Elementary Differential Equations Binder Ready Version 10th Edition by William Boyce – Ebook PDF Instant Download/Delivery: 1118157397, 9781118157398
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• ISBN 10:1118157397
• ISBN 13:9781118157398
• Author:William Boyce
Elementary Differential Equations, 10th Edition is written from the viewpoint of the applied mathematician, whose interest in differential equations may sometimes be quite theoretical and sometimes intensely practical. The authors have sought to combine a sound and accurate exposition of the elementary theory of differential equations with considerable material on methods of solution, analysis, and approximation that have proved useful in a wide variety of applications. While the general structure of the book remains unchanged, some notable changes have been made to improve the clarity and readability of basic material about differential equations and their applications. In addition to expanded explanations, the 10th edition includes new problems, updated figures and examples to help motivate students.
Elementary Differential Equations Binder Ready Version 10th Table of contents:
Chapter 1 Introduction
Some Basic Mathematical Models; Direction Fields
Solutions of Some Differential Equations
Classification of Differential Equations
Historical Remarks
Chapter 2 First Order Equations
Linear Equations; Method of Integrating Factors
Sepable 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
Chapter 3 Numerical Methods
Homogeneous Equations with Constant Coefficients
Solutions of Linear Homogeneous Equations; 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
Chapter 4 Applications of First Order Equation
General Theory of nth Order Linear Equations
Homogeneous Equations with Constant Coefficients
The Method of Undetermined Coefficients
The Method of Variation of Parameters
Chapter 5 Linear Second Order Equations
Review of Power Series
Series Solutions Near an Ordinary Point, Part I
Series Solutions Near an Ordinary Point, Part II
Euler Equations; Regular Singular Points
Series Solutions Near a Regular Singular Point, Part I
Series Solutions Near a Regular Singular Point, Part II
Bessel’s
Chapter 6 Applcations of Linear Second Order Equations
Definition of the Laplace Transform
Solution of Initial Value Problems
Step Functions
Differential Equations with Discontinuous Forcing Functions
Impulse Functions
The Convolution Integral
Chapter 7 Series Solutions of Linear Second Order Equations
Introduction
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
Chapter 8 Laplace Transforms
The Euler or Tangent Line Method
Improvements on the Euler Method
The Runge-Kutta Method
Multistep Methods
Systems of First Order Equations
More on Errors; Stability
Chapter 9 Linear Higher Order Equations
The Phase Plane: Linear Systems
Autonomous Systems and Stability
Locally Linear Systems
Competing Species
Predator-Prey Equations
Chapter 10 Linear Systems of Differential Equations
Two-Point Boundary Value 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
Appendix A Derivation of the Heat Conduction Equation
Appendix B Derivation of the Wave Equation
Chapter 11: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
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