Fundamentals of Differential Equations 9th Edition by Kent Nagle 9780134462233 0134462238

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• ISBN 10:0134462238 

• ISBN 13:9780134462233

• Author:Kent Nagle  

Fundamentals of Differential Equations
For one-semester sophomore- or junior-level courses in Differential Equations.   An introduction to the basic theory and applications of differential equations                                                                  Fundamentals of Differential Equations 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 longer version of this text, entitled Fundamentals of Differential Equations and Boundary Value Problems, 7th Edition, contains enough material for a two-semester course. This longer text consists of the main text plus three additional chapters (Eigenvalue Problems and Sturm—Liouville Equations; Stability of Autonomous Systems; and Existence and Uniqueness Theory).   Also available with MyLab Math MyLab™ Math is an online homework, tutorial, and assessment program designed to work with this text to engage students and improve results. Within its structured environment, students practice what they learn, test their understanding, and pursue a personalized study plan that helps them absorb course material and understand difficult concepts. Note: You are purchasing a standalone product; MyLab does not come packaged with this content. Students, if interested in purchasing this title with MyLab, ask your instructor for the correct package ISBN and Course ID. Instructors, contact your Pearson representative for more information.   If you would like to purchase both the physical text and MyLab, search for: 0134768744 / 9780134768748 Fundamentals of Differential Equations plus MyLab Math with Pearson eText — Title-Specific Access Card Package, 9/e   Package consists of:    0134764838 / 9780134764832 MyLab Math with Pearson eText — Standalone Access Card — for Fundamentals of Differential Equations 0321977068 / 9780321977069 Fundamentals of Differential Equations
 

Fundamentals of Differential Equations 9th Table of contents:

