Differential Equations and Boundary Value Problems: Computing and Modeling balances concepts, visualization, applications and skills, helping you develop the conceptual understanding and geometric visualization that are essential for science and engineering students. It utilizes computer algebra systems such as Mathematica, Maple, and MATLAB plus online platforms like Wolfram|Alpha and GeoGebra, along with traditional manual methods. The text begins and ends with discussion of mathematical modeling of real-world phenomena, evident in its figures, examples, problems and applications. The 6th Edition adds and updates content throughout, including an expanded Application Module for Section 6.4 that discusses COVID-19. Personalize learning with MyLab Math with Pearson eText This flexible digital platform combines unrivaled content, online assessments, and customizable features to personalize learning and improve results. Pearson eText is an easy-to-use digital textbook available within MyLab® that lets you read, highlight and take notes, all in one place. NOTE: Before purchasing, check with your instructor to confirm the correct ISBN. Several versions of the MyLab and Mastering® platforms exist for each title, and registrations are not transferable. To register for and use MyLab, you will need either a course ID from your instructor or an invitation link that your instructor will send you directly. Used books, rentals, and purchases made outside of Pearson If purchasing or renting from companies other than Pearson, the access codes for the MyLab platform may not be included, may be incorrect, or may be previously redeemed. Check with the seller before completing your purchase.
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1. First-Order Differential Equations 1.1 Differential Equations and Mathematical Models1.2 Integrals as General and Particular Solutions1.3 Slope Fields and Solution Curves1.4 Separable Equations and Applications1.5 Linear First-Order Equations1.6 Substitution Methods and Exact Equations 2. Mathematical Models and Numerical Methods 2.1 Population Models2.2 Equilibrium Solutions and Stability2.3 Acceleration - Velocity Models2.4 Numerical Approximation: Euler's Method2.5 A Closer Look at the Euler Method2.6 The Runge - Kutta Method 3. Linear Equations of Higher Order 3.1 Introduction: Second-Order Linear Equations3.2 General Solutions of Linear Equations3.3 Homogeneous Equations with Constant Coefficients3.4 Mechanical Vibrations3.5 Nonhomogeneous Equations and Undetermined Coefficients3.6 Forced Oscillations and Resonance3.7 Electrical Circuits3.8 Endpoint Problems and Eigenvalues 4. Introduction to Systems of Differential Equations 4.1 First-Order Systems and Applications4.2 The Method of Elimination4.3 Numerical Methods for Systems 5. Linear Systems of Differential Equations 5.1 Matrices and Linear Systems5.2 The Eigenvalue Method for Homogeneous Systems5.3 A Gallery of Solution Curves of Linear Systems5.4 Second-Order Systems and Mechanical Applications5.5 Multiple Eigenvalue Solutions5.6 Matrix Exponentials and Linear Systems5.7 Nonhomogeneous Linear Systems 6. Nonlinear Systems and Phenomena 6.1 Stability and the Phase Plane6.2 Linear and Almost Linear Systems6.3 Ecological Models: Predators and Competitors6.4 Nonlinear Mechanical Systems6.5 Chaos in Dynamical Systems 7. Laplace Transform Methods 7.1 Laplace Transforms and Inverse Transforms7.2 Transformation of Initial Value Problems7.3 Translation and Partial Fractions7.4 Derivatives, Integrals, and Products of Transforms7.5 Periodic and Piecewise Continuous Input Functions7.6 Impulses and Delta Functions 8. Power Series Methods 8.1 Introduction and Review of Power Series8.2 Series Solutions Near Ordinary Points8.3 Regular Singular Points8.4 Method of Frobenius: The Exceptional Cases8.5 Bessel's Equation8.6 Applications of Bessel Functions 9. Fourier Series Methods and Partial Differential Equations 9.1 Periodic Functions and Trigonometric Series9.2 General Fourier Series and Convergence9.3 Fourier Sine and Cosine Series9.4 Applications of Fourier Series9.5 Heat Conduction and Separation of Variables9.6 Vibrating Strings and the One-Dimensional Wave Equation9.7 Steady-State Temperature and Laplace's Equation 10. Eigenvalue Methods and Boundary Value Problems 10.1 Sturm - Liouville Problems and Eigenfunction Expansions10.2 Applications of Eigenfunction Series10.3 Steady Periodic Solutions and Natural Frequencies10.4 Cylindrical Coordinate Problems10.5 Higher-Dimensional Phenomena  References for Further Study Appendix: Existence and Uniqueness of Solutions Answers to Selected Problems Index
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Hallmark features of this title Emphasis on numerical methods includes early introduction of numerical solution techniques, mathematical modeling, stability and qualitative properties of differential equations, with generic numerical algorithms that can be implemented in various technologies.Application Modules follow key sections, most with computing projects that reinforce the corresponding text sections.Approximately 2000 problems range from computational to applied and conceptual problems. An expansive answer section includes answers to most odd- and even-numbered problems. Emphasis on technology and ODEs explores newer methods of computing differential equations, covering the software systems tailored specifically to differential equations as well as Maple, Mathematica and MATLAB.
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New and updated features of this title New content includes a new application of differential equations to the life sciences in Application Module 6.4: The Rayleigh, van der Pol, and FitzHugh-Nagumo Equations; The SIR Model and COVID-19. Characterized by the same careful and thorough exposition found throughout the text, this new unit gives students yet another perspective about differential equations.Extensively revised design: New use of full color enhances graphs and figures so that students can more easily discern different solutions in the figures.Added marginal notes aid in understanding the mathematics in the text; easier identification of application topics in the exercise set includes new run-in problem titles; new Your Turn headers in the Application Modules now clarify where the exposition ends and the students' investigations begin.16 new Interactive Figures illustrate how interactive computer applications with slider bars or touchpad controls can be used to change initial values or parameters in a differential equation, allowing students to immediately see in real time the resulting changes in the structure of its solutions. Using a mouse or touchpad, the initial point for an initial value problem can be dragged to a new location, and the corresponding solution curve is automatically redrawn and dragged along with its initial point. For examples, see Figures 1.3.5 and 3.2.4.
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Produktdetaljer

