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Differential Equations with Boundary Value Problems. Hollis
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ApproximatelyS$ 1.30
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A book that has been read but is in good condition. Very minimal damage to the cover including scuff marks, but no holes or tears. The dust jacket for hard covers may not be included. Binding has minimal wear. The majority of pages are undamaged with minimal creasing or tearing, minimal pencil underlining of text, no highlighting of text, no writing in margins. No missing pages.
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Located in: Brooklyn, New York, United States
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eBay item number:253577529838
Item specifics
- Condition
- ISBN
- 9780130159274
- EAN
- 9780130159274
About this product
Product Identifiers
Publisher
Prentice Hall PTR
ISBN-10
0130159271
ISBN-13
9780130159274
eBay Product ID (ePID)
2033947
Product Key Features
Number of Pages
635 Pages
Language
English
Publication Name
Differential Equations with Boundary Value Problems
Subject
Differential Equations / General
Publication Year
2001
Type
Textbook
Subject Area
Mathematics
Format
Hardcover
Dimensions
Item Height
1.1 in
Item Weight
39.2 Oz
Item Length
9.5 in
Item Width
7.3 in
Additional Product Features
Intended Audience
College Audience
LCCN
2001-050072
Dewey Edition
21
Illustrated
Yes
Dewey Decimal
515/.35
Table Of Content
1. Introduction. Prologue: What Are Differential Equations? Four Introductory Models. Fundamental Concepts and Terminology. 2. Linear First-Order Equations. Methods of Solution. Some Elementary Applications. Generalized Solutions. 3. Nonlinear First-Order Equations I. Direction Fields and Numerical Approximation. Separable Equations. Bernoulli and Riccati Equations. Reduction of Order. Nonlinear First-order Equations in Applications. 4. Nonlinear First-Order Equations II. Construction of Local Solutions. Existence and Uniqueness. Qualitative and Asymptotic Behavior. The Logistic Population Model. Numerical Methods. A First Look at Systems. 5. Linear Second-Order Equations I. Introduction: Modeling Vibrations. State Variables and Numerical Approximation. Operators and Linearity. Solutions and Linear Independence. Variation of Constants and Green's Functions. Power-Series Solutions. Polynomial Solutions. 6. Linear Second-Order Equations II. Homogeneous Equations with Constant Coefficients. Exponential Shift. Complex Roots. Real Solutions from Complex Solutions. Unforced Vibrations. Periodic Force and Response. 7. The Laplace Transform. Definition and Basic Properties. More Transforms and Further Properties. Heaviside Functions and Piecewise-Defined Inputs. Periodic Inputs. Impulses and the Dirac Distribution. Convolution. 8. Linear First-Order Systems. Introduction. Two Ad Hoc Methods. Vector-Valued Functions and Linear Independence. Evolution Matrices and Variation of Constants. Autonomous Systems: Eigenvalues and Eigenvectors. eAT and the Cayley-Hamilton Theorem. Asymptotic Stability. 9. Geometry of Autonomous Systems in the Plane. The Phase Plane. Phase Portraits of Homogeneous Linear Systems. Phase Portraits of Nonlinear Systems. Limit Cycles. Beyond the Plane. 10. Nonlinear Systems in Applications. Lotka-Volterra Systems in Ecology. Infectious Disease and Epidemics. Other Biological Models. Chemical Systems. Mechanics. 11. Diffusion Problems and Fourier Series. The Basic Diffusion Problem. Solutions by Separation of Variables. Fourier Series. Fourier Sine and Cosine Series. Sturm-Liouville Eigenvalue Problems. Singular Sturm-Liouville Problems. Eigenfunction Expansions. 12. Further Topics in PDEs. The Wave Equation. The 2-D Laplace Equation. The 2-D Diffusion Equation. Appendices.
Synopsis
Designed for use in an introductory differential equations course, this textbook emphasizes the behavior of the solutions rather than the application of formulas. It covers: linear and non-linear first-order equations, second-order linear equations, the Laplace transform, first-order linear systems,, This book provides readers with a solid introduction to differential equations and their applications emphasizing analytical, qualitative, and numerical methods. Numerical methods are presented early in the text, including a discussion of error estimates for the Euler, Heun, and Runge-Kutta methods. Systems and the phase plane are also introduced early, first in the context of pairs first-order equations, and then in the context of second-order linear equations. Other chapter topics include the Laplace transform, linear first-order systems, geometry of autonomous systems in the plane, nonlinear systems in applications, diffusion problems and Fourier series, and further topics in PDEs., For undergraduate (sophomore/junior) courses in Differential Equations. For students majoring in Mathematics, Engineering, Physical Sciences, Biological Science, or Computer Science. Assumes knowledge of Calculus. A solid introduction to Differential Equations and their applications emphasizing analytical, qualitative, and numerical methods.
LC Classification Number
QA371.H67 2001
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