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Fundamentals of Differential Equations Loose-Leaf Edition Plus Mylab Math with Pearson Etext - 18-Week Access Card Package 9th ed. [Multiple-component retail product]

Arthur David Snider, Edward Saff, R Nagle, Arthur Snider

Formaat: Multiple-component retail product, kõrgus x laius x paksus: 254x203x28 mm, kaal: 1315 g, Contains 1 Loose-leaf and 1 Digital online
Ilmumisaeg: 21-Jul-2019
Kirjastus: Pearson
ISBN-10: 0135997909
ISBN-13: 9780135997901

Teised raamatud teemal:

Mathematics - (Hetkel poes: 12 nimetust)

Multiple-component retail product
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Formaat: Multiple-component retail product, kõrgus x laius x paksus: 254x203x28 mm, kaal: 1315 g, Contains 1 Loose-leaf and 1 Digital online
Ilmumisaeg: 21-Jul-2019
Kirjastus: Pearson
ISBN-10: 0135997909
ISBN-13: 9780135997901

Teised raamatud teemal:

Mathematics - (Hetkel poes: 12 nimetust)

Püsilink: https://www.kriso.ee/db/9780135997901.html

For one-semeseter sophomore- or junior-level courses in Differential Equations.

Fundamentals of Differential Equations presents the basic theory of differential equations and offers a variety of modern applications in science and engineering. Also available in the version Fundamentals of Differential Equations with Boundary Value Problems, 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.

Chapter 1 Introduction

1.1 Background

(5)

1.2 Solutions and Initial Value Problems

(9)

1.3 Direction Fields

(8)

1.4 The Approximation Method of Euler

(15)

Chapter Summary

(1)

Review Problems for
Chapter 1

(2)

Technical Writing Exercises for
Chapter 1

(1)

Projects for
Chapter 1

(1)

A Picard's Method

(1)

B The Phase Line

(2)

C Applications to Economics

(1)

D Taylor Series Method

(2)

Chapter 2 First-Order Differential Equations

2.1 Introduction: Motion of a Falling Body

(3)

2.2 Separable Equations

(7)

2.3 Linear Equations

(9)

2.4 Exact Equations

(9)

2.5 Special Integrating Factors

(4)

2.6 Substitutions and Transformations

(20)

Chapter Summary

(1)

Review Problems for
Chapter 2

(1)

Technical Writing Exercises for
Chapter 2

(1)

Projects for
Chapter 2

(1)

A Oil Spill in a Canal

(1)

B Differential Equations in Clinical Medicine

(2)

C Torricelli's Law of Fluid Flow

(1)

D The Snowplow Problem

(1)

E Two Snowplows

(1)

F Clairaut Equations and Singular Solutions

(1)

G Multiple Solutions of a First-Order Initial Value Problem

(1)

H Utility Functions and Risk Aversion

(1)

I Designing a Solar Collector

(1)

J Asymptotic Behavior of Solutions to Linear Equations

(2)

Chapter 3 Mathematical Models and Numerical Methods Involving First-Order Equations

3.1 Mathematical Modeling

(2)

3.2 Compartmental Analysis

(10)

3.3 Heating and Cooling of Buildings

102

(7)

3.4 Newtonian Mechanics

109

(9)

3.5 Electrical Circuits

118

(3)

3.6 Numerical Methods: A Closer Look At Euler's Algorithm

121

(11)

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

132

(20)

Projects for
Chapter 3

141

(1)

A Dynamics of HIV Infection

141

(3)

B Aquaculture

144

(1)

C Curve of Pursuit

145

(1)

D Aircraft Guidance in a Crosswind

146

(1)

E Market Equilibrium: Stability and Time Paths

147

(1)

F Stability of Numerical Methods

148

(2)

G Period Doubling and Chaos

150

(2)

Chapter 4 Linear Second-Order Equations

4.1 Introduction: The Mass-Spring Oscillator

152

(5)

4.2 Homogeneous Linear Equations: The General Solution

157

(8)

4.3 Auxiliary Equations with Complex Roots

165

(9)

4.4 Nonhomogeneous Equations: the Method of Undetermined Coefficients

174

(6)

4.5 The Superposition Principle and Undetermined Coefficients Revisited

180

(7)

4.6 Variation of Parameters

187

(5)

4.7 Variable-Coefficient Equations

192

(9)

4.8 Qualitative Considerations for Variable-Coefficient and Nonlinear Equations

201

(11)

4.9 A Closer Look at Free Mechanical Vibrations

212

(9)

4.10 A Closer Look at Forced Mechanical Vibrations

221

(20)

Chapter Summary

229

(2)

Review Problems for
Chapter 4

231

(1)

Technical Writing Exercises for
Chapter 4

232

(1)

Projects for
Chapter 4

233

(1)

A Nonlinear Equations Solvable by First-Order Techniques

233

(1)

B Apollo Reentry

234

(1)

C Simple Pendulum

235

(1)

D Linearization of Nonlinear Problems

236

(1)

E Convolution Method

237

(1)

F Undetermined Coefficients Using Complex Arithmetic

237

(2)

G Asymptotic Behavior of Solutions

239

(1)

H Gravity Train

240

(1)

Chapter 5 Introduction to Systems and Phase Plane Analysis

5.1 Interconnected Fluid Tanks

241

(2)

5.2 Differential Operators and the Elimination Method for Systems

243

(9)

5.3 Solving Systems and Higher-Order Equations Numerically

252

(9)

5.4 Introduction to the Phase Plane

261

(13)

5.5 Applications to Biomathematics: Epidemic and Tumor Growth Models

274

(9)

