Overview of: Final exam
The final exam for Math 1241 is based on parts 2-6 from the Math 1241 thread. It is a cumulative exam, meaning it covers all the materials from the previous four modules, plus the new material on two-dimensional differential equations.
Material for the exam
Discrete-time dynamical systems (Discrete dynamical systems from Math 1241 thread).
See discrete dynamical system exam for a description of material and study aids for this section.
Differentiation (The derivative from Math 1241 thread).
See derivative exam for a description of material and study aids for this section.
Applications of differentiation (Applications of differentiation from Math 1241 thread).
See applications of differentiation exam for a description of material and study aids for this section.
Autonomous differential equations (Autonomous differential equations from Math 1241 thread).
See differential equation exam for a description of material and study aids for this section.
Two-dimensional autonomous differential equations (Two-dimensional autonomous differential equations from Math 1241 thread).
- What it means for two autonomous differential equations to be coupled.
- Estimating a solution to a two-dimensional differential equation using the Forward Euler algorithm
- Understanding the correspondence between the phase plane plot and plots versus time.
- Finding equilibria by solving the two equations made by setting the rates of change to zero.
- Plotting nullclines in the phase plane.
- Finding equilibria by finding the points where the nullclines intersect.
- Plotting direction arrows (i.e., vector field) on the nullclines and in the regions of the phase plane that are divided by the nullclines.
- Sketching a solution in the phase plane based on direction arrows.
- The predator-prey system, the competition equations, the disease model, and the neuron model are good example equations, but you aren't expected to memorize them.
Study aids
Review problems
The majority of the questions that may appear in the final exam are available so that you can practice them. In both these problems and on the actual exam, the set of problems as well as values of numbers, variables, parameters, and other quantities are selected randomly. You will want to generate multiple versions of the problems to see the larger array of problems. Given the random nature, we cannot guarantee that you will actually see all the problems that will appear on the exam. But the more problems you work on, the greater the chance you will work on problems that will show up on the test.
The format of the exam questions may differ from the practice problems in that the exam problems may have been modified to remove any answer blanks and the instructions specific to entering answers in the right format for computer grading.
For all problems on this exam, you will be expected to show your work, and the grading will be based on the work that you show.
Free form questions
See the problems listed in the first four exams (1 2 3 4). In addition, Review questions: Two dimensional autonomous differential equation problems contains short answer problems that reflect the format of questions as they would appear on the exam.
Computer-scored problems
See the problems listed in first four exams (1 2 3 4). In addition, contains problems where the computer will the score your answer for you, so you can see how well you did. When these questions appear on the exam, they may be modified to the short answer format.
Worksheets
The worksheets from the Math 1241 thread are also good review.
Review session
We will hold a review session on the study day, Thursday, December 11, in the regular class room, a little later than the usual class time.
Date: Thursday, December 11
Time: 3:15 PM - 4:15 PM
Location: STSS 114
Brownies provided.
Final exam logistics
Date: Friday, December 12
Time: 1:30 PM - 4:30 PM
Location is based on section. (View section in upper right of main course page.)
Sections 12,13: Akerman Hall 209
Section 14: Akerman Hall 225
Section 15: Akerman Hall 227
Section 11, 16: Akerman Hall 319
Final exam rules
- You are allowed 180 minutes to take the exam.
- You are allowed to have one letter sized sheet of paper of notes. Double-sided is OK. No restrictions to what can be on the sheet of paper.
- You are allowed to have a calculator in the exam, including a graphing calculator.
- No textbook or electronic equipment (other than calculator) allowed.
- All students must have their official University ID card with them at the time of the final exam and must show it to one of the proctors when handing in their exam. The proctor will not accept a final exam from a student without an ID card.
Provisions are available for students who have two Math common final exams at the same time. See instructor if you have any conflict with the final exam time.