Last edited 7dec00 by

Math 306 Study Guide for the Final 7pm Thursday 14dec00

0. Watch this website for clarifications and useful hints to queries submitted by students in preparation for the final.

1. Review session is at 8pm Tuesday 12dec00 in a room TBA. Watch this website for the room number. Too many people have a final on Wednesday evening. Therefore the review session is a day earlier than announced.

2. Walk-in hours are in the grafiXlab, 10-noon, Wednesday, 13dec00. Make private appointments by e-mail.

3. You may bring your journal to the final. You may not bring loose pieces of paper, xeroxes of handouts, webpages, or the textbooks. Your journal should be hand-written and its pictures hand-drawn, with the exception of typed pages you wrote yourself and glued into the journal earlier. You are encouraged to add entries in preparation for the final.

4. The accuracy of the drawings you do on the final matters. So bring pencils, eraser, ruler and right-angle. Review the methods for free-hand drawing of circles, parabolas and ellipses.

5. While studying for the final be sure you acquire a clear and factual command of the broad themes of the course, including precise statements of definitions, theorems, and the essential steps in the major proofs (the one's we spent more than a week on!)

6. Since no pedagogical purpose is served by awarding partial credit on a final, be prepared to give complete answers, supported by logical thinking, apt examples, accurate and well labeled illustrations, and unambiguous arguments.

7. Go over all class handouts, corrected tests and homework problems, your notes and handouts from the student presentations (Project 4 in the past two weeks) and the comments I made on your work which was returned to you.

8. The final will include details and factual questions on the previously untested 17th century (Descartes, Fermat, Galileo, Kepler, Barrow, Newton, Leibniz). Here is a sample problem: Derive Kepler's third law from Kepler's 1st and 2nd law. Note that the correct answer here depends on your knowing and stating that Kepler's first two laws are equivalent to Newton's 2 laws, and giving the main step in the derivation of Kepler's equal area law from Newton's inverse square law.

9. Questions on the medieval period will be of a broader nature whose answers you may elaborate with examples and illustration. A sample question might be: Trace the problem of extracting the square root through the history of the calculus. You might discuss the diagonal of a square (Greek), the geometric mean, Alkhowarizmi's figurative arithmetic, Theon's square algorithm, Newton's method, and the binomial theorem for fractional powers.

10. Materials explicitly covered on the midterm will be reconsidered only in connection with the subsequent development of the calculus. Thus, on a question concerning quadrature you musn't stop with Archimedes' measuring the area of the parabolic segment. There's Cavalieri, Fermat, and Newton to consider too.