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Über dieses Produkt
Product Identifiers
PublisherPrentice Hall PTR
ISBN-100132397307
ISBN-139780132397308
eBay Product ID (ePID)59004996
Product Key Features
Number of Pages648 Pages
LanguageEnglish
Publication NameElementary Differential Equations
Publication Year2007
SubjectDifferential Equations / General
TypeTextbook
AuthorC. Henry Edwards, David E. Penney
Subject AreaMathematics
FormatHardcover
Dimensions
Item Height1.1 in
Item Weight46.4 Oz
Item Length8.3 in
Item Width10.2 in
Additional Product Features
Edition Number6
Intended AudienceCollege Audience
LCCN2008-299267
Dewey Edition22
IllustratedYes
Dewey Decimal515/.35
Table Of ContentC O N T E N T S Preface vii CHAPTER 1 First-Order Differential Equations 1 1.1 Differential Equations and Mathematical Models 1 1.2 Integrals as General and Particular Solutions 10 1.3 Slope Fields and Solution Curves 19 1.4 Separable Equations and Applications 32 1.5 Linear First-Order Equations 46 1.6 Substitution Methods and Exact Equations 59 1.7 Population Models 74 1.8 Acceleration-Velocity Models 85 CHAPTER 2 Linear Equations of Higher Order 100 2.1 Introduction: Second-Order Linear Equations 100 2.2 General Solutions of Linear Equations 113 2.3 Homogeneous Equations with Constant Coefficients 124 2.4 Mechanical Vibrations 135 2.5 Nonhomogeneous Equations and Undetermined Coefficients 148 2.6 Forced Oscillations and Resonance 162 2.7 Electrical Circuits 173 2.8 Endpoint Problems and Eigenvalues 180 CHAPTER 3 Power Series Methods 194 3.1 Introduction and Review of Power Series 194 3.2 Series Solutions Near Ordinary Points 207 3.3 Regular Singular Points 218 3.4 Method of Frobenius: The Exceptional Cases 233 3.5 Bessel''s Equation 248 3.6 Applications of Bessel Functions 257 v vi Contents CHAPTER 4 Laplace Transform Methods 266 4.1 Laplace Transforms and Inverse Transforms 266 4.2 Transformation of Initial Value Problems 277 4.3 Translation and Partial Fractions 289 4.4 Derivatives, Integrals, and Products of Transforms 297 4.5 Periodic and Piecewise Continuous Input Functions 304 4.6 Impulses and Delta Functions 316 CHAPTER 5 Linear Systems of Differential Equations 326 5.1 First-Order Systems and Applications 326 5.2 The Method of Elimination 338 5.3 Matrices and Linear Systems 347 5.4 The Eigenvalue Method for Homogeneous Systems 366 5.5 Second-Order Systems and Mechanical Applications 381 5.6 Multiple Eigenvalue Solutions 393 5.7 Matrix Exponentials and Linear Systems 407 5.8 Nonhomogeneous Linear Systems 420 CHAPTER 6 Numerical Methods 430 6.1 Numerical Approximation: Euler''s Method 430 6.2 A Closer Look at the Euler Method 442 6.3 The Runge-Kutta Method 453 6.4 Numerical Methods for Systems 464 CHAPTER 7 Nonlinear Systems and Phenomena 480 7.1 Equilibrium Solutions and Stability 480 7.2 Stability and the Phase Plane 488 7.3 Linear and Almost Linear Systems 500 7.4 Ecological Models: Predators and Competitors 513 7.5 Nonlinear Mechanical Systems 526 7.6 Chaos in Dynamical Systems 542 References for Further Study 555 Appendix: Existence and Uniqueness of Solutions 559 Answers to Selected Problems 573 Index I-1
SynopsisFor briefer traditional courses in elementary differential equations that science, engineering, and mathematics students take following calculus. The Sixth Edition of this widely adopted book remains the same classic differential equations text it's always been, but has been polished and sharpened to serve both instructors and students even more effectively.Edwards and Penney teach students to first solve those differential equations that have the most frequent and interesting applications. Precise and clear-cut statements of fundamental existence and uniqueness theorems allow understanding of their role in this subject. A strong numerical approach emphasizes that the effective and reliable use of numerical methods often requires preliminary analysis using standard elementary techniques., This book gives readers the means to solve differential equations that enjoy the most frequent & interesting applications. It illustrates the standard elementary techniques of solving differential equations, & presents precise & clear-cut statements of the fundamental existence & uniqueness theorems.
LC Classification NumberQA371
As told toCalvis, David
