Fundamentals of Differential Equations and Boundary Value Problems

Description

For one-semester sophomore- or junior-level courses in Differential Equations.

 

                                                      

Fundamentals of Differential Equations and Boundary Value Problems presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software. 

New within the Book

• Several pedagogical changes were made including amplification of the distinction between phase plane solutions and actual trajectories in Chapter 5, incorporation of matrix and Jacobian formulations for autonomous systems, and revised discussion of limit cycles in Chapter 12.
• New problems added to exercise sets deal with such topics as axon gating variables and oscillations of a helium-filled balloon on a cord. Additionally, novel problems accompany the new projects, focusing on economic models, disease control, synchronization, signal propagation, and phase plane analyses of neural responses.
• New examples have been added dealing with variation of parameters, Laplace transforms, the Gamma function, and eigenvectors (among others). 

Content Updates

• Chapter 1 has a new project called “Applications to Economics” deals with models for an agrarian economy as well as the growth of capital.
• Chapter 4 contains a new project called “Gravity Train” which invites to reader to utilize differential equations in the design of an underground tunnel from Moscow to St. Petersburg, Russia, using gravity for propulsion.
• Chapter 5 has two new projects.
• “The 2014-2015 Ebola Epidemic” describes a system of differential equations for modelling for the spread of the disease in West Africa. The model incorporates such features as contact tracing, number of contacts, likelihood of infection, and efficacy of isolation.
• Phase-locked loops constitute the theme of a new project that utilizes differential equations to analyze a technique for measuring or matching high frequency radio oscillations.
• Chapter 7, the Laplace Transforms chapter, has been updated so that the treatments of discontinuous and periodic functions are now divided into two sections that are more appropriate for 50 minute lectures: Section 7.6 “Transforms of Discontinuous Functions” and Section 7.7 “Transforms of Periodic and Power Functions.”
• Chapter 10 has a new project that broadens the analysis of the wave and heat equations to explore the telegrapher’s and cable equations.
• Chapter 12 contains a new section “Neurons and the FitzHugh-Nagumo Equations.” It outlines the (Nobel prize-winning) work of Hodgkin and Huxley in modeling the electrochemical generation of action potentials inside axons and guides the reader through computer phase plane simulations of the remarkable responses produced by various stimula.
• Appendix G is a new appendix which lists commercial software and freeware for direction fields, phase portraits, and numerical methods for solving differential equations.

Also available with MyLab Math                                             

For the first time with this edition, MyLab ^™  Math is available for differential equations. MyLab Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

• Exercises with immediate feedback–Nearly 850 assignable exercises are based on the textbook exercises, and regenerate algorithmically to give students unlimited opportunity for practice and mastery. MyLab Math provides helpful feedback when students enter incorrect answers and includes optional learning aids including Help Me Solve This, View an Example, videos, and an eText. The instructor can decide if and when to allow students access to the learning aids–by assignment, or at the exercise level–so students get the right level of support while also preparing them to work independently. 
• A new suite of instructional videos provide meaningful support to students and flexibility for instructors in how they are used. Instructors can assign questions that relate to the videos in order to gauge student comprehension of concepts, by selecting exercises via the Guide to Video-Based Assignments. Or, instructors can use the videos in class or as a supplementary resource on specific topics.
• The complete interactive eText is available to students through their MyLab Math courses for the lifetime of the edition, giving students unlimited access to the eText within any course using that edition of the textbook.  The Pearson eText offers interactive links throughout, so students can watch videos on key examples as they read.
• Learning Catalytics^™ helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking.
• Help students develop critical thinking skills.
• Monitor responses to find out where students are struggling.
• Rely on real-time data to adjust teaching strategy.
• Automatically group students for discussion, teamwork, and peer-to-peer learning.
• Accessibility and achievement go hand in hand. MyLab Math is compatible with the JAWS screen reader, and enables multiple-choice and free-response problem types to be read and interacted with via keyboard controls and math notation input. MyMathLab also works with screen enlargers, including ZoomText, MAGic, and SuperNova. And, all MyMathLab videos have closed-captioning. More information is available at http://mymathlab.com/accessibility.
• A  comprehensive gradebook with enhanced reporting functionality allows for efficient course management.
• The Reporting Dashboard provides insight to view, analyze, and report learning outcomes. Student performance data is presented at the class, section, and program levels in an accessible, visual manner to make accessible all information required to keep students on track.
• Item Analysis tracks class-wide understanding of particular exercises to refine class lectures or adjust the course/department syllabus. Just-in-time teaching has never been easier!

