لایب سان

• ISBN-10 : 1337559881
• ISBN-13 : 978-1337559881

Cover -- Contents -- Preface for this Metric Edition -- Chapter 1: Introduction to Differential Equations -- 1.1 Definitions 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 Coefficients -- 4.4 Undetermined Coefficients-Superposition Approach -- 4.5 Undetermined Coefficients-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 Definition 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 Coefficients -- 8.3.2 Variation of Parameters -- 8.4 Matrix Exponential -- Chapter 8 In Review