Differential Equations: Techniques, Theory, and Applications 1st edition

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

• Chapter 1: Introduction
  • 1.1: What is a differential equation?
  • 1.2: What is a solution?
  • 1.3: More on direction fields: Isoclines
  
  
• Chapter 2: First-Order Equations
  • 2.1: Linear equations
  • 2.2: Separable equations
  • 2.3: Applications: Time of death, time at depth, and ancient timekeeping
  • 2.4: Existence and uniqueness theorems
  • 2.5: Population and financial models
  • 2.6: Qualitative solutions of autonomous equations
  • 2.7: Change of variable
  • 2.8: Exact equations
  
  
• Chapter 3: Numerical Methods
  • 3.1: Euler's method
  • 3.2: Improving Euler's method: The Heun and Runge-Kutta Algorithms
  • 3.3: Optical illusions and other applications
  
  
• Chapter 4: Higher-Order Linear Homogeneous Equations
  • 4.1: Introduction to second-order equations
  • 4.2: Linear operators
  • 4.3: Linear independence
  • 4.4: Constant coefficient second-order equations
  • 4.5: Repeated roots and reduction of order
  • 4.6: Higher-order equations
  • 4.7: Higher-order constant coefficient equations
  • 4.8: Modeling with second-order equations
  
  
• Chapter 5: Higher-Order Linear Nonhomogeneous Equations
  • 5.1: Introduction to nonhomogeneous equations
  • 5.2: Annihilating operators
  • 5.3: Applications of nonhomogeneous equations
  • 5.4: Electric circuits
  
  
• Chapter 6: Laplace Transforms
  • 6.1: Laplace transforms
  • 6.2: The inverse Laplace transform
  • 6.3: Solving initial value problems with Laplace transforms
  • 6.4: Applications
  • 6.5: Laplace transforms, simple systems, and Iwo Jima
  • 6.6: Convolutions
  • 6.7: The delta function
  
  
• Chapter 7: Power Series Solutions
  • 7.1: Motivation for the study of power series solutions
  • 7.2: Review of power series
  • 7.3: Series solutions
  • 7.4: Nonpolynomial coefficients
  • 7.5: Regular singular points
  • 7.6: Bessel's equation
  
  
• Chapter 8: Linear Systems I
  • 8.1: Nelson at Trafalgar and phase portraits
  • 8.2: Vectors, vector fields, and matrices
  • 8.3: Eigenvalues and eigenvectors
  • 8.4: Solving linear systems
  • 8.5: Phase portraits via ray solutions
  • 8.6: More on phase portraits: Saddle points and nodes
  • 8.7: Complex and repeated eigenvalues
  • 8.8: Applications: Compartment models
  • 8.9: Classifying equilibrium points
  
  
• Chapter 9: Linear Systems II
  • 9.1: The matrix exponential, Part I
  • 9.2: A return to the Existence and Uniqueness Theorem
  • 9.3: The matrix exponential, Part II
  • 9.4: Nonhomogeneous constant coefficient systems
  • 9.5: Periodic forcing and the steady-state solution
  
  
• Chapter 10: Nonlinear Systems
  • 10.1: Introduction: Darwin's finches
  • 10.2: Linear approximation: The major cases
  • 10.3: Linear approximation: The borderline cases
  • 10.4: More on interacting populations
  • 10.5: Modeling the spread of disease
  • 10.6: Hamiltonians, gradient systems, and Lyapunov functions
  • 10.7: Pendulums
  • 10.8: Cycles and limit cycles
  
  
• Chapter 11: Partial Differential Equations and Fourier Series
  • 11.1: Introduction: Three interesting partial differential equations
  • 11.2: Boundary value problems
  • 11.3: Partial differential equations: A first look
  • 11.4: Advection and diffusion
  • 11.5: Functions as vectors
  • 11.6: Fourier series
  • 11.7: The heat equation
  • 11.8: The wave equation: Separation of variables
  • 11.9: The wave equation: D'Alembert's method
  • 11.10: Laplace's equation