ISBN
9780137540518
Publisert
2022-01-09
Utgave
6. utgave
Utgiver
Vendor
Pearson
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Lisensnøkkel fysisk

Biographical note

About our authors

Henry Edwards  is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960; he retired after 40 years of classroom teaching (including calculus or differential equations almost every term) at the universities of Tennessee, Wisconsin and Georgia, with a brief interlude at the Institute for Advanced Study (Princeton) as an Alfred P. Sloan Research Fellow. He has received numerous teaching awards, including the University of Georgia's honoratus medal in 1983 (for sustained excellence in honors teaching), its Josiah Meigs award in 1991 (the institution's highest award for teaching), and the 1997 statewide Georgia Regents award for research university faculty teaching excellence.

His scholarly career has ranged from research and dissertation direction in topology to the history of mathematics to computing and technology in the teaching and applications of mathematics. In addition to being author or co-author of calculus, advanced calculus, linear algebra, and differential equations textbooks, he is well-known to calculus instructors as author of The Historical Development of the Calculus (Springer-Verlag, 1979). During the 1990s he served as a principal investigator on three NSF-supported projects: (1) A school mathematics project including Maple for beginning algebra students, (2) A Calculus-with-Mathematica program, and (3) A MATLAB-based computer lab project for numerical analysis and differential equations students. In 2013 Prof. Edwards was named a Fellow of the American Mathematical Society.

David E. Penney, University of Georgia, completed his Ph.D. at Tulane University in 1965 under the direction of Prof. L. Bruce Treybig while teaching at the University of New Orleans. Earlier he had worked in experimental biophysics at Tulane University and the Veteran's Administration Hospital in New Orleans under the direction of Robert Dixon McAfee, where Dr. McAfee's research team's primary focus was on the active transport of sodium ions by biological membranes. Penney's primary contribution here was the development of a mathematical model (using simultaneous ordinary differential equations) for the metabolic phenomena regulating such transport, with potential future applications in kidney physiology, management of hypertension, and treatment of congestive heart failure. He also designed and constructed servomechanisms for the accurate monitoring of ion transport, a phenomenon involving the measurement of potentials in microvolts at impedances of millions of megohms.

Penney began teaching calculus at Tulane in 1957 and taught that course almost every term with enthusiasm and distinction until his retirement at the end of the last millennium. During his tenure at the University of Georgia he received numerous university-wide teaching awards and directed several doctoral dissertations and 7 undergraduate research projects. He authored research papers in number theory and topology, and was the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra and liberal arts mathematics. Penney passed away in 2014.

David T. Calvis is Professor of Mathematics at Baldwin Wallace University near Cleveland, Ohio.  He completed a Ph.D. in complex analysis from the University of Michigan in 1988 under the direction of Fred Gehring.  While at Michigan he also received a Master's degree in Computer, Information, and Control Engineering.  Having initially served at Hillsdale College in Michigan, he has been at Baldwin Wallace since 1990, most recently assisting with the creation of an Applied Mathematics program there.  He has received a number of teaching awards, including BWU's Strosacker Award for Excellence in Teaching and Student Senate Teaching Award.  He is the author of materials dealing with the use of computer algebra systems in mathematics instruction, and has extensive classroom experience teaching differential equations and related topics.