MATH235 FALL 2007

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• Syllabus (morning class)
  
  
• Syllabus (afternoon class)
  
  
• Mathematical Notation and Concept Sheet
  
  
• Basic Properties of Algebra
  
  
• 4 Limit Proofs
  
  
• 3 More Limit Proofs
  
  
• Limit Tool Sheet
  
  
• Pinching Theorem Proof
  
  HOMEWORK ASSIGNMENTS:
  8/27: Section 2.6 #1,3,5,11,13,15
  8/28: Section 2.6 #7,17,18,19,21,28
  8/29: Section 2.6 problems and proofs above, but this time, start to redo them more completely and correctly. For proofs, be sure to clearly delineate your work showing how you determined delta from your actual rigorous proof of the result. In the proofs, be sure to give reasons for your steps.
  8/31: See 8/29 assignment. You should now have a good understanding of the both the mathematical and visual ideas of limit. The rigorous proof we'll continue to work on. ALSO, write up proper rigorous proofs for Examples 2 and 3 in your book. They've done the background work for you.
  9/3: Keep working on proofs. Remember your favorite algebra techniques: expand, factor, common denominator, rationalize!
  9/4: Finish proofs (or do more for more practice!). We'll use our developed analytical skills to now move on and prove general limit results that will make life easier, instead of the specific ones we've been proving.
  9/5: Read Section 2.5. Think about how you would PROVE the results listed in Theorem 2.5.1. Review pre-calc topics as needed in Sections 1.1--1.4, 2.1--2.3. By now you should realize what you need! QUIZ coming soon on 2.6 problems!
  9/7: Do what you need to do to have the ideas and proofs we've discussed well in hand. We'll be off and running with it next week. See "4 Limit Proofs" link above for the proof of the result we worked with today, and some others.
  9/10: Try to finish writing up the proof of the result you worked on in groups today BEFORE looking at the polished one on our "4 Limit Proofs" link above. Another link with 3 more theorems and proofs is coming soon above. Read the results and proofs numbered 2., 5., and 6, and the proof that the limit of a constant is the constant that follows result 2. Also, read the results and look over the proofs for the gifts (3. and 4.)
  9/11: Prove the result handed out in class today (also at the link below in case it got wet in the rain!) ALSO, Prove the 2.6 HW problem (#19) that was on our quiz yesterday. In both, justify every step and don't skip steps. Homework Proof
  
  9/12: Section 2.6: #26,27 (Appeal to our Limit Theorems--these are quick and easy now!)
  AND Section 2.5: #1,3-5,8-11,13,14,16,17,31-33,40-42,46-48,57-60,62,63, 75.
  
  9/14: Use a delta-epsilon proof to prove the limit result for Section 2.5 exercise 14.
  ALSO, use an N-epsilon proof to prove the lim as x -> infinity of 1/(x-a)=0 (this is one of the results in 2.5 equation (7)).
  
  9/17: Section 2.5: #19-23, 43-45, 53-56, 76.
  
  
• 3 Quiz 1 Solutions
  
  
• 3 More Quiz 1 Solutions
  
  9/18: Section 2.7: #6-9, 11-13, 15, 17b, 22, 23. REMINDER: Test 1 will be held Fri. Sept. 28!
  
  9/19: Section 2.5: #51, 52, 65, 68 AND Section 2.7: #13 (now with our super powered new tool!), 14, 18, 19b, 20. For 19b and 20, once again, LIMIT BOY saves the day!).
  
  9/21: Section 2.5: #25-30, 49, 50, 69-71. Section 2.6 #28(c) also say WHY, AND STUDY for TEST 1!!
  
  9/24: REFRESH your TRIG!!! READ Appendix B.I and Appendix B.II.
  FINISH and understand both worksheets handed out in class today!!
  
  9/25: Read LT18. (This idea is also discussed in your book at the top of p. 110 and very bottom of p.109).
  ALSO Read Section 2.8 (in particular, p.112- mid p.113 and very bottom of p.116 contain material we did not yet talk about in class that you'll need to understand!)
  Section 2.8 HW Exercises: #1, 6, 12, 13-35 odd, 36, 39, 44, 45, 51
  
  9/26: KEEP STUDYING for TEST 1 on Friday!!
  
  10/1: Find f '(c) for f(x)=k, f(x)=x, and section 3.2 #7,9 using both forms of the definition of f '(c) discussed in class today.
  10/2: Prove 1., 2., and 3. below (justify every step and don't skip steps!):
  1. The product rule for derivatives using the limit as x->c definition (instead of the limit as h->0 definition as done in class). That is, prove (fg) '(x) = f(x)g '(x) + f '(x)g(x).
  2. The reciprocal rule: If g is differentiable c, then the reciprocal function (1/g) is differentiable at c whereever it is defined. (When is the function 1/g undefined?!?) Thus, derive the rule (1/g) '(x)= - g '(x)/[g(x)]^2. When is this valid?
  3. Use the rules in 1. and 2. to prove the quotient rule WITHOUT using a limit definition of differentiability. That is, use the results in 1. and 2. to show that (f /g) '(x) = [g(x)f '(x)- f(x)g '(x)]/[g(x)]^2.
  4. ALSO, do Section 3.2 Exercise #45
  
  10/3: Section 3.2: #43, 44 AND Section 3.3: #29-31, 70, 73-75, 76a.
  