 Chapter 1 Introduction
1.1 Background
1.1 Exercises
1.2 Solutions and Initial Value Problems
Solution
Solution
Solution
Solution
Solution
Solution
Solution
Solution
Solution
1.2 Exercises
1.3 Direction Fields
Solution
The Method of Isoclines
Remark
1.3 Exercises
1.4 The Approximation Method of Euler
Solution
Remark
Solution
Solution
1.4 Exercises
Chapter 1 Summary
Review Problems for Chapter 1
Technical Writing Exercises for Chapter 1
Projects for Chapter 1
A Picard’s Method
B The Phase Line
C Applications to Economics
Agrarian Economy
Growth of Capital
D Taylor Series Method
Chapter 2 First-Order Differential Equations
2.1 Introduction: Motion of a Falling Body
2.2 Separable Equations
Solution
Solution
Solution
Formal Justification of Method
2.2 Exercises
2.3 Linear Equations
Solution
Solution
Solution
2.3 Exercises
2.4 Exact Equations
Solution
2.4 Exercises
2.5 Special Integrating Factors
Solution
Solution
2.5 Exercises
2.6 Substitutions and Transformations
Homogeneous Equations
Solution
Equations of the Form dydx=G(ax+by)
Solution
Bernoulli Equations
Solution
Equations with Linear Coefficients
Solution
2.6 Exercises
Chapter 2 Summary
Review Problems for Chapter 2
Technical Writing Exercises for Chapter 2
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
Chapter 3 Mathematical Models and Numerical Methods Involving First-Order Equations
3.1 Mathematical Modeling
Formulate the Problem
Develop the Model
Test the Model
3.2 Compartmental Analysis
Mixing Problems
Solution
Solution
Population Models
Solution
Solution
3.2 Exercises
3.3 Heating and Cooling of Buildings
Solution
Solution
Solution
3.3 Exercises
3.4 Newtonian Mechanics
Solution
Solution
Solution
Solution
3.4 Exercises
3.5 Electrical Circuits
Solution
Solution
3.5 Exercises
3.6 Numerical Methods: A Closer Look At Euler’s Algorithm
Solution
Solution
3.6 Exercises
3.7 Higher-Order Numerical Methods: Taylor and Runge–Kutta
Solution
Solution
Solution
Solution
3.7 Exercises
Projects for Chapter 3
A Dynamics of HIV Infection
B Aquaculture
C Curve of Pursuit
D Aircraft Guidance in a Crosswind
E Market Equilibrium: Stability and Time Paths
F Stability of Numerical Methods
Multistep Methods
G Period Doubling and Chaos
Chapter 4 Linear Second-Order Equations
4.1 Introduction: The Mass-Spring Oscillator
Solution
Solution
Solution
Solution
4.1 Exercises
4.2 Homogeneous Linear Equations: The General Solution
Solution
Solution
Solution
Solution
4.2 Exercises
4.3 Auxiliary Equations with Complex Roots
Solution
Proof
Solution
Solution
Solution
Solution
4.3 Exercises
4.4 Nonhomogeneous Equations: the Method of Undetermined Coefficients
Solution
Solution
Solution
Solution
4.4 Exercises
4.5 The Superposition Principle and Undetermined Coefficients Revisited
Proof
Solution
Proof
Solution
Solution
Solution
Solution
Solution
4.5 Exercises
4.6 Variation of Parameters
Solution
Solution
Solution
4.6 Exercises
4.7 Variable-Coefficient Equations
Solution
Solution
Solution
Solution
Solution
4.7 Exercises
4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations
Proof
Solution
Solution
Solution
4.8 Exercises
4.9 A Closer Look at Free Mechanical Vibrations
Solution
Underdamped or Oscillatory Motion (b2<4mk)
Overdamped Motion (b2>4mk)
Critically Damped Motion (b2=4mk)
Solution
Solution
4.9 Exercises
4.10 A Closer Look at Forced Mechanical Vibrations
Solution
Solution
Solution
4.10 Exercises
Chapter 4 Summary
Homogeneous Linear Equations (Constant Coefficients)
Linearly Independent Solutions: y1, y2.
General Solution to Homogeneous Equation: c1y1+c2y2.
Form of General Solution.
Nonhomogeneous Linear Equations (Constant Coefficients)
General Solution to Nonhomogeneous Equation: yp+c1y1+c2y2.
Undetermined Coefficients: f(t)=pn(t)eαt{ cos βt sin βt }.
Variation of Parameters: y(t)=v1(t)y1(t)+v2(t)y2(t).
Superposition Principle.
Cauchy–Euler (Equidimensional) Equations
Review Problems for Chapter 4
Technical Writing Exercises for Chapter 4
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
H Gravity Train†
Chapter 5 Introduction to Systems and Phase Plane Analysis
5.1 Interconnected Fluid Tanks
5.2 Differential Operators and the Elimination Method* for Systems
Solution
Solution
Solution
Solution
Solution
5.2 Exercises
5.3 Solving Systems and Higher-Order Equations Numerically
Normal Form
Solution
Euler’s Method for Systems in Normal Form
Solution
Solution
An Application to Population Dynamics
Solution
5.3 Exercises
5.4 Introduction to the Phase Plane
Solution
Remark
Solution
5.4 Exercises
5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models
Solution
5.5 Exercises
5.6 Coupled Mass-Spring Systems
Solution
Solution
5.6 Exercises
5.7 Electrical Systems
Solution
Solution
5.7 Exercises
5.8 Dynamical Systems, Poincaré Maps, and Chaos
5.8 Exercises
Chapter 5 Summary
Review Problems for Chapter 5
Projects for Chapter 5
A Designing a Landing System for Interplanetary Travel
B Spread of Staph Infections in Hospitals—Part I
References
C Things That Bob
D Hamiltonian Systems
E Cleaning Up the Great Lakes
F The 2014-2015 Ebola Epidemic
G Phase-Locked Loops
Chapter 6 Theory of Higher-Order Linear Differential Equations
6.1 Basic Theory of Linear Differential Equations
Solution
Solution
Solution
Proof
Solution
6.1 Exercises
6.2 Homogeneous Linear Equations with Constant Coefficients
Distinct Real Roots
Solution
Complex Roots
Solution
Repeated Roots
Solution
Solution
6.2 Exercises
6.3 Undetermined Coefficients and the Annihilator Method
Solution
Solution
Solution
6.3 Exercises
6.4 Method Of Variation of Parameters
Solution
6.4 Exercises
Chapter 6 Summary
Review Problems for Chapter 6
