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This Fourth Edition of the expanded version of Zill's best-selling A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS places an even greater emphasis on modeling and the use of technology in problem solving and now features more everyday applications. Both Zill texts are identical through the first nine chapters, but this version includes six additional chapters that provide in-depth coverage of boundary-value problem-solving and partial differential equations, subjects just introduced in the shorter text. Previous editions of these two texts have enjoyed such great success in part because the authors pique students' interest with special features and in-text aids. Pre-publication reviewers also praise the authors' accessible writing style and the text's organization, which makes it easy to teach from and easy for students to understand and use. Understandable, step-by-step solutions are provided for every example. And this edition makes an even greater effort to show students how the mathematical concepts have relevant, everyday applications. Among the boundary-value related topics covered in this expanded text are: plane autonomous systems and stability; orthogonal functions; Fourier series; the Laplace transform; and elliptic, parabolic, and hyperparabolic partial differential equations, and their applications.

Tabla de contenidos provista por Syndetics

• Preface(p. xi)
• Acknowledgments(p. xv)
• 1 Introduction to Differential Equations(p. 1)
• 1.1 Definitions and Terminology(p. 2)
• 1.2 Initial-Value Problems(p. 15)
• 1.3 Differential Equations as Mathematical Models(p. 22)
• Chapter 1 in Review(p. 37)
• 2 First-Order Differential Equations(p. 39)
• 2.1 Solution Curves Without the Solution(p. 40)
• 2.2 Separable Variables(p. 51)
• 2.3 Linear Equations(p. 60)
• 2.4 Exact Equations(p. 72)
• 2.5 Solutions by Substitutions(p. 80)
• 2.6 A Numerical Solution(p. 86)
• Chapter 2 in Review(p. 92)
• 3 Modeling with First-Order Differential Equations(p. 95)
• 3.1 Linear Equations(p. 96)
• 3.2 Nonlinear Equations(p. 109)
• 3.3 Systems of Linear and Nonlinear Differential Equations(p. 121)
• Chapter 3 in Review(p. 130)
• Project Module: Harvesting of Renewable Natural Resources(p. 133)
• 4 Higher-Order Differential Equations(p. 138)
• 4.1 Preliminary Theory: Linear Equations(p. 139)
• 4.1.1 Initial-Value and Boundary-Value Problems(p. 139)
• 4.1.2 Homogeneous Equations(p. 142)
• 4.1.3 Nonhomogeneous Equations(p. 148)
• 4.2 Reduction of Order(p. 154)
• 4.3 Homogeneous Linear Equations with Constant Coefficients(p. 158)
• 4.4 Undetermined Coefficients--Superposition Approach(p. 167)
• 4.5 Undetermined Coefficients--Annihilator Approach(p. 178)
• 4.6 Variation of Parameters(p. 188)
• 4.7 Cauchy-Euler Equation(p. 193)
• 4.8 Solving Systems of Linear Equations by Elimination(p. 201)
• 4.9 Nonlinear Equations(p. 207)
• Chapter 4 in Review(p. 212)
• 5 Modeling with Higher-Order Differential Equations(p. 215)
• 5.1 Linear Equations: Initial-Value Problems(p. 216)
• 5.1.1 Spring/Mass Systems: Free Undamped Motion(p. 216)
• 5.1.2 Spring/Mass Systems: Free Damped Motion(p. 220)
• 5.1.3 Spring/Mass Systems: Driven Motion(p. 224)
• 5.1.4 Series Circuit Analogue(p. 227)
• 5.2 Linear Equations: Boundary-Value Problems(p. 237)
• 5.3 Nonlinear Equations(p. 247)
• Chapter 5 in Review(p. 259)
• Project Module: The Collapse of the Tacoma Narrows Suspension Bridge(p. 263)
• 6 Series Solutions of Linear Equations(p. 267)
