Differential Equations: Tutorial Bank 1st edition

Access is contingent on use of this textbook in the instructor's classroom.

• Chapter 1: Introduction to Ordinary Differential Equations
  • 1.1: Introduction
  • 1.2: Constructing Models
  
  
• Chapter 2: First-Order Differential Equations
  • 2.1: Existence and Uniqueness
  • 2.2: Slope Fields
  • 2.3: Qualitative Analysis of Autonomous Equations
  • 2.4: Separable Equations and Applications
  • 2.5: Linear Equations and Applications
  • 2.6: Exact Equations
  • 2.7: Homogeneous Equations
  • 2.8: Solution Methods for Special Cases
  
  
• Chapter 3: Second-Order Linear Differential Equations
  • 3.1: Existence and Uniqueness
  • 3.2: Fundamental Solutions of Homogeneous Equations; Wronskian
  • 3.3: Reduction of Order
  • 3.4: Homogeneous Equations with Constant Coefficients
  • 3.5: Free Mechanical Vibrations
  • 3.6: Nonhomogeneous Equations
  • 3.7: Method of Annihilators
  • 3.8: Method of Undetermined Coefficients
  • 3.9: Variation of Parameters
  • 3.10: Forced Mechanical Vibrations
  • 3.11: Electrical Networks
  
  
• Chapter 4: Higher-Order Linear Differential Equations
  • 4.1: Existence and Uniqueness
  • 4.2: Fundamental Solutions of Homogeneous Equations; Wronskian
  • 4.3: Nonhomogeneous Equations with Constant Coefficients
  • 4.4: Variation of Parameters
  
  
• Chapter 5: LaPlace Transforms
  • 5.1: Introduction
  • 5.2: Derivatives and Initial-Value Problems
  • 5.3: Step Functions and Translation; Piecewise-Continuous Forcing
  • 5.4: Impulses
  • 5.5: Convolution
  • 5.6: Applications
  
  
• Chapter 6: Series Solutions
  • 6.1: Introduction
  • 6.2: Series Solutions Near an Ordinary Point
  • 6.3: Series Solutions Near a Regular Singular Point
  • 6.4: Method of Frobenius
  
  
• Chapter 7: Systems of Differential Equations
  • 7.1: Review: Solving Systems Using Matrices
  • 7.2: Introduction
  • 7.3: Method of Eigenvalues and Eigenvectors
  • 7.4: Modeling with Systems of Equations
  
  
• Chapter 8: Numerical Solutions
  • 8.1: Euler's Method
  • 8.2: Runge-Kutta Method
  • 8.3: Method Comparison
  • 8.4: Finite Difference Method