Differential Equations: From Calculus to Dynamical Systems 2nd edition

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• Chapter 1: Introduction to Differential Equations
  • 1.1: Basic Terminology
  • 1.2: Families of Solutions, Initial-Value Problems
  • 1.3: Modeling with Differential Equations
  
  
• Chapter 2: First-order Differential Equations
  • 2.1: Separable First-order Equations
  • 2.2: Graphical Methods, the Slope Field
  • 2.3: Linear First-order Differential Equations
  • 2.4: Existence and Uniqueness of Solutions
  • 2.5: More Analytic Methods for Nonlinear First-order Equations
  • 2.6: Numerical Methods
  • 2.7: Autonomous Equations, the Phase Line
  
  
• Chapter 3: Second-order Differential Equations
  • 3.1: General Theory of Homogeneous Linear Equations
  • 3.2: Homogeneous Linear Equations with Constant Coefficients
  • 3.3: The Spring-mass Equations
  • 3.4: Nonhomogeneous Linear Equations
  • 3.5: The Forced Spring-mass System
  • 3.6: Linear Second-order Equations with Non-constant Coefficients
  • 3.7: Autonomous Second-order Differential Equations
  
  
• Chapter 4: Linear Systems of First-order Differential Equations
  • 4.1: Introduction to Systems
  • 4.2: Matrix Algebra
  • 4.3: Eigenvalues and Eigenvectors
  • 4.4: Analytic Solutions of the Linear System x′ = Ax
  • 4.5: Large Linear Systems; the Matrix Exponential
  
  
• Chapter 5: Geometry of Autonomous Systems
  • 5.1: The Phase Plane for Autonomous Systems
  • 5.2: Geometric Behavior of Linear Autonomous Systems
  • 5.3: Geometric Behavior of Nonlinear Autonomous Systems
  • 5.4: Bifurcations for Systems
  • 5.5: Student Projects
  
  
• Chapter 6: Laplace Transforms
  • 6.1: Definition and Some Simple Laplace Transforms
  • 6.2: Solving Equations, the Inverse Laplace Transform
  • 6.3: Extending the Table
  • 6.4: The Unit Step Function
  • 6.5: Convolution and the Impulse Function
  
  
• Chapter 7: Introduction to Partial Differential Equations
  • 7.1: Solving Partial Differential Equations
  • 7.2: Orthogonal Functions and Trigonometric Fourier Series
  • 7.3: Boundary-Value Problems: Sturm-Liouville Equations
  
  
• Chapter 8: Solving Second-order Partial Differential Equations
  • 8.1: Classification of Linear Second-order Partial Differential Equations
  • 8.2: The 1-dimensional Heat Equation
  • 8.3: The 1-dimensional Wave Equation
  • 8.4: Numerical Solution of Parabolic and Hyperbolic Equations
  • 8.5: Laplace's Equation
  • 8.6: Student Project: Harvested Diffusive Logistic Equation