A First Course in Differential Equations with Modeling Applications (Metric Version - Not available for student purchase in the U.S.) 11th edition

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• Chapter 1: Introduction to Differential Equations
  • 1.1: Definitions and Terminology
  • 1.2: Initial-Value Problems
  • 1.3: Differential Equations as Mathematical Models
  • 1: Chapter 1 In Review
  
  
• Chapter 2: First-Order Differential Equations
  • 2.1: Solution Curves Without a Solution
  • 2.2: Separable Equations
  • 2.3: Linear Equations
  • 2.4: Exact Equations
  • 2.5: Solutions by Substitutions
  • 2.6: A Numerical Method
  • 2: 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
  • 3: Chapter 3 In Review
  
  
• Chapter 4: Higher-Order Differential Equations
  • 4.1: Preliminary Theory—Linear 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
  • 4.9: Solving Systems of Linear DEs by Elimination
  • 4.10: Nonlinear Differential Equations
  • 4: Chapter 4 In Review
  
  
• Chapter 5: Modeling with Higher-Order Differential Equations
  • 5.1: Linear Models: Initial-Value Problems
  • 5.2: Linear Models: Boundary-Value Problems
  • 5.3: Nonlinear Models
  • 5: 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
  • 6: Chapter 6 In Review
  
  
• Chapter 7: The Laplace Transform
  • 7.1: Definition of the Laplace Transform
  • 7.2: Inverse Transforms and Transforms of Derivatives
  • 7.3: Operational Properties I
  • 7.4: Operational Properties II
  • 7.5: The Dirac Delta Function
  • 7.6: Systems of Linear Differential Equations
  • 7: Chapter 7 In Review
  
  
• Chapter 8: Systems of Linear First-Order Differential Equations
  • 8.1: Preliminary Theory—Linear Systems
  • 8.2: Homogeneous Linear Systems
  • 8.3: Nonhomogeneous Linear Systems
  • 8.4: Matrix Exponential
  • 8: 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
  • 9: Chapter 9 In Review
  
  
• Chapter A: Appendices
  • A.A: Integral-Defined Functions
  • A.B: Matrices