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Differential Equations and Boundary Value Problems : Computing and Modeling

ISBN: 9780130652454 | 0130652458
Edition: 4th
Format: Hardcover
Publisher: Prentice Hall
Pub. Date: 1/1/2008

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SummaryTable of Contents
For introductory courses in Differential Equations. This best-selling text by these well-known authors blends the traditional algebra problem solving skills with the conceptual development and geometric visualization of a modern differential equations course that is essential to science and engineering students. It reflects the new qualitative approach that is altering the learning of elementary differential equations, including the wide availability of scientific computing environments like Maple, Mathematica, and MATLAB. Its focus balances th... MORE
... MORE
Application Modulesviii
Prefacexi
First-Order Differential Equations
1(76)
Differential Equations and Mathematical Models
1(9)
Integrals as General and Particular Solutions
10(8)
Slope Fields and Solution Curves
18(13)
Separable Equations and Applications
31(15)
Linear First-Order Equations
46(12)
Substitution Methods and Exact Equations
58(19)
Mathematical Models and Numerical Methods
77(67)
Population Models
77(13)
Equilibrium Solutions and Stability
90(8)
Acceleration-Velocity Models
98(12)
Numerical Approximation: Euler's Method
110(12)
A Closer Look at the Euler Method
122(10)
The Runge-Kutta Method
132(12)
Linear Equations of Higher Order
144(98)
Introduction: Second-Order Linear Equations
144(14)
General Solutions of Linear Equations
158(12)
Homogeneous Equations with Constant Coefficients
170(12)
Mechanical Vibrations
182(13)
Nonhomogeneous Equations and Undetermined Coefficients
195(14)
Forced Oscillations and Resonance
209(13)
Electrical Circuits
222(7)
Endpoint Problems and Eigenvalues
229(13)
Introduction to Systems of Differential Equations
242(39)
First-Order Systems and Applications
242(12)
The Method of Elimination
254(11)
Numerical Methods for Systems
265(16)
Linear Systems of Differential Equations
281(85)
Matrices and Linear Systems
281(19)
The Eigenvalue Method for Homogeneous Systems
300(15)
Second-Order Systems and Mechanical Applications
315(13)
Multiple Eigenvalue Solutions
328(16)
Matrix Exponentials and Linear Systems
344(14)
Nonhomogeneous Linear Systems
358(8)
Nonlinear Systems and Phenomena
366(69)
Stability and the Phase Plane
366(12)
Linear and Almost Linear Systems
378(15)
Ecological Models: Predators and Competitors
393(13)
Nonlinear Mechanical Systems
406(17)
Chaos in Dynamical Systems
423(12)
Laplace Transform Methods
435(62)
Laplace Transforms and Inverse Transforms
435(11)
Transformation of Initial Value Problems
446(11)
Translation and Partial Fractions
457(10)
Derivatives, Integrals, and Products of Transforms
467(8)
Periodic and Piecewise Continuous Input Functions
475(11)
Impulses and Delta Functions
486(11)
Power Series Methods
497(75)
Introduction and Review of Power Series
497(13)
Series Solutions Near Ordinary Points
510(13)
Regular Singular Points
523(16)
Method of Frobenius: The Exceptional Cases
539(15)
Bessel's Equation
554(9)
Applications of Bessel Functions
563(9)
Fourier Series Methods
572(73)
Periodic Functions and Trigonometric Series
572(9)
General Fourier Series and Convergence
581(8)
Fourier Sine and Cosine Series
589(12)
Applications of Fourier Series
601(5)
Heat Conduction and Separation of Variables
606(15)
Vibrating Strings and the One-Dimensional Wave Equation
621(14)
Steady-State Temperature and Laplace's Equation
635(10)
Eigenvalues and Boundary Value Problems
645(66)
Sturm-Liouville Problems and Eigenfunction Expansions
645(13)
Applications of Eigenfunction Series
658(10)
Steady Periodic Solutions and Natural Frequencies
668(10)
Cylindrical Coordinate Problems
678(15)
Higher-Dimensional Phenomena
693(18)
References for Further Study711(3)
Appendix: Existence and Uniqueness of Solutions714(15)
Answers to Selected Problems729
Index1

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