  10/5: Section 3.2: #21, 22
  AND Section 3.3: #1, 5, 9, 11, 19, 21, 23, 35-38, 70, 71
  AND Section 3.4: Finish any derivations of the six trig function derivative formulas that you didn't get done in class (essentially, 3.4 #34)
  AND Section 3.4: #1, 3, 5, 7, 13, 15, 17, #33(a)-(d),(h),(i).
  
  10/8: Section 3.3: #41(a),(c), 43, 45, 47, 79, 82, 84, 85
  AND Section 3.4: #19, 23.
  
  10/9: NOW take your new rule (you!) proved today in class out for a spin:
  Section 3.5: #1, 5, 9, 13, 17, 19, 21, 29, 33, 42, 65, 67, 71.
  
  10/10: Let's kick into higher gear now with our chain rule:
  Section 3.5: #47, 48, 51(a), 54(a), 63, 66, 68(b), 69, 75.
  For #54(a), change the angle to evaluate to radians instead of degrees, and express your answer in units of pounds/radian.
  
  
• Test 1 Solutions
  
  10/12: Section 3.6: #1, 3, 5, 17, 19, 25, 35, 37, 41, 45, 47, 60(b).
  
  10/15: Section 3.1: #5, 7
  AND Section 3.2: #17, 19, 28, 29
  AND Section 3.3: #55, 57.
  
  10/16: Section 3.2: #33, 34, 40
  AND Section 3.3: #52-54, 59, 65-67
  AND Section 3.4: #25a,b, 26, 27
  AND Section 3.5: #43
  AND Section 3.6: #33, 55.
  
  10/17: Section 3.1: #1, 3, 14
  AND Section 3.3: #39, 40
  AND Section 3.4: #29, 31, 32
  AND Section 4.1: #1, 3, 5, 6, 11, 13, 15.
  
  10/19: Happy Fall Break!!
  
  NOTE: Quiz on slope/tangent line/rate of change HW (10/15-10/17) likely on Tues 10/23
  AND Test #2 on Halloween!
  
  10/22: Section 4.1: #20, 21, 29, 40, 41. Reminder: always convert angles to radian measure!
  
  10/24: Read pages mid. 208-209 (Start at Example 1) and Read Section 4.9 pp. 233-234 (Rolle's Thm and Examples 1,2).
  AND Do Section 4.9 #1, 2, 20
  
  
• Quiz 3 solutions (AM class)
  
  
• Quiz 3 solutions (PM class)
  
  10/26: Read Section 4.9 pp. 234-236 (Mean Value Thm and Example 3).
  AND Do Section 4.9 #7, 11, 13, 14, 37
  
  10/29, 10/30: Keep studying for Test #2 (covers everything we did from 10/1 thru 10/26 (inclusive!))
  Homework for 4.2 coming for Weds.
  
  10/31: Section 4.2 #3, 7, 11, 13, 17, 21, 22, 27(c), 29(a), 31, 38.
  
  11/2: Section 4.3 #5, 9, 15, 17, 21, 27, 37, 41, 45, 47.
  
  11/6: Section 4.6 #3, 7, 13, 19, 23, 24, 29, 32, 34, 40 and READ Section 4.7!
  
  11/7: Section 4.7 #3, 5, 9, 12, 15, 17, 21, 26, 27, 29, 39, 43, 51, 58, 59, 60.
  
  
• Test 2 Solutions
  
  11/13: Section 5.5 #1, 3 and Section 5.6 #9-11 (express as limits as n -> infinity), 42.
  
  11/19: Section 5.7 #1, 3, 9, 13, 19, 22, 24, 27, 39, 45, 47, 51, 61(a).
  
  11/20: Section 5.2 #9, 11, 13, 17, 19, 21, 23, 25, 43, 45, 47. ALSO, PROVE Result 8 stated in class today.
  (Result 8 in words is: The indefinite integral of k*f = k*(the indefinite integral of f). Result 8 is the indefinite integral result analogous to Result 2, the corresponding definite integral result. Notice that the proofs are VERY different, by the different nature of the definitions of definite and indefinite integrals!
  
  TEST #3 will be held on Friday, Nov. 30, and will cover everything we did since the end of October: section 4.2 material thru 11/20 material (indefinite integrals). HAPPY THANKSGIVING!!!
  
  
• Quiz 4 solutions
  
  11/26: Section 5.3 #3, 5, 7, 11, 15, 17, 21, 31, 35, 38, 39, 41.
  
  11/27: Section 5.8 #1, 17, 25, 29
  AND Section 5.9 #1, 3, 5, 12a, 15, 16, 25, 31.
  
  11/28: Section 5.6 #12a,b,d, 13, 20 and 21 (Hint: see Example 1(b)), 33
  AND Section 5.7 #33, 37, 49
  AND Section 5.8 #31.
  
  TEST #3 news: NO GRAPHING CALCULATORS!! You may arrive a little early and stay a little late as usual!
  Test covers material we covered since the last test (10/29) thru 11/26 material (u-substitution for indefinite integrals).
  
  12/3: Section 6.1 #3, 5, 11, 13, 15, 17, 23, 25, 31, 37.
  
  12/4: Section 6.2 #1, 3, 5, 13, 17, 19, 31, 37, 42, 43, 61.
  
  
• Blank Copy of Test 1
  
  
• Blank Copy of Test 2
  
  
• Blank Copy of Test 3
  
  
• Test 3 Solutions

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