R. Kent Nagle (deceased) taught at the University of South Florida. He was a research mathematician and an accomplished author. His legacy is honored in part by the Nagle Lecture Series which promotes mathematics education and the impact of mathematics on society. He was a member of the American Mathematical Society for 21 years. Throughout his life, he imparted his love for mathematics to everyone, from students to colleagues.

 

Edward B. Saff received his B.S. in applied mathematics from Georgia Institute of Technology and his Ph.D. in Mathematics from the University of Maryland. After his tenure as Distinguished Research Professor at the University of South Florida, he joined the Vanderbilt University Mathematics Department faculty in 2001 as Professor and Director of the Center for Constructive Approximation. His research areas include approximation theory, numerical analysis, and potential theory. He has published more than 240 mathematical research articles, co-authored 9 books, and co-edited 11 volumes. Other recognitions of his research include his election as a Foreign Member of the Bulgarian Academy of Sciences (2013); and as a Fellow of the American Mathematical Society (2013). He is particularly active on the international scene, serving as an advisor and NATO collaborator to a French research team at INRIA Sophia-Antipolis; a co-director of an Australian Research Council Discovery Award; an annual visiting research collaborator at the University of Cyprus in Nicosia; and as an organizer of a sequence of international research conferences that helps foster the careers of mathematicians from developing countries.

 

Arthur David Snider has 50+ years of experience in modeling physical systems in the areas of heat transfer, electromagnetics, microwave circuits, and orbital mechanics, as well as the mathematical areas of numerical analysis, signal processing, differential equations, and optimization. He holds degrees in mathematics (BS, MIT; PhD, NYU) and physics (MA, Boston U), and is a registered professional engineer. He served 45 years on the faculties of mathematics, physics, and electrical engineering at the University of South Florida. He worked 5 years as a systems analyst at MIT’s Draper Instrumentation Lab, and has consulted for General Electric, Honeywell, Raytheon, Texas, Instruments, Kollsman, E-Systems, Harris, and Intersil. He has authored nine textbooks and roughly 100 journal articles. Hobbies include bluegrass fiddle, acting, and handball.

About the Book                                                                                   

• Students learn the basic theory of differential equations while exploring a variety of modern applications in science and engineering.
• Modernized treatment of the introduction to systems chapter and phase plane analysis increases student comprehension of the material.
• Flexible organization allows for various course configurations and emphasis (theory, applications and techniques, and concepts).
• Motivating Problems begin most chapters with a discussion of a physics or engineering problem
• Applications-driven sections are included in the chapter on linear second-order equations.
• Review of Linear Algebraic Equations and Matrices — The chapter on matrix methods for linear systems (Chapter 9) begins with two introductory sections on the theory of linear algebraic systems and matrix algebra.
• Review of Integration Techniques appendix provides a review of the methods for integrating functions analytically. This offers students a useful refresh prior to beginning the differential equations course.          
• NEW! Examples have been added dealing with variation of parameters, Laplace transforms, the Gamma function, and eigenvectors (among others).

