MTH 435 Fall 05 -- Tips for the Final

Our Final Exam is scheduled for Wednesday, December 21, 7 pm-10 pm, in Tyler 106.

The Final Exam is comprehensive and it covers classes 1-25 and homework assignments 1-10. Hence, Tips for Exam 1 and Tips for Exam 2 are still important to review as well as Exams 1, 2. However, there will be much emphasis on later classes, 19-25: continuity, uniform continuity, differentiability, the Max-Min Theorem, the Intermediate Value Theorem, the Mean Value Theorem. Make sure that you review thoroughly Homework 9 and Homework 10. (Homework 10 is for extra credit as far as your grade is concerned but it will be included in the Final.) Solutions to Homework 9 are posted, solutions to Homework 10 will be posted on Saturday or Sunday. As always, you are expected to know and be able to state all definitions, propositions, and theorems given in class and in homework assignments as well as their proofs. By "stating a theorem", we mean a complete statement, including all assumptions, in complete, correct fashion and not just its conclusion scribbled hastily. You should know all of the important examples studied in class. You are expected to know solutions to all homework problems. Some problems on the exam may be very similar to homework problems.

A few sample candidates for the Final from the part after Exam 2:

-- Problem. (a) State the Intermediate Value Theorem. (b) Prove something along the lines of Homework 10, #4.
-- Problem. (a) State the Mean Value Theorem. (b) Prove something like in Th. 23.3 or Th. 24.1.
-- Problem. (a) State the Max-Min Theorem. (b) Prove something along the lines of Homework 9 # 4.
-- Problem. (a) State the definition of uniform continuity. (b) Show that 1/x is not uniformly continuous in (0,1).
-- Problem. (a) State the definition of differentiability. (b) Prove something along the lines of Homework 10 # 3.
-- Problem. Prove something like (a) or (b) of Th. 22.1

These are only examples of the types of problems you should expect (they may or may not appear). I hope you all get As!