You're allowed to prepare and use a cheat sheet for the final exam, written on one piece of 8.5 x 11 inch paper, using both sides. You can put anything you want on the cheat sheet, but I recommend not writing out examples, since these are lengthy and particular. You'll probably want a table of Laplace transforms.
The final exam is comprehensive. so the topic list is pretty much the same as the course syllabus.
- First order equations
- separable
- first-order linear
- exact equations
- substitutions: Bernoulli and homogeneous*
- solution intervals
- Second and higher-order linear equations
- homogeneous equations: exp(lambda t) is your friend
- distinct real, repeated real, and complex roots
- nonhomogeneous equations
- judicious guessing
- variation of parameters
- reduction of order
- homogeneous equations: exp(lambda t) is your friend
- Laplace transforms
- definition
- Laplace transforms of elementary functions and derivatives
- solving initial value problems
- s- and t-translation
- Heaviside function
- Dirac delta function
- convolution
- Systems of differential equations
- finding general solution of x' = Ax problems (real distinct, real repeated, and complex eigenvalues)
- solving x' = Ax problems with initial values for the vector x.
- linearizing nonlinear systems about equilibrium points
Expect 8 to 10 problems chosen from the above outline, likely two or three for each of the four main sections.
The problems will be designed to focus on your understanding of the issues and methods, rather than your ability to do tricky arithmetic and calculus quickly. Previous exams are good indications of problem complexity.
For systems of equations, HW9 and HW10 problems are pretty good indications of problem complexity, though the whole of HW10 problem 2 is probably too much and too fresh for an exam.
- arrive a few minutes early
- bring a pencil, eraser, and a pen
- read the instructions and follow them --worth some portion of your grade
- read the problem statements and do what is asked
- be careful with algebra and calculus --don't rush!
- keep cool and collected, try not to freak out about grades
- check your answers by substituting them into the ODE
- know your section number
Wednesday, May 16, 2018 3:30-5:30pm
| sections | room | time |
|---|---|---|
| 1 2 4 6 9 | Spaulding 120 | 3:30-5:30pm Wed May 16 |
| 3 5 7 8 | Murkland 115 | 3:30-5:30pm Wed May 16 |
| extra time | Kingsbury W390 | 2:30-5:30pm Wed May 16 |