A First Course in Differential Equations with Modeling Applications

Description

Straightforward and easy to read, A FIRST COURSE IN DIFFERENTIAL EQUATIONS WITH MODELING APPLICATIONS, 11th Edition, gives you a thorough overview of the topics typically taught in a first course in differential equations. Your study of differential equations and its applications will be supported by a bounty of pedagogical aids, including an abundance of examples, explanations, "Remarks" boxes, definitions, and MindTap Math - an available option which includes an online version of the book, lecture videos, a pre-course assessment, and more. Cover Contents Preface Chapter 1: Introduction to Differential Equations 1.1 De˜nitions and Terminology 1.2 Initial-Value Problems 1.3 Differential Equations as Mathematical Models Chapter 1 In Review Chapter 2: First-Order Differential Equations 2.1 Solution Curves Without a Solution 2.1.1 Direction Fields 2.1.2 Autonomous First-Order DEs 2.2 Separable Equations 2.3 Linear Equations 2.4 Exact Equations 2.5 Solutions by Substitutions 2.6 A Numerical Method Chapter 2 In Review Chapter 3: Modeling with First-Order Differential Equations 3.1 Linear Models 3.2 Nonlinear Models 3.3 Modeling with Systems of First-Order DEs Chapter 3 In Review Chapter 4: Higher-Order Differential Equations 4.1 Preliminary Theory—Linear Equations 4.1.1 Initial-Value and Boundary-Value Problems 4.1.2 Homogeneous Equations 4.1.3 Nonhomogeneous Equations 4.2 Reduction of Order 4.3 Homogeneous Linear Equations with Constant Coef˜cients 4.4 Undetermined Coefcients—Superposition Approach 4.5 Undetermined Coefcients—Annihilator Approach 4.6 Variation of Parameters 4.7 Cauchy-Euler Equations 4.8 Green’s Functions 4.8.1 Initial-Value Problems 4.8.2 Boundary-Value Problems 4.9 Solving Systems of Linear DEs by˚Elimination 4.10 Nonlinear Differential Equations Chapter 4 In Review Chapter 5: Modeling with Higher-Order Differential Equations 5.1 Linear Models: Initial-Value Problems 5.1.1 Spring/Mass Systems: Free Undamped Motion 5.1.2 Spring/Mass Systems: Free Damped Motion 5.1.3 Spring/Mass Systems: Driven Motion 5.1.4 Series Circuit Analogue 5.2 Linear Models: Boundary-Value Problems 5.3 Nonlinear Models Chapter 5 In Review Chapter 6: Series Solutions of Linear Equations 6.1 Review of Power Series 6.2 Solutions About Ordinary Points 6.3 Solutions About Singular Points 6.4 Special Functions Chapter 6 In Review Chapter 7: The Laplace Transform 7.1 De˜nition of the Laplace Transform 7.2 Inverse Transforms and Transforms of˚Derivatives 7.2.1 Inverse Transforms 7.2.2 Transforms of Derivatives 7.3 Operational Properties I 7.3.1 Translation on the S-Axis 7.3.2 Translation on the t-Axis 7.4 Operational Properties II 7.4.1 Derivatives of a Transform 7.4.2 Transforms of Integrals 7.4.3 Transform of a Periodic Function 7.5 The Dirac Delta Function 7.6 Systems of Linear Differential Equations Chapter 7 In Review Chapter 8: Systems of Linear First-Order Differential Equations 8.1 Preliminary Theory—Linear Systems 8.2 Homogeneous Linear Systems 8.2.1 Distinct Real Eigenvalues 8.2.2 Repeated Eigenvalues 8.2.3 Complex Eigenvalues 8.3 Nonhomogeneous Linear Systems 8.3.1 Undetermined Coef˜cients 8.3.2 Variation of Parameters 8.4 Matrix Exponential Chapter 8 In Review Chapter 9: Numerical Solutions of Ordinary Differential Equations 9.1 Euler Methods and Error Analysis 9.2 Runge-Kutta Methods 9.3 Multistep Methods 9.4 Higher-Order Equations and Systems 9.5 Second-Order Boundary-Value Problems Chapter 9 In Review Appendices Appendix A: Integral-Defined Functions Appendix B: Matrices Appendix C: Laplace Transforms Answers for Selected Odd-Numbered Problems Index