5.6 Coupled Mass-Spring Systems

283

(6)

5.7 Electrical Systems

289

(6)

5.8 Dynamical Systems, Poincare Maps, and Chaos

295

(24)

Chapter Summary

304

(2)

Review Problems for
Chapter 5

306

(1)

Projects for
Chapter 5

307

(1)

A Designing a Landing System for Interplanetary Travel

307

(1)

B Spread of Staph Infections in Hospitals---Part I

308

(2)

C Things That Bob

310

(1)

D Hamiltonian Systems

311

(2)

E Cleaning Up the Great Lakes

313

(1)

F The 2014--2015 Ebola Epidemic

314

(3)

G Phase-Locked Loops

317

(2)

Chapter 6 Theory of Higher-Order Linear Differential Equations

6.1 Basic Theory of Linear Differential Equations

319

(8)

6.2 Homogeneous Linear Equations with Constant Coefficients

327

(7)

6.3 Undetermined Coefficients and the Annihilator Method

334

(4)

6.4 Method Of Variation of Parameters

338

(12)

Chapter Summary

342

(1)

Review Problems for
Chapter 6

343

(1)

Technical Writing Exercises for
Chapter 6

344

(1)

Projects for
Chapter 6

345

(1)

A Computer Algebra Systems and Exponential Shift

345

(1)

B Justifying the Method of Undetermined Coefficients

346

(1)

C Transverse Vibrations of a Beam

347

(1)

D Higher-Order Difference Equations

347

(3)

Chapter 7 Laplace Transforms

7.1 Introduction: A Mixing Problem

350

(3)

7.2 Definition of the Laplace Transform

353

(8)

7.3 Properties of the Laplace Transform

361

(5)

7.4 Inverse Laplace Transform

366

(10)

7.5 Solving Initial Value Problems

376

(7)

7.6 Transforms of Discontinuous Functions

383

(9)

7.7 Transforms of Periodic and Power Functions

392

(5)

7.8 Convolution

397

(8)

7.9 Impulses and the Dirac Delta Function

405

(7)

7.10 Solving Linear Systems with Laplace Transforms

412

(9)

Chapter Summary

414

(1)

Review Problems for
Chapter 7

415

(1)

Technical Writing Exercises for
Chapter 7

416

(1)

Projects for
Chapter 7

417

(1)

A Duhamel's Formulas

417

(1)

B Frequency Response Modeling

418

(2)

C Determining System Parameters

420

(1)

Chapter 8 Series Solutions of Differential Equations

8.1 Introduction: The Taylor Polynomial Approximation

421

(5)

8.2 Power Series and Analytic Functions

426

(9)

8.3 Power Series Solutions to Linear Differential Equations

435

(10)

8.4 Equations with Analytic Coefficients

445

(5)

8.5 Cauchy--Euler (Equidimensional) Equations

450

(4)

8.6 Method of Frobenius

454

(11)

8.7 Finding a Second Linearly Independent Solution

465

(9)

8.8 Special Functions

474

(22)

Chapter Summary

487

(2)

Review Problems for
Chapter 8

489

(1)

Technical Writing Exercises for
Chapter 8

490

(1)

Projects for
Chapter 8

491

(1)

A Alphabetization Algorithms

491

(1)

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

492

(1)

C Airy's Equation

493

(1)

D Buckling of a Tower

493

(2)

E Aging Spring and Bessel Functions

495

(1)

Chapter 9 Matrix Methods for Linear Systems

9.1 Introduction

496

(4)

9.2 Review 1: Linear Algebraic Equations

500

(4)

9.3 Review 2: Matrices and Vectors

504

(11)

9.4 Linear Systems in Normal Form

515

(8)

9.5 Homogeneous Linear Systems with Constant Coefficients

523

(11)

9.6 Complex Eigenvalues

534

(4)

9.7 Nonhomogeneous Linear Systems

538

(7)

9.8 The Matrix Exponential Function

545

(15)

Chapter Summary

553

(2)

Review Problems for
Chapter 9

555

(1)

Technical Writing Exercises for
Chapter 9

556

(1)

Projects for
Chapter 9

557

(1)

A Uncoupling Normal Systems

557

(1)

B Matrix Laplace Transform Method

558

(1)

C Undamped Second-Order Systems

559

(1)

Chapter 10 Partial Differential Equations

10.1 Introduction: A Model for Heat Flow

560

(3)

10.2 Method of Separation of Variables

563

(8)

10.3 Fourier Series

571

(16)

10.4 Fourier Cosine and Sine Series

587

(5)

10.5 The Heat Equation

592

(12)

10.6 The Wave Equation

604

(12)

10.7 Laplace's Equation

616

(12)

Chapter Summary

628

(2)

Technical Writing Exercises for
Chapter 10

630

(1)

Projects for
Chapter 10

631

(1)

A Steady-State Temperature Distribution in a Circular Cylinder

631

(2)

B Laplace Transform Solution of the Wave Equation

633

(1)

C Green's Function

634

(1)

D Numerical Method for Δu --- ƒ on α Rectangle

635

(2)

E The Telegrapher's Equation and the Cable Equation

637

Appendices

A Review of Integration Techniques

(8)

B Newton's Method

(2)

C Simpson's Rule

(2)

D Cramer's Rule

(1)

E Method of Least Squares

(2)

F Runge--Kutta Procedure for n Equations

(1)

G Software for Analyzing Differential Equations

Answers to Odd-Numbered Problems

(1)

Index

Fundamentals of Differential Equations Loose-Leaf Edition Plus Mylab Math with Pearson Etext - 18-Week Access Card Package 9th ed. [Multiple-component retail product]

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