Technical Writing Exercises for Chapter 6
Projects for Chapter 6
A Computer Algebra Systems and Exponential Shift
B Justifying the Method of Undetermined Coefficients
C Transverse Vibrations of a Beam
D Higher-Order Difference Equations
Chapter 7 Laplace Transforms
7.1 Introduction: A Mixing Problem
7.2 Definition of the Laplace Transform
Solution
Solution
Solution
Solution
Proof
Solution
Solution
Existence of the Transform
Solution
Proof
7.2 Exercises
7.3 Properties of the Laplace Transform
Proof
Solution
Proof
Solution
Solution
Proof
Solution
7.3 Exercises
7.4 Inverse Laplace Transform
Solution
Solution
Solution
Solution
1. Nonrepeated Linear Factors
Solution
2. Repeated Linear Factors
Solution
3. Quadratic Factors
Solution
7.4 Exercises
7.5 Solving Initial Value Problems
Solution
Solution
Solution
Solution
Solution
7.5 Exercises
7.6 Transforms of Discontinuous Functions
Solution
Proof
Solution
Solution
Solution
Solution
7.6 Exercises
7.7 Transforms of Periodic and Power Functions
Proof
Solution
Solution
Solution
7.7 Exercises
7.8 Convolution
Proof
Proof
Solution
Solution
Solution
Solution
7.8 Exercises
7.9 Impulses and the Dirac Delta Function
Solution
7.9 Exercises
7.10 Solving Linear Systems with Laplace Transforms
Solution
7.10 Exercises
Chapter 7 Summary
Review Problems for Chapter 7
Technical Writing Exercises for Chapter 7
Projects for Chapter 7
A Duhamel’s Formulas
B Frequency Response Modeling
C Determining System Parameters
Chapter 8 Series Solutions of Differential Equations
8.1 Introduction: The Taylor Polynomial Approximation
Solution
Solution
Solution
8.1 Exercises
8.2 Power Series and Analytic Functions
Power Series
Remark.
Solution
Solution
Shifting the Summation Index
Solution
Solution
Solution
Analytic Functions
8.2 Exercises
8.3 Power Series Solutions to Linear Differential Equations
Solution
Solution
Solution
Solution
8.3 Exercises
8.4 Equations with Analytic Coefficients
Solution
Solution
Solution
Solution
8.4 Exercises
8.5 Cauchy–Euler (Equidimensional) Equations
Solution
8.5 Exercises
8.6 Method of Frobenius
Solution
Solution
Solution
Solution
Solution
Solution
8.6 Exercises
8.7 Finding a Second Linearly Independent Solution
Solution
Solution
Solution
Solution
8.7 Exercises
8.8 Special Functions
Hypergeometric Equation
Bessel’s Equation
Legendre’s Equation
8.8 Exercises
Chapter 8 Summary
Power Series
Power Series Method for an Ordinary Point
Regular Singular Points
Method of Frobenius
Finding a Second Linearly Independent Solution
Special Functions
Review Problems for Chapter 8
Technical Writing Exercises for Chapter 8
Projects for Chapter 8
A Alphabetization Algorithms
B Spherically Symmetric Solutions to Schrödinger’s Equation for the Hydrogen Atom
C Airy’s Equation
D Buckling of a Tower
E Aging Spring and Bessel Functions
Chapter 9 Matrix Methods for Linear Systems
9.1 Introduction
Solution
Solution
Solution
9.1 Exercises
9.2 Review 1: Linear Algebraic Equations
Solution
Solution
Solution
Solution
9.2 Exercises
9.3 Review 2: Matrices and Vectors
Algebra of Matrices
Matrix Addition and Scalar Multiplication.
Properties of Matrix Addition and Scalar Multiplication.
Matrix Multiplication.
Matrices as Linear Operators.
The Matrix Formulation of Linear Algebraic Systems.
Matrix Transpose.
Matrix Identity.
Matrix Inverse.
Finding the Inverse of a Matrix.
Solution
Determinants.
Calculus of Matrices
Solution
Solution
9.3 Exercises
9.4 Linear Systems in Normal Form
Solution
Solution
Solution
Solution
9.4 Exercises
9.5 Homogeneous Linear Systems with Constant Coefficients
Solution
Solution
Proof
Solution
Proof
Solution
Solution
9.5 Exercises
9.6 Complex Eigenvalues
Solution
Solution
9.6 Exercises
9.7 Nonhomogeneous Linear Systems
Undetermined Coefficients
Solution
Variation of Parameters
Solution
9.7 Exercises
9.8 The Matrix Exponential Function
Proof
Solution
Solution
9.8 Exercises
Chapter 9 Summary
Homogeneous Normal Systems
Fundamental Solution Set:
Fundamental Matrix:
General Solution to Homogeneous System:
Homogeneous Systems with Constant Coefficients.
Nonhomogeneous Normal Systems
General Solution to Nonhomogeneous System:
Undetermined Coefficients.
Variation of Parameters:
Matrix Exponential Function
Generalized Eigenvectors
Review Problems for Chapter 9
Technical Writing Exercises for Chapter 9
Projects for Chapter 9
A Uncoupling Normal Systems
B Matrix Laplace Transform Method
C Undamped Second-Order Systems
Chapter 10 Partial Differential Equations
10.1 Introduction: A Model for Heat Flow
10.2 Method of Separation of Variables
Solution
Solution
10.2 Exercises
10.3 Fourier Series
Solution
Solution
Solution
Solution
Solution
Orthogonal Expansions
Convergence of Fourier Series
Solution
10.3 Exercises
10.4 Fourier Cosine and Sine Series
Solution
Solution
10.4 Exercises
10.5 The Heat Equation
Solution
Solution
Solution
Solution
Existence and Uniqueness of Solutions
Proof
10.5 Exercises
10.6 The Wave Equation
Solution
Solution
Solution
Solution
Existence and Uniqueness of Solutions
Proof
10.6 Exercises
10.7 Laplace’s Equation
Solution
Solution
Solution
Existence and Uniqueness of Solutions
10.7 Exercises
Chapter 10 Summary
Separation of Variables.
Fourier Series.
Technical Writing Exercises for Chapter 10
Projects for Chapter 10
A Steady-State Temperature Distribution in a Circular Cylinder
B Laplace Transform Solution of the Wave Equation
C Green’s Function
D Numerical Method for Δu=f on α Rectangle
E The Telegrapher’s Equation and the Cable Equation
Appendices
Appendix A Review of Integration Techniques
Differentiation
Method of Substitution

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