• 6.1 Solutions About Ordinary Points(p. 268)
• 6.1.1 Review of Power Series(p. 268)
• 6.1.2 Power Series Solutions(p. 271)
• 6.2 Solutions About Singular Points(p. 280)
• 6.3 Two Special Equations(p. 292)
• Chapter 6 in Review(p. 304)
• 7 The Laplace Transform(p. 306)
• 7.1 Definition of the Laplace Transform(p. 307)
• 7.2 Inverse Transform and Transforms of Derivatives(p. 314)
• 7.3 Translation Theorems(p. 324)
• 7.3.1 Translation on the s-Axis(p. 324)
• 7.3.2 Translation on the t-Axis(p. 328)
• 7.4 Additional Operational Properties(p. 338)
• 7.5 Dirac Delta Function(p. 351)
• 7.6 Systems of Linear Equations(p. 354)
• Chapter 7 in Review(p. 361)
• 8 Systems of Linear First-Order Differential Equations(p. 364)
• 8.1 Preliminary Theory(p. 365)
• 8.2 Homogeneous Linear Systems with Constant Coefficients(p. 375)
• 8.2.1 Distinct Real Eigenvalues(p. 376)
• 8.2.2 Repeated Eigenvalues(p. 380)
• 8.2.3 Complex Eigenvalues(p. 384)
• 8.3 Variation of Parameters(p. 393)
• 8.4 Matrix Exponential(p. 399)
• Chapter 8 in Review(p. 404)
• Project Module: Earthquake Shaking of Multistory Buildings(p. 406)
• 9 Numerical Solutions of Ordinary Differential Equations(p. 410)
• 9.1 Euler Methods and Error Analysis(p. 411)
• 9.2 Runge-Kutta Methods(p. 417)
• 9.3 Multistep Methods(p. 424)
• 9.4 Higher-Order Equations and Systems(p. 427)
• 9.5 Second-Order Boundary-Value Problems(p. 433)
• Chapter 9 in Review(p. 438)
• 10 Plane Autonomous Systems and Stability(p. 439)
• 10.1 Autonomous Systems, Critical Points, and Periodic Solutions(p. 440)
• 10.2 Stability of Linear Systems(p. 448)
• 10.3 Linearization and Local Stability(p. 458)
• 10.4 Modeling Using Autonomous Systems(p. 470)
• Chapter 10 in Review(p. 480)
• 11 Orthogonal Functions and Fourier Series(p. 483)
• 11.1 Orthogonal Functions(p. 484)
• 11.2 Fourier Series(p. 489)
• 11.3 Fourier Cosine and Sine Series(p. 495)
• 11.4 Sturm-Liouville Problem(p. 504)
• 11.5 Bessel and Legendre Series(p. 511)
• 11.5.1 Fourier-Bessel Series(p. 512)
• 11.5.2 Fourier-Legendre Series(p. 515)
• Chapter 11 in Review(p. 519)
• 12 Partial Differential Equations and Boundary-Value Problems in Rectangular Coordinates(p. 521)
• 12.1 Separable Partial Differential Equations(p. 522)
• 12.2 Classical Equations and Boundary-Value Problems(p. 527)
• 12.3 Heat Equation(p. 533)
• 12.4 Wave Equation(p. 536)
• 12.5 Laplace's Equation(p. 542)
• 12.6 Nonhomogeneous Equations and Boundary Conditions(p. 547)
• 12.7 Orthogonal Series Expansions(p. 551)
• 12.8 Boundary-Value Problems Involving Fourier Series in Two Variables(p. 555)
• Chapter 12 in Review(p. 559)
• 13 Boundary-Value Problems in other Coordinate Systems(p. 561)
• 13.1 Problems Involving Laplace's Equation in Polar Coordinates(p. 562)
• 13.2 Problems in Polar and Cylindrical Coordinates: Bessel Functions(p. 567)
• 13.3 Problems in Spherical Coordinates: Legendre Polynomials(p. 575)
• Chapter 13 in Review(p. 578)
• 14 Integral Transform Method(p. 581)
• 14.1 Error Function(p. 582)
• 14.2 Applications of the Laplace Transform(p. 584)
• 14.3 Fourier Integral(p. 595)
• 14.4 Fourier Transforms(p. 601)
• Chapter 14 in Review(p. 607)
• 15 Numerical Solutions of Partial Differential Equations(p. 610)
• 15.1 Elliptic Equations(p. 611)
• 15.2 Parabolic Equations(p. 617)
• 15.3 Hyperbolic Equations(p. 625)
• Chapter 15 in Review(p. 630)
• Appendixes(p. 1)
• I Gamma Function(p. 1)
• II Introduction to Matrices(p. 3)
• III Laplace Transforms(p. 25)
• Selected Answers for Odd-Numbered Problems(p. 1)
• Index(p. 1)