Math402/Advanced Calculus I Test Study Guide-Fall 1998

-----Test # 1------

First Test:Thursday, October 1, 1998

....General Information About The Exam....

The test will be worth 80 points and will 
constitute roughly 25% of the total number of test points
for the course.

You will have 1hr and 20min to work on the test.

All of your work must be placed in the "Blue Book(s)"
that will be provided for you.

The answers in the Blue Book(s) must appear in the same order
as they appear on the test sheet, and so you will need to
plan ahead and leave necessary space if you intend to
work the problems out of order.

Your answers will be graded on the basis of correctness,
completeness, and neatness.

The best philosophy you can have during the exam is to
leave as little to the imagination as is possible. The basic
rule is that you write down only things that are true and
give reasons as to why they are true.

The point value of each question will be noted for each
question. Take this into consideration while managing
your time during the exam. Don't spend 50% of your time
during the examination answering questions that count
for only 20% of the total. 

Partial credit will be awarded and so you should try to do 
some work on as many questions as you can. More weight will
be placed on your ability to demonstrate a correct process 
that may be followed to arrive at the correct answer than 
the final answer itself. Therefore, a correct final answer 
with no supporting work will receive little to no credit, 
and a correct process that contains some minor error(s) 
that caused an incorrect final answer will receive up to 
100% of the full credit, depending on the extent of the 
error(s).

Do not feel bad if you are unable to finish the exam.
Letter grade assignment for the test will be based 
on a curve with cut-offs less than or equal to straight 
percentage, and so it is possible to earn a good grade 
without completing the answers to all of the questions. 
Talk to your friends after the exam. The amount of work 
that others were able to complete will be a good 
indicator of your situation.

    

....Specific Information About The Exam....

The test will include only course material covered up to
and including Thursday, September 26, 1998.

Assigned homework problems will form the foundation for many 
of the test questions. As much as 75% of the exam may either
be taken directly from the homework or be very similar to 
homework problems.

Other test questions will either be drawn from class notes
or directly from the text. 

The best preparation for the exam is to practice working 
problems and read over your class notes for understanding. 

Remember that the more problems you work, the 
better prepared you will be for the exam. You are 
encouraged to attempt even more problems than were placed 
on the Assignment Web Page.


The following specific topics should be studied:

1. All assigned homework up to and including section 2.2
   (includinging assignments made that are not in the text)

2. Be able to state the field axioms of the Reals

3. Be able to state the Positivity Axion

4. Be able to define a "greater than" b , a "greater than  or equal" b ,
   a "less than" b and a "less than or equal to" b in terms of 3

5. Be able to define open/closed intervals (pg 4,5 and notes)

6. Be able to define an inductive set

7. Be able to define N, Z & Q

8. Be able to define Sup and Inf

9. Be able to state the Completeness Axiom 

10. Be able to state the Principle of Mathematica Induction

11.Be able to Prove the Achimedean Property and state 
   the corollaries covered in class
   
12. Be able to define absolute value

13 Be able to Prove the Triangle nequality and state the properties 
   of absolute value that were covered in class
   
14. Be able to define a sequence

15. Be able to define convergent sequence

16 Be able to prove {1/n} converges to 0 (using the definition)

17. Be able to prove the sum of two convergent sequrnces is convergent
    and state the other properties of convergent sequences covered in class.
    
18. Be able to define monotonically increasing(decreasing) sequence

19. Be able to state the Monotone Convergence Theorem

20. Be able to state the Bolzano-Weierstrass Theorem    

21. Be able to state the Nested Interval Theorem

Note: the proof of 18, 19, 20 will be required for the next test    

(last updated 1:45AM on 9-24-98)