Tuesday, December 17, 1:30-4:30pm in 1320 Digital Computer Laboratory

Bring your I-card to the exam. No I-card = no exam.

Students with a DRES accommodation should arrange to take their exam at DRES, on Tuesday, December 17 from 12:00pm onwards, or on Wednesday, December 18.

Conflict exam – Tuesday, December 17, 7:00-10:00pm (evening). You can request here to take the conflict exam, but read the next paragraph before you do so:

• The conflict exam will be given only if you present written evidence that you will miss (or did miss) an exam for a legitimate reason. Religious time conflicts, university-related sports competitions, family emergencies and illness are examples of legitimate reasons for an absence. If a conflict can be predicted in advance, then the evidence should be presented at least one week prior to the scheduled exam date. In case of religious observances, complete this form (NA) as soon as possible.

• In case of illness, an absence letter from the Dean of Students will suffice. 
• Travel and leisure plans, even for family events, are never a legitimate reason for missing an exam.

Exam Coverage

The midterm is designed as a 2-hour exam, with some multiple-choice and some short-answer problems. You will have 3 hours to work on the exam. The exam includes the formula sheets from Midterms 1,2,3. 

The exam is comprehensive: all material covered during the semester is examinable, except for the topics announced as non-examinable, which are Putzer’s method for the matrix exponential and the lectures during the last week of the course on the proof of the existence and uniqueness theorem.

See the handouts page for class material and coverage. 

All Webassign Homework and Written Homework are examinable. 

How to study

Follow the study advice for Midterm 1, Midterm 2, and Midterm 3. 

Active study is the key to success. Write summary notes of the important concepts and methods, based on your lecture notes and class handouts on each section (solutions are posted on the handouts page). Passive study, such as flipping through your notes, will not prepare you for the exam.

The test could cover:

• modeling
• solving
• graphing
• interpreting

To help with “solving” DEs, make a checklist of the main types of DEs/systems we have covered, and the method used to solve each type.
Practice looking at the form of a DE and do not fixate on the variable letters e.g. d²x/dt² = -a²x is the same DE as d²y/dt² = -a²y.
Express the methods as algorithms or checklists: step 1, step 2, and so on, so that you have a plan of action for each type of problem.
After solving a DE or system of DEs, always check your work by “verifying” – plug your solution into the DE to check that it works.

Ask yourself how do I decide which method to use? This flowchart can help for 2nd order linear DEs. 

Memorize the solutions of the following differential equations, and practice writing down the solution until you can do it without thinking:

• dy/dt – ay=0      or dy/dt = ay               (solution y=Ce^at)
• dy/dt=ay-b where a and b are constants (solution y=(b/a)+Ce^at)
• d²y/dt² – a²y=0 or d²y/dt² = a²y     (solution y=c₁e^at+c₂e^-at)
• d²y/dt² + a²y=0 or d²y/dt² = -a²y   (solution y=c₁cos(at)+c₂sin(at))

Memorize:

• Existence and Uniqueness Theorem for 1st order linear DEs (Lecture 6; second side of the handout); draw a picture to illustrate, like we did in class
• Existence and Uniqueness Theorem for 1st order nonlinear DEs (Lecture 7); draw a picture to illustrate, like we did in class
• Statement of the Population Model with natural (intrinsic) growth rate and (environmental) carrying capacity (Lecture 8; see last exercise)
• Existence and Uniqueness Theorem for 2nd order linear DEs (Lecture 12)
• General solution Theorem for 2nd order linear homogeneous (Lecture 12)
• Euler’s formula e^ib=cos(b)+i sin(b)
• Rules 1, 2, 3 for Undetermined Coefficients (Lecture 15)
• Definition of an equilibrium point for an autonomous system of DEs (Lecture 23)
• Statement of the General Solution Theorem for homogeneous linear system of n equations (Lecture 24)
• Trace-determinant diagram (download it here), and practice drawing the diagram
• Statement of the Competing Species system (Homework 11)
• How to compute r'(t) and theta'(t) (the polar coordinate form of a system) (Lecture 32)

Then work some problems: 

• Re-work all homework problems – and ask the professor about any problems you do not know how to do. 
• Answers for most textbook problems are given at the end of the book, on pages 589-635.  
• Do the Webassign practice problems (on Chapters 1-3, to remind you of those methods)
• Once you are confident on the fundamentals, assign yourself “backwards” challenges such as “Find an example of a 2×2 matrix whose phase portrait is a spiral source.”
• See the practice problems for Midterm 1, Midterm 2, and Midterm 3. 
• Re-work Midterms 1,2 and 3 (look at the full solutions you received by email several days after each midterm, and if you cannot find them then contact the professor and ask for the solutions to be re-sent). Some problems from these midterms might reappear on the final exam. 
• There is no practice exam. 

Collaborative Study Sessions 

• Wednesday 4-5pm (243 Altgeld Hall)
• Thursday 5-6pm (443 Altgeld Hall)
• Monday 11am-12pm (241 Altgeld Hall, note unusual room)
• Monday 4:30-5:30pm (243 Altgeld Hall)
• Tuesday 11am-12pm (243 Altgeld Hall)

Office hour Friday 2:30-3:30pm (376 Altgeld Hall)

Exam rules

You must not communicate with other students or anyone else except the proctors, during the exam. This includes the turn-in period after the exam.
No written materials or electronic materials of any kind are allowed.
No phones, calculators, iPods or electronic devices of any kind are allowed for ANY reason, including checking the time. You may use a simple wristwatch, but not a smartwatch.
Put all electronic devices in your bag before the exam begins; they must not be on your person.
Cheating of any kind or violations of exam rules will be treated extremely seriously.