• Robust opportunities for exercises and assignments give instructors flexibility and students a wide range of practice.
• Projects relating to the material covered appear at the end of each chapter. They may involve more challenging applications, delve deeper into theory, or introduce more advanced topics.
• Exercises, which are graduated in difficulty and varied by type, include a wide variety of applications such as barometric pressure, compound interest, the mathematical equivalence of an impulse force and a velocity boost.
• Chapter Summaries and Review Problems at the end of each chapter help students comprehend fully the learning and promote knowledge retention.
• Technical Writing Exercises help students develop their communication skills, an essential aspect of professional activity.
• Optional use of Mathematica^®, MATLAB^®, and Maple^™ computer software gives students opportunity to conduct numerical experiments and tackle realistic applications that give additional insights into the subject. Online Manuals for Maple, MATLAB, and Mathematica offer sample worksheets and suggestions on incorporating these technologies into the courses.

Also available with MyLab Math                                                           

NEW! For the first time, MyLab ^™ Math  is available for this text. MyLab Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

• Exercises with immediate feedback—Nearly 850 assignable exercises are based on the textbook exercises, and regenerate algorithmically to give students unlimited opportunity for practice and mastery. MyLab Math provides helpful feedback when students enter incorrect answers and includes optional learning aids including Help Me Solve This, View an Example, videos, and an eText. The instructor can decide if and when to allow students access to the learning aids—by assignment, or at the exercise level—so students get the right level of support while also preparing them to work independently. 
• A suite of instructional videos, featuring the authors, provide meaningful support to students and flexibility for instructors in how they are used. Instructors can assign questions that relate to the videos in order to gauge student comprehension of concepts, by selecting exercises via the Guide to Video-Based Assignments. Or, instructors can use the videos in class or as a supplementary resource on specific topics.
• The complete interactive eText is available to students through their MyLab Math courses for the lifetime of the edition, giving students unlimited access to the eText within any course using that edition of the textbook.  The Pearson eText offers interactive links throughout, so students can watch videos on key examples as they read.
• Learning Catalytics^™ helps instructors generate class discussion, customize lectures, and promote peer-to-peer learning with real-time analytics. As a student response tool, Learning Catalytics uses students’ smartphones, tablets, or laptops to engage them in more interactive tasks and thinking.
• Help students develop critical thinking skills.
• Monitor responses to find out where students are struggling.
• Rely on real-time data to adjust teaching strategy.
• Automatically group students for discussion, teamwork, and peer-to-peer learning.
• Accessibility and achievement go hand in hand. MyLab Math is compatible with the JAWS screen reader, and enables multiple-choice and free-response problem types to be read and interacted with via keyboard controls and math notation input. MyMathLab also works with screen enlargers, including ZoomText, MAGic, and SuperNova. And, all MyMathLab videos have closed-captioning. More information is available at http://mymathlab.com/accessibility.
• A comprehensive gradebook with enhanced reporting functionality allows for efficient course management.
• The Reporting Dashboard provides insight to view, analyze, and report learning outcomes. Student performance data is presented at the class, section, and program levels in an accessible, visual manner to make accessible all required information to keep students on track.
• Item Analysis tracks class-wide understanding of particular exercises to so refine class lectures or adjust the course/department syllabus. Just-in-time teaching has never been easier!

For one-semester sophomore- or junior-level courses in Differential Equations.

 

An introduction to the basic theory and applications of differential equations                                                                 

Fundamentals of Differential Equations and Boundary Value Problems presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software. For the first time, MyLab™ Math is available for this text, providing online homework with immediate feedback, the complete eText, and more. 

 

Note that a shorter version of this text, entitled Fundamentals of Differential Equations, 9th Edition, contains enough material for a one-semester course. This shorter text consists of chapters 1-10 of the main text.

Also available with MyLab Math

MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts.

Note: You are purchasing a standalone product; MyLab does not come packaged with this content. Students, if interested in purchasing this title with MyLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.

 

If you would like to purchase both the physical text and MyLab, search for:

0134665694 / 9780134665696 Fundamentals of Differential Equations and Boundary Value Problems Plus MyLab Math with Pearson eText — Access Card

Package consists of:

• 0321431308 / 9780321431301 MyLab Math — Glue-in Access Card
• 0321654064 / 9780321654069 MyLab Math Inside Star Sticker
• 0321977106 / 9780321977106 Fundamentals of Differential Equations and Boundary Value Problems