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Elementary Differential Equations and Boundary Value Problems

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ISBN-10: 0471319996

ISBN-13: 9780471319993

Edition: 7th 2001 (Revised)

Authors: William E. Boyce, Richard C. DiPrima

List price: $127.95
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Retaining previously successful features, this edition exploits students' access to computers by including many new examples and problems that incorporate computer technology. Historical footnotes trace the development of the discipline.
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Book details

List price: $127.95
Edition: 7th
Copyright year: 2001
Publisher: John Wiley & Sons, Incorporated
Publication date: 8/8/2000
Binding: Hardcover
Pages: 768
Size: 6.24" wide x 10.20" long x 1.22" tall
Weight: 3.542
Language: English

Some Basic Mathematical Models; Direction Fields
Solutions of Some Differential Equations
Classification of Differential Equations
Historical Remarks
First Order Differential Equations
Linear Equations with Variable Coefficients
Separable Equations
Modeling with First Order Equations
Differences Between Linear and Nonlinear Equations
Autonomous Equations and Population Dynamics
Exact Equations and Integrating Factors
Numerical Approximations: Euler's Method
The Existence and Uniqueness Theorem
First Order Difference Equations
Second Order Linear Equations
Homogeneous Equations with Constant Coefficients
Fundamental Solutions of Linear Homogeneous Equations
Linear Independence and the Wronskian
Complex Roots of the Characteristic Equation
Repeated Roots; Reduction of Order
Nonhomogeneous Equations; Method of Undetermined Coefficients
Variation of Parameters
Mechanical and Electrical Vibrations
Forced Vibrations
Higher Order Linear Equations
General Theory of nth Order Linear Equations
Homogeneous Equations with Constant Coeffients
The Method of Undetermined Coefficients
The Method of Variation of Parameters
Series Solutions of Second Order Linear Equations
Review of Power Series
Series Solutions near an Ordinary Point, Part I
Series Solutions near an Ordinary Point, Part II
Regular Singular Points
Euler Equations
Series Solutions near a Regular Singular Point, Part I
Series Solutions near a Regular Singular Point, Part II
Bessel's Equation
The Laplace Transform
Definition of the Laplace Transform
Solution of Initial Value Problems
Step Functions
Differential Equations with Discontinuous Forcing Functions
Impulse Functions
The Convolution Integral
Systems of First Order Linear Equations
Review of Matrices
Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
Basic Theory of Systems of First Order Linear Equations
Homogeneous Linear Systems with Constant Coefficients
Complex Eigenvalues
Fundamental Matrices
Repeated Eigenvalues
Nonhomogeneous Linear Systems
Numerical Methods
The Euler or Tangent Line Method
Improvements on the Euler Method
The Runge-Kutta Method
Multistep Methods
More on Errors; Stability
Systems of First Order Equations
Nonlinear Differential Equations and Stability
The Phase Plane; Linear Systems
Autonomous Systems and Stability
Almost Linear Systems
Competing Species
Predator-Prey Equations
Liapunov's Second Method
Periodic Solutions and Limit Cycles
Chaos and Strange Attractors; the Lorenz Equations
Partial Differential Equations and Fourier Series
Two-Point Boundary Valve Problems
Fourier Series
The Fourier Convergence Theorem
Even and Odd Functions
Separation of Variables; Heat Conduction in a Rod
Other Heat Conduction Problems
The Wave Equation; Vibrations of an Elastic String
Laplace's Equation
Derivation of the Heat Conduction Equation
Derivation of the Wave Equation
Boundary Value Problems and Sturm-Liouville Theory
The Occurrence of Two Point Boundary Value Problems
Sturm-Liouville Boundary Value Problems
Nonhomogeneous Boundary Value Problems
Singular Sturm-Liouville Problems
Further Remarks on the Method of Separation of Variables: A Bessel Series Expansion
Series of Orthogonal Functions: Mean Convergence
Answers to Problems