MATH236 SPRING 2008

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• HOMEWORK Assigned (check regularly for updates!)
  
  1/9 Print off and reminisce on M235: Limit Tools, Calculus Tools, Derivative Tools, and Integral Tools from links below!!
  
  1/11 Section 7.4:
  #1,4,333, 5, 11, 17, 21, 23, 29, 39, 41, 45, 47, 51, 55. Prove Thm. 7.4.5 in the case of f decreasing. For Thm 7.4.3 (Existence), read the proofs of (a) iff (c).
  
  1/16 Section 7.5: #1-7, 9(a)-(f), 11 AND Section 7.3 #41, 43 AND PROVE the following:
  lim as x goes to 0+ of ln(x) approaches -(infinity). Use the M,delta definition below:
  lim as x goes to c+ of f(x) approaches -(infinity) iff for every M>0 there exists delta > 0 s.t. x an element of (c,c+delta) implies f(x)<-M. Write the forward proof correctly and justify each step. Hint: You may need to do some backwards work to figure out delta. Just like with epsilon-delta proofs where delta is a function of epsilon, for this proof, your choice for delta will depend on M.
  
  1/18 Section 7.5: #9(g),(h), 13-15
  AND Section 7.1: #9, 11(b), 15, 19, 25, 27, 29, 31, 35, 37,
  AND Section 7.2: #1, 7, 11, 13, 17, 21, 51, 65, 67, 70, 71, 79
  I know it looks like a lot, but we don't have class again 'til Wednesday (and some of them go pretty quick)!! Don't forget: QUIZ on THURSDAY 1/24!
  
  1/24 Section 7.1: #5, 13, 23, 36(a),(b), 45(b)
  AND Section 7.2: #39, 45, 47, 81, 89, 91, 95, 131, 152(d)
  AND Section 7.3: #13, 21
  AND Section 7.4: #25
  
  1/25 Section 7.2: #25, 27, 33, 35, 59, 61, 99, 101, 105, 111-121 odd, 139, 141.
  
  1/26 In Lieu of a Saturday Make-up class: Read about the hyperbolic functions (Section 7.6). These functions arise naturally in solutions to differential equations modeling physical and engineering scenarios. These particular combinations of exponentials come up so often and are so useful, they get their own names (see definition 7.6.1)!
  
  Test #1 will be held on Weds. Feb. 6. It will cover everything we'll have done since the beginning of the semester through Fri. Feb. 1.
  
  1/30 Section 8.1: #1(a),(c), 3, 5, 7(a)-(c), 9(c), 13, 19, 29
  AND Section 8.2: #1(a), 5(a), 7(b), 11
  
  1/31 Section 8.1: #9(a),(b),(d), 18
  AND Section 8.2: #12, 15, 19, 21, 25, 27, 29(a),(b), 31, 33, 49(a)
  
  2/1 Section 8.1: #1(e), 15
  AND Section 8.2: #3(a), 7(a), 16, 29(c). For #16, just do the indefinite integration. Ignore limits of integration.
  
  Reminder: Test #1 Weds. Feb. 6. No calculators!!!
  
  2/7 Section 9.2: #1, 3, 5, 9, 15, 17, 19, 33, 37, 43, 47(a), 49(b), 53
  
  2/11 Section 9.3: #1, 5, 11, 13, 19, 23, 25, 31(a)
  
  
• Integrating Trig Products and Powers Handout
  
  2/13 Section 9.4: #1, 3, 5, 7, 11, 13, 25, 27, 37(a) and derive the reduction formula for cot(x) to the nth power.
  
  2/14 Section 9.5: #1, 3, 5, 13, 21, 23, 27, 39, 43 Happy Valentine's Day :-) !!
  
  
• Partial Fraction Integration Examples
  
  2/18 Section 9.6: #5, 9, 13, 17, 23, 29, 33, 41, 48
  
  2/22 Section 9.8: #5, 11, 17, 19, 21, 25, 29, 37.
  NOTE: Use n=4 instead of n=10 in the book's directions! Also, use our method and error bound for Simpson's rule instead of the book's!! Obviously then, your answers will differ from the book's answers for many of the problems!!
  
  
• Blank Copy of Quiz #2
  
  
• Some Ch. 9 HW problems for test practice. Make yourself something similar with other problems, perhaps even ones not assigned for HW!!
  
  2/27 and 2/28 Section 10.1: #1, 3, 5, 7, 17, 21, 23, 27, 29, 35, 43(a), 45, 47, 48
  
  3/10 Section 10.2: #3, 5, 11, 13, 19, 21, 27, 33, 35
  
  Reminder: Test #2 on Integration (Ch. 9 material and 10.1) is Monday March 17!! You can bring a clean copy of the Trig Products and Powers Handout and a basic calculator!
  
