Fundamentals of Differential Equations and Boundary Value Problems, 7th edition
Published by Pearson (May 10th 2017)  Copyright © 2018
7th edition

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For onesemester sophomore or juniorlevel courses in Differential Equations.
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An introduction to the basic theory and applications of differential equations
Fundamentals of Differential Equations and Boundary Value Problems presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. This flexible text allows instructors to adapt to various course emphases (theory, methodology, applications, and numerical methods) and to use commercially available computer software. For the first time, MyLab™ Math is available for this text, providing online homework with immediate feedback, the complete eText, and more.
Note that a shorter version of this text, entitled Fundamentals of Differential Equations, 9th Edition, contains enough material for a onesemester course. This shorter text consists of chapters 110 of the main text.
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Table of contents
1. Introduction
1.1 Background
1.2 Solutions and Initial Value Problems
1.3 Direction Fields
1.4 The Approximation Method of Euler
2. FirstOrder Differential Equations
2.1 Introduction: Motion of a Falling Body
2.2 Separable Equations
2.3 Linear Equations
2.4 Exact Equations
2.5 Special Integrating Factors
2.6 Substitutions and Transformations
3. Mathematical Models and Numerical Methods Involving First Order Equations
3.1 Mathematical Modeling
3.2 Compartmental Analysis
3.3 Heating and Cooling of Buildings
3.4 Newtonian Mechanics
3.5 Electrical Circuits
3.6 Numerical Methods: A Closer Look At Euler’s Algorithm
3.7 HigherOrder Numerical Methods: Taylor and RungeKutta
4. Linear SecondOrder Equations
4.1 Introduction: The MassSpring Oscillator
4.2 Homogeneous Linear Equations: The General Solution
4.3 Auxiliary Equations with Complex Roots
4.4 Nonhomogeneous Equations: The Method of Undetermined Coefficients
4.5 The Superposition Principle and Undetermined Coefficients Revisited
4.6 Variation of Parameters
4.7 VariableCoefficient Equations
4.8 Qualitative Considerations for VariableCoefficient and Nonlinear Equations
4.9 A Closer Look at Free Mechanical Vibrations
4.10 A Closer Look at Forced Mechanical Vibrations
5. Introduction to Systems and Phase Plane Analysis
5.1 Interconnected Fluid Tanks
5.2 Differential Operators and the Elimination Method for Systems
5.3 Solving Systems and HigherOrder Equations Numerically
5.4 Introduction to the Phase Plane
5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models
5.6 Coupled MassSpring Systems
5.7 Electrical Systems
5.8 Dynamical Systems, Poincaré Maps, and Chaos
6. Theory of HigherOrder Linear Differential Equations
6.1 Basic Theory of Linear Differential Equations
6.2 Homogeneous Linear Equations with Constant Coefficients
6.3 Undetermined Coefficients and the Annihilator Method
6.4 Method of Variation of Parameters
7. Laplace Transforms
7.1 Introduction: A Mixing Problem
7.2 Definition of the Laplace Transform
7.3 Properties of the Laplace Transform
7.4 Inverse Laplace Transform
7.5 Solving Initial Value Problems
7.6 Transforms of Discontinuous Functions
7.7 Transforms of Periodic and Power Functions
7.8 Convolution
7.9 Impulses and the Dirac Delta Function
7.10 Solving Linear Systems with Laplace Transforms
8. Series Solutions of Differential Equations
8.1 Introduction: The Taylor Polynomial Approximation
8.2 Power Series and Analytic Functions
8.3 Power Series Solutions to Linear Differential Equations
8.4 Equations with Analytic Coefficients
8.5 CauchyEuler (Equidimensional) Equations
8.6 Method of Frobenius
8.7 Finding a Second Linearly Independent Solution
8.8 Special Functions
9. Matrix Methods for Linear Systems
9.1 Introduction
9.2 Review 1: Linear Algebraic Equations
9.3 Review 2: Matrices and Vectors
9.4 Linear Systems in Normal Form
9.5 Homogeneous Linear Systems with Constant Coefficients
9.6 Complex Eigenvalues
9.7 Nonhomogeneous Linear Systems
9.8 The Matrix Exponential Function
10. Partial Differential Equations
10.1 Introduction: A Model for Heat Flow
10.2 Method of Separation of Variables
10.3 Fourier Series
10.4 Fourier Cosine and Sine Series
10.5 The Heat Equation
10.6 The Wave Equation
10.7 Laplace's Equation
11. Eigenvalue Problems and SturmLiouville Equations
11.1 Introduction: Heat Flow in a Nonuniform Wire
11.2 Eigenvalues and Eigenfunctions
11.3 Regular SturmLiouville Boundary Value Problems
11.4 Nonhomogeneous Boundary Value Problems and the Fredholm Alternative
11.5 Solution by Eigenfunction Expansion
11.6 Green's Functions
11.7 Singular SturmLiouville Boundary Value Problems.
11.8 Oscillation and Comparison Theory
12. Stability of Autonomous Systems
12.1 Introduction: Competing Species
12.2 Linear Systems in the Plane
12.3 Almost Linear Systems
12.4 Energy Methods
12.5 Lyapunov's Direct Method
12.6 Limit Cycles and Periodic Solutions
12.7 Stability of HigherDimensional Systems
13. Existence and Uniqueness Theory
13.1 Introduction: Successive Approximations
13.2 Picard's Existence and Uniqueness Theorem
13.3 Existence of Solutions of Linear Equations
13.4 Continuous Dependence of Solutions
Appendix A Review of Integration Techniques
Appendix B Newton's Method
Appendix C Simpson's Rule
Appendix D Cramer's Rule
Appendix E Method of Least Squares
Appendix F RungeKutta Procedure for n Equations
Appendix G Software for Analyzing Differential Equations
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