Author(s): Kenneth B. Howell
Series: 1
Publisher: CRC Press
Year: 2012
Language: English
Pages: 864
Front Cover......Page 1
Table of Contents......Page 6
Preface (with Important Information for the Reader)......Page 14
Part I: The Basics......Page 16
Chapter 1: The Starting Point: Basic Concepts and Terminology......Page 18
Chapter 2: Integration and Differential Equations......Page 36
Part II: First-Order Equations......Page 52
Chapter 3: Some Basics about First-Order Equations......Page 54
Chapter 4: Separable First-Order Equations......Page 82
Chapter 5: Linear First-Order Equations......Page 110
Chapter 6: Simplifying Through Substitution......Page 122
Chapter 7: The Exact Form and General Integrating Factors......Page 134
Chapter 8: Slope Fields: Graphing Solutions Without the Solutions......Page 160
Chapter 9: Euler's Numerical Method......Page 192
Chapter 10: The Art and Science of Modeling with First-Order Equations......Page 212
Part III: Second- and Higher-Order Equations......Page 240
Chapter 11: Higher-Order Equations: Extending First-Order Concepts......Page 242
Chapter 12: Higher-Order Linear Equations and the Reduction of Order Method......Page 260
Chapter 13: General Solutions to Homogeneous Linear Differential Equations......Page 276
Chapter 14: Verifying the Big Theorems and an Introduction to Differential Operators......Page 296
Chapter 15: Second-Order Homogeneous Linear Equations with Constant Coefficients......Page 314
Chapter 16: Springs: Part I......Page 334
Chapter 17: Arbitrary Homogeneous Linear Equations with Constant Coefficients......Page 350
Chapter 18: Euler Equations......Page 370
Chapter 19: Nonhomogeneous Equations in General......Page 384
Chapter 20: Method of Undetermined Coefficients (aka: Method of Educated Guess)......Page 396
Chapter 21: Springs: Part II......Page 416
Chapter 22: Variation of Parameters (A Better Reduction of Order Method)......Page 432
Part IV: The Laplace Transform......Page 448
Chapter 23: The Laplace Transform (Intro)......Page 450
Chapter 24: Differentiation and the Laplace Transform......Page 480
Chapter 25: The Inverse Laplace Transform......Page 498
Chapter 26: Convolution......Page 510
Chapter 27: Piecewise-Defined Functions and Periodic Functions......Page 524
Chapter 28: Delta Functions......Page 556
Part V: Power Series and Modified Power Series Solutions......Page 574
Chapter 29: Series Solutions: Preliminaries......Page 576
Chapter 30: Power Series Solutions I: Basic Computational Methods......Page 602
Chapter 31: Power Series Solutions II: Generalizations and Theory......Page 646
Chapter 32: Modified Power Series Solutions and the Basic Method of Frobenius......Page 682
Chapter 33: The Big Theorem on the Frobenius Method, with Applications......Page 720
Chapter 34: Validating the Method of Frobenius......Page 744
Part VI: Systems of Differential Equations (A Brief Introduction)......Page 764
Chapter 35: Systems of Differential Equations: A Starting Point......Page 766
Chapter 36: Critical Points, Direction Fields and Trajectories......Page 790
Appendix: Author’s Guide to Using This Text......Page 822
Answers to Selected Exercises......Page 832
Back Cover......Page 864
