Exam location & times: Olin Hall 103
1:00-3:00 p.m.
Saturday, Dec. 16

General Rules

• You are allowed one new 4"-by-6" note card or two 3"-by-5" note cards with anything you wish written on both sides for use during the exam. You may also use your note cards from exams 1-3.
• No other notes or books are allowed at the exam.
• A table of integrals like the one supplied with the Chapter 7 exam will be provided.
• You must have your graphing calculator with you, with angular measure set to radian mode.

• Look over your old homework assignments and in-class exercises.
• Do a few of the chapter review problems and "Check Your Understanding" true/false problems.   Answers will be posted outside my office.
• For the comprehensive part of the final exam, also review the unit exams and quizzes you have taken.
• Organize your knowledge and thinking as you prepare your note card(s).

• Chapter 11 (sections 1-11): Differential equations
  1. What is a differential equation? How do you verify a function is a solution of a differential equation?
  2. Slope fields: construction and use
  3. Euler's method
  4. Separation of variables
  5. Growth and decay
     • Continuous and annual percentage growth rates
     • Newton's law of heating/cooling
     • Equilibrium solutions
     • Stable and unstable equilibrium solutions
  6. Applications and modeling: a wide variety of problems, but many involve input/output rates
  7. Models of population growth
     • dP/dt = kP
     • Logistic model
  8. Systems of differential equations
     • S-I-R model
     • Interacting species: independent, predator-prey, symbiotic, competing
     • Phase plane analysis: trajectories/orbits, peak values, equilibrium points
  9. Analyzing the phase plane: nullclines, solution trajectories
  10. Second-order differential equations: oscillations
      • d²y/dt² = - ky where k = (omega)² > 0.
      • Guess and check
      • Initial-value and boundary-value problems
  11. Linear second-order differential equations
      Characteristic equation cases
      • b²-4ac > 0
      • b²-4ac = 0
      • b²-4ac < 0
• Chapters 7-10: Integration, applications, series, and approximation of functions
  • Exam 1 review
  • Exam 2 review
    Focus on geometric, financial, and probability-related applications.
  • Exam 3 review
• Old Calculus II final exam (ps) (pdf)
  Answers
  Solutions are posted outside my office.