  3/13 Section 10.3: #5, 7, 11, 13, 15, 25, 31, 35, 37, 38, 43-45, 49, 57, 61a
  
  3/20 Section 11.1: #1-21 odd, 25, 35b.
  
  Reminder: HW Quiz #3 Thurs. March 27. Sections 10.2, 10.3, 11.1
  
  3/27 Section 11.2: #1-23 odd, 30.
  
  
• Solutions to Test #2
  
  3/31 Read Section 11.3. Homework coming Weds.!
  
  4/2 Section 11.3: 1(b),(c), 3-15 odd, 23, 27, 29, 33, 35, 41
  
  4/3 Section 11.4: 1, 3, 5aceg, 7, 9, 13, 19, 20, 25, 27, 29, 31, 39
  
  4/4 Get Comfy with Sections 11.3 and 11.4: Re-read, finish up HW, do more for fun, work with friends, etc... Be ready for lots of new series tests starting Monday!
  
  
• Solutions to Quiz #3 (whoops, meant to post earlier!)
  
  4/7 Section 11.5: 1-31 odd.
  
  4/10 Section 11.6: 1-11 odd, 15-25 odd, 29, 31, 36, 41, 42
  
  4/11 Section 11.7: 1-17 odd, 21, 25, 29, 33, 35
  
  
• Solutions to Quiz #4
  
  Reminder: Test #3 on Limits, Sequences, and Series (10.2, 10.3, 11.1-11.7) is Friday April 18 (as usual, come a few minutes early, leave a few minutes late!!) You can bring a basic calculator!
  
  
• Taylor Remainder Proof Worksheet
  
  
• Step-by-step guide to computing Taylor series
  
  
• Example 1: computing a Taylor series and more!
  
  
• Example 2: computing a Taylor series and more!
  
  4/18 Section 11.9: 1, 11, 13, 15, 23, 25, 33 AND Section 11.10: 3, 9, 11, 15, 17
  NOTE:
  This weekend's HW is to give you practice computing Taylor series and Remainders. Use the above links (and your book) for help and guidance. Next week we'll talk about convergence and expand (get it, ha ha:) our use of Taylor series!)
  
  4/21 Section 11.10
  Bound the error in using the nth degree Taylor polynomial to approximate f(x) at x=b for the functions and values of a and n given in Section 11.10 exercises #3 (use b=0.5), #9 (use b=3), and #11 (use b=pi/4).
  ALSO,for the function in exercise #17, determine the smallest degree n of the Maclaurin polynomial such that the error (|remainder|) can be guaranteed to be less than 0.0001 in approximating f(x) at x=b for (i) b=0.5 and (ii) b= -0.5.
  NOTE: For each of the above problems, you have already computed the remainder (error) term in 4/18 HW!!
  
  4/23 Section 11.8: 1, 5, 9, 13, 19, 23, 29 AND Section 11.10: Show that the Maclaurin Series' for the functions e^x, cos(x), and the inverse tangent function have the intervals of convergence given in Table 11.10.1. NOTE: See Link above to Example 1 computing a similar convergence result for ln(x) expanded about a=1.
  ALSO:
  USE the series' and convergence results in Table 11.10.1 to (relatively quickly!) do exercises in Section 11.10: 29, 31, 37, 39, 55, 57 (See Examples 5 and 6)
  
  LAST HW OF SEMESTER!!!!
  
  
• Solutions to Test #3
  
  
• Blank Copy of Test #1
  
  
• Blank Copy of Test #2
  
  
• Blank Copy of Test #3
  
  
  
  Tutoring Center Link
  
  
• Top 10 Job Skills 2005 from Monster.com
  
  
• What it means to be a college student, OUCH!
  
  
• Syllabus Math 236
  
  
• Shorthand Symbols and Proof Techniques
  
  
• Basic Propeties From Algebra
  
  
• Limit Tools Math 235
  
  
• Important Calculus Tools Math 235
  
  
• Derivative Tools Math 235
  
  
• Integral Tools Math 235
  
  
• Step by Step Numerical Integration
  
  
• QUIZ 1 KEY
  
  
• QUIZ 2 KEY
  
  
• QUIZ 3 KEY
  
  
• QUIZ 4 KEY
  
  
• LAB 1 KEY
  
  
• TEST 1
  
  
• TEST 2
  
  
• TEST 3
  
  
• TEST 1 KEY
  
  
• TEST 2 KEY
  
  
• TEST 3 KEY
  
  
• Root Test Work Sheet (PRINT)
  
  
• Taylor Series
  
  
• Example Taylor Series
  
  
• Example 2 Taylor Series
  
  

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