope Fields and Qualitative Assessments

2.4 Analytical Solution of First-Order Ordinary Differential Equations

2.5 First-Order Ordinary Differential Equations and Maple

2.6 Numerical Methods for First-Order Ordinary Differential Equations

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

3.1 Systems of Differential Equations

3.2 Applied Systems of Differential Equations

3.3 Phase Portraits and Qualitative Assessment

3.4 Solving Homogeneous and Nonhomogeneous Systems of ODEs

3.5 Numerical Solutions to Systems of Ordinary Differential Equations

4: Problem Solving with Linear, Integer, and Mixed Integer Programming

4.1 Formulating Linear Programming Problems

4.2 Understanding Two-Variable Linear Programming: A Graphical Simplex

4.3 Solving the Linear Program: The Simplex Method and Maple

4.4 Linear Programming with Maple's Commands

4.5 Sensitivity Analysis with Maple

4.6 Integer and Mixed Integer Problems with Maple

5: Model Fitting and Linear Regression

5.1 Introduction

5.2 The Different Curve Fitting Criterion

5.3 Plotting the Residuals for a Least-Squares Fit

5.4 Case Studies

6: Statistical and Probabilistic Problem Solving with Maple

6.1 Introduction

6.2 Basic Statistics: Univariate Data.

6.3 Introduction to Classical Probability

6.4 Reliability in Engineering and Business

6.5 Case Study: Airlines Overbooking Model

6.6 Continuous Probability Models

6.7 The Normal Distribution

6.8 Confidence Intervals and Hypothesis Testing

7: Problem Solving with Simulation

7.1 Introduction

7.2 Monte Carlo Simulation

7.3 Probability and Monte Carlo Simulation Using Deterministic Behavior

7.4 Probability and Monte Carlo Simulation Using Probabilistic Behavior

7.5 Case Studies: Applied Simulation Models

Index.

Notes:

Includes index.

Description based on print version record.

ISBN:

0-429-89134-2

0-429-89135-0

0-429-46963-2

9780429469633

OCLC:

1103320709