Fundamentals of Differential Equations, 9th edition

For 1-semester courses in Differential Equations.

Introduces basic theory and applications

Fundamentals of Differential Equations, 9th Edition explores modern applications of differential equations in science and engineering. It adapts to various course emphases (theory, methodology, applications and numerical methods) and commercially available computer software. A longer version, Fundamentals of Differential Equations and Boundary Value Problems, 7th Edition, contains enough material for a 2-semester course.

• 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 MyLabMath                                                          

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 750 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!

• Several pedagogical changes were made including amplification of the distinction between phase plane solutions and actual trajectories in Chapter 5, and incorporation of matrix and Jacobian formulations for autonomous systems.
• 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.
• 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, MyLab™ Math is available with this edition 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 750 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. MyLab Math also works with screen enlargers, including ZoomText, MAGic, and SuperNova. And, all MyLab Math 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!