Differential Equations With Boundary-value Problems With Ilrn Tutorial
by Zill, Dennis G.; Cullen, Michael R.Edition: 6th
Format: Paperback
Pub. Date: 2004-10-19
Publisher(s): Brooks Cole
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Summary
Now enhanced with the innovative DE Tools CD-ROM and the iLrn teaching and learning system, this proven text explains the "how" behind the material and strikes a balance between the analytical, qualitative, and quantitative approaches to the study of differential equations. This accessible text speaks to students through a wealth of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and group projects. This book was written with the student's understanding firmly in mind. Using a straightforward, readable, and helpful style, this book provides a thorough treatment of boundary-value problems and partial differential equations.
Table of Contents
| Preface | p. xi |
| Acknowledgments | p. xv |
| Introduction to Differential Equations | p. 1 |
| Definitions and Terminology | p. 2 |
| Initial-Value Problems | p. 15 |
| Differential Equations as Mathematical Models | p. 22 |
| Chapter 1 in Review | p. 37 |
| First-Order Differential Equations | p. 39 |
| Solution Curves Without the Solution | p. 40 |
| Separable Variables | p. 51 |
| Linear Equations | p. 60 |
| Exact Equations | p. 72 |
| Solutions by Substitutions | p. 80 |
| A Numerical Solution | p. 86 |
| Chapter 2 in Review | p. 92 |
| Modeling with First-Order Differential Equations | p. 95 |
| Linear Equations | p. 96 |
| Nonlinear Equations | p. 109 |
| Systems of Linear and Nonlinear Differential Equations | p. 121 |
| Chapter 3 in Review | p. 130 |
| Project Module: Harvesting of Renewable Natural Resources | p. 133 |
| Higher-Order Differential Equations | p. 138 |
| Preliminary Theory: Linear Equations | p. 139 |
| Initial-Value and Boundary-Value Problems | p. 139 |
| Homogeneous Equations | p. 142 |
| Nonhomogeneous Equations | p. 148 |
| Reduction of Order | p. 154 |
| Homogeneous Linear Equations with Constant Coefficients | p. 158 |
| Undetermined Coefficients--Superposition Approach | p. 167 |
| Undetermined Coefficients--Annihilator Approach | p. 178 |
| Variation of Parameters | p. 188 |
| Cauchy-Euler Equation | p. 193 |
| Solving Systems of Linear Equations by Elimination | p. 201 |
| Nonlinear Equations | p. 207 |
| Chapter 4 in Review | p. 212 |
| Modeling with Higher-Order Differential Equations | p. 215 |
| Linear Equations: Initial-Value Problems | p. 216 |
| Spring/Mass Systems: Free Undamped Motion | p. 216 |
| Spring/Mass Systems: Free Damped Motion | p. 220 |
| Spring/Mass Systems: Driven Motion | p. 224 |
| Series Circuit Analogue | p. 227 |
| Linear Equations: Boundary-Value Problems | p. 237 |
| Nonlinear Equations | p. 247 |
| Chapter 5 in Review | p. 259 |
| Project Module: The Collapse of the Tacoma Narrows Suspension Bridge | p. 263 |
| Series Solutions of Linear Equations | p. 267 |
| Solutions About Ordinary Points | p. 268 |
| Review of Power Series | p. 268 |
| Power Series Solutions | p. 271 |
| Solutions About Singular Points | p. 280 |
| Two Special Equations | p. 292 |
| Chapter 6 in Review | p. 304 |
| The Laplace Transform | p. 306 |
| Definition of the Laplace Transform | p. 307 |
| Inverse Transform and Transforms of Derivatives | p. 314 |
| Translation Theorems | p. 324 |
| Translation on the s-Axis | p. 324 |
| Translation on the t-Axis | p. 328 |
| Additional Operational Properties | p. 338 |
| Dirac Delta Function | p. 351 |
| Systems of Linear Equations | p. 354 |
| Chapter 7 in Review | p. 361 |
| Systems of Linear First-Order Differential Equations | p. 364 |
| Preliminary Theory | p. 365 |
| Homogeneous Linear Systems with Constant Coefficients | p. 375 |
| Distinct Real Eigenvalues | p. 376 |
| Repeated Eigenvalues | p. 380 |
| Complex Eigenvalues | p. 384 |
| Variation of Parameters | p. 393 |
| Matrix Exponential | p. 399 |
| Chapter 8 in Review | p. 404 |
| Project Module: Earthquake Shaking of Multistory Buildings | p. 406 |
| Numerical Solutions of Ordinary Differential Equations | p. 410 |
| Euler Methods and Error Analysis | p. 411 |
| Runge-Kutta Methods | p. 417 |
| Multistep Methods | p. 424 |
| Higher-Order Equations and Systems | p. 427 |
| Second-Order Boundary-Value Problems | p. 433 |
| Chapter 9 in Review | p. 438 |
| Plane Autonomous Systems and Stability | p. 439 |
| Autonomous Systems, Critical Points, and Periodic Solutions | p. 440 |
| Stability of Linear Systems | p. 448 |
| Linearization and Local Stability | p. 458 |
| Modeling Using Autonomous Systems | p. 470 |
| Chapter 10 in Review | p. 480 |
| Orthogonal Functions and Fourier Series | p. 483 |
| Orthogonal Functions | p. 484 |
| Fourier Series | p. 489 |
| Fourier Cosine and Sine Series | p. 495 |
| Sturm-Liouville Problem | p. 504 |
| Bessel and Legendre Series | p. 511 |
| Fourier-Bessel Series | p. 512 |
| Fourier-Legendre Series | p. 515 |
| Chapter 11 in Review | p. 519 |
| Partial Differential Equations and Boundary-Value Problems in Rectangular Coordinates | p. 521 |
| Separable Partial Differential Equations | p. 522 |
| Classical Equations and Boundary-Value Problems | p. 527 |
| Heat Equation | p. 533 |
| Wave Equation | p. 536 |
| Laplace's Equation | p. 542 |
| Nonhomogeneous Equations and Boundary Conditions | p. 547 |
| Orthogonal Series Expansions | p. 551 |
| Boundary-Value Problems Involving Fourier Series in Two Variables | p. 555 |
| Chapter 12 in Review | p. 559 |
| Boundary-Value Problems in other Coordinate Systems | p. 561 |
| Problems Involving Laplace's Equation in Polar Coordinates | p. 562 |
| Problems in Polar and Cylindrical Coordinates: Bessel Functions | p. 567 |
| Problems in Spherical Coordinates: Legendre Polynomials | p. 575 |
| Chapter 13 in Review | p. 578 |
| Integral Transform Method | p. 581 |
| Error Function | p. 582 |
| Applications of the Laplace Transform | p. 584 |
| Fourier Integral | p. 595 |
| Fourier Transforms | p. 601 |
| Chapter 14 in Review | p. 607 |
| Numerical Solutions of Partial Differential Equations | p. 610 |
| Elliptic Equations | p. 611 |
| Parabolic Equations | p. 617 |
| Hyperbolic Equations | p. 625 |
| Chapter 15 in Review | p. 630 |
| Appendixes | p. 1 |
| Gamma Function | p. 1 |
| Introduction to Matrices | p. 3 |
| Laplace Transforms | p. 25 |
| Selected Answers for Odd-Numbered Problems | p. 1 |
| Index | p. 1 |
| Table of Contents provided by Syndetics. All Rights Reserved. |
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