Fundamentals of Differential Equations with Boundary Value Problems, 7th edition
Your access includes:
 Search, highlight, and take notes
 Easily create flashcards
 Use the app for access anywhere
 14day refund guarantee
$10.99per month
4month term, pay monthly or pay $43.96
Learn more, spend less

Listen on the go
Learn how you like with full eTextbook audio

Special partners and offers
Enjoy perks from special partners and offers for students

Find it fast
Quickly navigate your eTextbook with search

Stay organized
Access all your eTextbooks in one place

Easily continue access
Keep learning with autorenew
Overview
Fundamentals of Differential Equations and Boundary Value Problems presents the basic theory of differential equations along with modern applications in science and engineering. It adapts to various course emphases (theory, methodology, applications, numerical methods) and to use of commercially available software.
Published by Pearson (January 1st 2021)  Copyright © 2022
ISBN13: 9780137394524
Subject: Advanced Math
Category: Differential Equations
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 Improved Euler’s Method
 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 Elimination Method for Systems with Constant Coefficients
 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
Your questions answered
Pearson+ is your onestop shop, with eTextbooks and study videos designed to help students get better grades in college.
A Pearson eTextbook is an easy‑to‑use digital version of the book. You'll get upgraded study tools, including enhanced search, highlights and notes, flashcards and audio. Plus learn on the go with the Pearson+ app.
Your eTextbook subscription gives you access for 4 months. You can make a one‑time payment for the initial 4‑month term or pay monthly. If you opt for monthly payments, we will charge your payment method each month until your 4‑month term ends. You can turn on auto‑renew in My account at any time to continue your subscription before your 4‑month term ends.
When you purchase an eTextbook subscription, it will last 4 months. You can renew your subscription by selecting Extend subscription on the Manage subscription page in My account before your initial term ends.
If you extend your subscription, we'll automatically charge you every month. If you made a one‑time payment for your initial 4‑month term, you'll now pay monthly. To make sure your learning is uninterrupted, please check your card details.
To avoid the next payment charge, select Cancel subscription on the Manage subscription page in My account before the renewal date. You can subscribe again in the future by purchasing another eTextbook subscription.
Channels is a video platform with thousands of explanations, solutions and practice problems to help you do homework and prep for exams. Videos are personalized to your course, and tutors walk you through solutions. Plus, interactive AI‑powered summaries and a social community help you better understand lessons from class.
Channels is an additional tool to help you with your studies. This means you can use Channels even if your course uses a non‑Pearson textbook.
When you choose a Channels subscription, you're signing up for a 1‑month, 3‑month or 12‑month term and you make an upfront payment for your subscription. By default, these subscriptions auto‑renew at the frequency you select during checkout.
When you purchase a Channels subscription it will last 1 month, 3 months or 12 months, depending on the plan you chose. Your subscription will automatically renew at the end of your term unless you cancel it.
We use your credit card to renew your subscription automatically. To make sure your learning is uninterrupted, please check your card details.