Master your Minecraft
 
 

Special Offers see all

Enter to WIN a $100 Credit

Subscribe to PowellsBooks.news
for a chance to win.
Privacy Policy

Tour our stores


    Recently Viewed clear list


    The Powell's Playlist | October 21, 2014

    Anne Rice: IMG The Powell’s Playlist: Anne Rice



    These are the songs that wake me up, take me out of my worries and anxieties, wash my brain cells, and send me to the keyboard to write with new... Continue »

    spacer
Qualifying orders ship free.
$217.25
New Hardcover
Ships in 1 to 3 days
Add to Wishlist
available for shipping or prepaid pickup only
Qty Store Section
6 Local Warehouse Mathematics- Differential Equations

Differential Equations and Boundary Value Problems: Computing and Modeling

by

Differential Equations and Boundary Value Problems: Computing and Modeling Cover

 

Synopses & Reviews

Publisher Comments:

This practical book reflects the new technological emphasis that permeates differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB; it does not concentrate on traditional manual methods but rather on new computer-based methods that lead to a wider range of more realistic applications. The book starts and ends with discussions of mathematical modeling of real-world phenomena, evident in figures, examples, problems, and applications throughout the book. For mathematicians and those in the field of computer science and engineering.

 

About the Author

C. Henry Edwards is emeritus professor of mathematics at the University of Georgia. He earned his Ph.D. at the University of Tennessee in 1960, and recently 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.

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 as well as directing several doctoral dissertations and seven undergraduate research projects. He is the author of research papers in number theory and topology and is the author or co-author of textbooks on calculus, computer programming, differential equations, linear algebra, and liberal arts mathematics.

Table of Contents

1. First Order Differential Equations.

Differential Equations and Mathematical Models. Integrals as General and Particular Solutions. Slope Fields and Solution Curves. Separable Equations and Applications. Linear First Order Equations. Substitution Methods and Exact Equations.

2. Mathematical Models and Numerical Methods.

Population Models. Equilibrium Solutions and Stability. Acceleration-Velocity Models. Numerical Approximation: Euler's Method. A Closer Look at the Euler Method, and Improvements. The Runge-Kutta Method.

3. Linear Equations of Higher Order.

Introduction: Second-Order Linear Equations. General Solutions of Linear Equations. Homogeneous Equations with Constant Coefficients. Mechanical Vibrations. Nonhomogeneous Equations and Undetermined Coefficients. Forced Oscillations and Resonance. Electrical Circuits. Endpoint Problems and Eigenvalues.

4. Introduction to Systems of Differential Equations.

First-Order Systems and Applications. The Method of Elimination. Numerical Methods for Systems.

5. Linear Systems of Differential Equations.

Linear Systems and Matrices. The Eigenvalue Method for Homogeneous Systems. Second Order Systems and Mechanical Applications. Multiple Eigenvalue Solutions. Matrix Exponentials and Linear Systems. Nonhomogenous Linear Systems.

6. Nonlinear Systems and Phenomena.

Stability and the Phase Plane. Linear and Almost Linear Systems. Ecological Models: Predators and Competitors. Nonlinear Mechanical Systems. Chaos in Dynamical Systems.

7. Laplace Transform Methods.

Laplace Transforms and Inverse Transforms. Transformation of Initial Value Problems. Translation and Partial Fractions. Derivatives, Integrals, and Products of Transforms. Periodic and Piecewise Continuous Forcing Functions. Impulses and Delta Functions.

8. Power Series Methods.

Introduction and Review of Power Series. Series Solutions Near Ordinary Points. Regular Singular Points. Method of Frobenius: The Exceptional Cases. Bessel's Equation. Applications of Bessel Functions.

9. Fourier Series Methods.

Periodic Functions and Trigonometric Series. General Fourier Series and Convergence. Even-Odd Functions and Termwise Differentiation. Applications of Fourier Series. Heat Conduction and Separation of Variables. Vibrating Strings and the One-Dimensional Wave Equation. Steady-State Temperature and Laplace's Equation.

10. Eigenvalues and Boundary Value Problems.

Sturm-Liouville Problems and Eigenfunction Expansions. Applications of Eigenfunction Series. Steady Periodic Solutions and Natural Frequencies. Applications of Bessel Functions. Higher-Dimensional Phenomena.

References.

Appendix: Existence and Uniqueness of Solutions.

Answers to Selected Problems.

Index.

Product Details

ISBN:
9780131561076
Author:
Edwards, C. Henry
Publisher:
Pearson
Author:
Penney, David
Author:
Penney, David E.
Author:
Edwards, Henry
Author:
Cram101 Textbook Reviews
Author:
Calvis, David
Subject:
Advanced
Subject:
Differential Equations
Subject:
Boundary value problems
Subject:
Mathematics-Differential Equations
Subject:
Education-General
Copyright:
Edition Number:
4
Edition Description:
Trade paper
Series:
Featured Titles for Differential Equations
Publication Date:
September 2007
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Y
Pages:
816
Dimensions:
10 x 8 x 1.2 in 1433 gr

Related Subjects

Computers and Internet » Computers Reference » Computer Simulation
Science and Mathematics » Mathematics » Differential Equations
Science and Mathematics » Mathematics » Functional Analysis
Science and Mathematics » Mathematics » General

Differential Equations and Boundary Value Problems: Computing and Modeling New Hardcover
0 stars - 0 reviews
$217.25 In Stock
Product details 816 pages Prentice Hall - English 9780131561076 Reviews:
spacer
spacer
  • back to top

FOLLOW US ON...

     
Powell's City of Books is an independent bookstore in Portland, Oregon, that fills a whole city block with more than a million new, used, and out of print books. Shop those shelves — plus literally millions more books, DVDs, and gifts — here at Powells.com.