(0) items

Fundamentals of Differential Equations,9780321747730
This item qualifies for


Your order must be $59 or more, you must select US Postal Service Shipping as your shipping preference, and the "Group my items into as few shipments as possible" option when you place your order.

Bulk sales, PO's, Marketplace Items, eBooks, Apparel, and DVDs not included.

Fundamentals of Differential Equations

by ; ;


Pub. Date:
Includes 2-weeks free access to
step-by-step solutions for this book.
Step-by-Step solutions are actual worked out problems to the questions at the end of each chapter that help you understand your homework and study for your exams. Chegg and eCampus are providing you two weeks absolutely free. 81% of students said using Step-by-Step solutions prepared them for their exams.
List Price: $178.67

Rent Textbook


Buy New Textbook

Currently Available, Usually Ships in 24-48 Hours


Downloadable Offline Access
  • Apple Devices
  • Android Devices
  • Windows Devices
  • Mac Devices


Used Textbook

We're Sorry
Sold Out

More New and Used
from Private Sellers
Starting at $78.50
See Prices

Questions About This Book?

Why should I rent this book?
Renting is easy, fast, and cheap! Renting from can save you hundreds of dollars compared to the cost of new or used books each semester. At the end of the semester, simply ship the book back to us with a free UPS shipping label! No need to worry about selling it back.
How do rental returns work?
Returning books is as easy as possible. As your rental due date approaches, we will email you several courtesy reminders. When you are ready to return, you can print a free UPS shipping label from our website at any time. Then, just return the book to your UPS driver or any staffed UPS location. You can even use the same box we shipped it in!
What version or edition is this?
This is the 8th edition with a publication date of 3/21/2011.
What is included with this book?
  • The New copy of this book will include any supplemental materials advertised. Please check the title of the book to determine if it should include any CDs, lab manuals, study guides, etc.
  • The Rental copy of this book is not guaranteed to include any supplemental materials. You may receive a brand new copy, but typically, only the book itself.

Related Products

  • Fundamentals of Differential Equations
    Fundamentals of Differential Equations
  • Fundamentals of Differential Equations
    Fundamentals of Differential Equations
  • Fundamentals of Differential Equations
    Fundamentals of Differential Equations
  • Fundamentals of Differential Equations bound with IDE CD (Saleable Package)
    Fundamentals of Differential Equations bound with IDE CD (Saleable Package)
  • Fundamentals of Differential Equations bound with IDE CD (Saleable Package)
    Fundamentals of Differential Equations bound with IDE CD (Saleable Package)


Fundamentals of Differential Equationspresents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Available in two versions, these flexible texts offer the instructor many choices in syllabus design, course emphasis (theory, methodology, applications, and numerical methods), and in using commercially available computer software. Fundamentals of Differential Equations, Eighth Editionis suitable for a one-semester sophomore- or junior-level course. Fundamentals of Differential Equations with Boundary Value Problems,#xA0;Sixth Edition, contains enough material for a two-semester course that covers and builds on boundary value problems. The Boundary Value Problems version consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm-Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).

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

           Chapter Summary

           Technical Writing Exercises

           Group Projects for Chapter 1

           A. Taylor Series Method

           B. Picard's Method

           C. The Phase Line


2. First-Order 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

           Chapter Summary

           Review Problems

           Technical Writing Exercises

           Group Projects for Chapter 2

           A. Oil Spill in a Canal

           B. Differential Equations in Clinical Medicine

           C. Torricelli's Law of Fluid Flow

           D. The Snowplow Problem

           E. Two Snowplows

           F. Clairaut Equations and Singular Solutions

           G. Multiple Solutions of a First-Order Initial Value Problem

           H. Utility Functions and Risk Aversion

           I. Designing a Solar Collector

           J. Asymptotic Behavior of Solutions to Linear Equations


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 Improved Euler's Method

3.7 Higher-Order Numerical Methods: Taylor and Runge-Kutta

           Group Projects for Chapter 3

           A. Dynamics of HIV Infection

           B. Aquaculture

           C. Curve of Pursuit

           D. Aircraft Guidance in a Crosswind

           E. Feedback and the Op Amp

           F. Bang-Bang Controls

           G. Market Equilibrium: Stability and Time Paths

           H. Stability of Numerical Methods

           I. Period Doubling and Chaos


4. Linear Second-Order Equations

4.1 Introduction: The Mass-Spring 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 Variable-Coefficient Equations

4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations

4.9 A Closer Look at Free Mechanical Vibrations

4.10 A Closer Look at Forced Mechanical Vibrations

           Chapter Summary

           Review Problems

           Technical Writing Exercises

           Group Projects for Chapter 4

           A. Nonlinear Equations Solvable by First-Order Techniques

           B. Apollo Reentry

           C. Simple Pendulum

           D. Linearization of Nonlinear Problems

           E. Convolution Method

           F. Undetermined Coefficients Using Complex Arithmetic

           G. Asymptotic Behavior of Solutions


5. Introduction to Systems and Phase Plane Analysis

5.1 Interconnected Fluid Tanks

5.2 Elimination Method for Systems with Constant Coefficients

5.3 Solving Systems and Higher-Order Equations Numerically

5.4 Introduction to the Phase Plane

5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models

5.6 Coupled Mass-Spring Systems

5.7 Electrical Systems

5.8 Dynamical Systems, Poincaré Maps, and Chaos

           Chapter Summary

           Review Problems

           Group Projects for Chapter 5

           A. Designing a Landing System for Interplanetary Travel

           B. Spread of Staph Infections in Hospitals-Part 1

           C. Things That Bob

           D. Hamiltonian Systems

           E. Cleaning Up the Great Lakes


6. Theory of Higher-Order 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

           Chapter Summary

           Review Problems

           Technical Writing Exercises

           Group Projects for Chapter 6

           A. Computer Algebra Systems and Exponential Shift

           B. Justifying the Method of Undetermined Coefficients

           C. Transverse Vibrations of a Beam


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 and Periodic Functions

7.7 Convolution

7.8 Impulses and the Dirac Delta Function

7.9 Solving Linear Systems with Laplace Transforms

           Chapter Summary

           Review Problems

           Technical Writing Exercises

           Group Projects for Chapter 7

           A. Duhamel's Formulas

           B. Frequency Response Modeling

           C. Determining System Parameters


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 Cauchy-Euler (Equidimensional) Equations

8.6 Method of Frobenius

8.7 Finding a Second Linearly Independent Solution

8.8 Special Functions

           Chapter Summary

           Review Problems

           Technical Writing Exercises

           Group Projects for Chapter 8

           A. Alphabetization Algorithms

           B. Spherically Symmetric Solutions to Shrödinger's Equation for the Hydrogen Atom

           C. Airy's Equation

           D. Buckling of a Tower

           E. Aging Spring and Bessel 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

           Chapter Summary

           Review Problems

           Technical Writing Exercises

           Group Projects for Chapter 9

           A. Uncoupling Normal Systems

           B. Matrix Laplace Transform Method

           C. Undamped Second-Order Systems

           D. Undetermined Coefficients for System Forced by Homogeneous


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

           Chapter Summary

           Technical Writing Exercises

           Group Projects for Chapter 10

           A. Steady-State Temperature Distribution in a Circular Cylinder

           B. A Laplace Transform Solution of the Wave Equation

           C. Green's Function

           D. Numerical Method for u=f on a Rectangle



A. Newton's Method

B. Simpson's Rule

C. Cramer's Rule

D. Method of Least Squares

E. Runge-Kutta Procedure for n Equations


Answers to Odd-Numbered Problems



Please wait while the item is added to your cart...