Spring 2007 Math 153H-1 Information
Contact Information: Lawrence Roberts
A345 Wells Hall
{instructor's first name} {at} math {dot} msu {dot} edu
Office Hours:
M 10:30 - 11:30 am
W 3:00 - 4:00 pm
Th 2:00 - 3:00 pm
These are subject to change depending upon demand, but those hours listed on this website will be correct.
If you cannot make these times, send me an email and we can make an appointment.
The syllabus can be found at
Class notes Homework 1 pg. 406 - 408, # 7, 15, 19, 27, 31, 35, 41, 45, 49, 56. Read the problems carefully!
The book shifts between which axis to rotate around. For examples look at pages 400 - 405. For next lecture read pages 409-411.
Homework 2 pg. 414-415 # 5, 7, 17, 23, 33, 35, 36. Read "Length of a parametrically defined curve", pg.417-418
(if you need to review parametric curves, see pg 195-197 or so). Mimic this argument to derive the formula for the length of y=f(x) in the blue box on page 420.
Homework 3 pg. 423-424 # 5, 7, 9, 16, 19, 21, 26, 28, 29, 30. The formulas for surface areas of revolution are in section 6.5.
Do problems 13, 21, 30 on pages 445 - 446.
Homework 4 pg. 484-485 # 11, 17, 19, 21, 23, 26, 33, 39, 41, 43, 45, 47, 49, 53, 69, 73.
Use the formula for the derivative of ln x and substitution for the integrals. Read pgs 466-472 for Friday.
Homework 5 (for MONDAY Jan. 22) pg. 473-475 # 13, 16, 17, 25, 29, 31, 33, 36, 39, 43, 45, 48, 49
Homework 6 pg. 485 # 57, 61, 65
pg. 493-494 # 21, 27, 31, 35, 39, 45, 49, 54, 57, 61
pg. 500-501 # 38, 39, 43, 44, 46, 51, 53, 55
pg. 502 # 93, 96, 97, 99
Homework 7 pg. 509-511 # 2, 3, 5, 12, 19, 21, 25. Read pgs 511-513 do problems #1, 3, 5, 17, 19, 20 on pgs 515-516
Homework 8 pg. 530-532 # 5, 13, 27, 29, 35, 50, 55, 59, 61, 68, 70, 121, 122, 123, 129.
Homework 9 pg. 530-532 # 73, 75, 79, 81, 85, 89, 90, 91, 92, 95, 97, 100, 101, 103, 106, 107, 109. Readsection 8.5 ( 8.5 ... in chapter 8, we'll come back to section 7.8 later)
Homework 10 pg. 585-586 #3, 7, 9, 11, pg. 591 # 7, 13, 17, 25, 30, 31, 32Look at the review sections for Chapter 6, Chapter 7.
Review Problems pg. 461-463 1, 9, 15, 17, 21. pg 547 - 549 everything 1 - 93 is good, but especially13, 14, 27, 29, 30, 73, 75, 77. Also 101, 107, 118, derive the formula for the derivative of sin^{-1}x and reviewsection 7.5. pg 585 1, 5, 7, 13, pg 591 9, 11 (use tan^{2} = sec^{2} - 1 to integrate tan^{2}), 19. All this is far more than anyone could reasonably expect to do.
Homework 11 Read section 8.1
Homework 12 Section 7.8 1, 5, 10, 13, 17, 23, 47, 53, 57, 67, 69, 79
Homework 13 Section 8.1 47, 49, 51, 53, 54, 55, 57, 65, 69, 77. Section 8.2 1,3,5,7
Homework 14 Read section 8.3 pgs 570 - 575. pg. 568-570 7, 9, 13, 15, 19, 23, 25, 26, 29, 35, 39, 40, 43
Homework 15 Section 8.3 pgs. 3, 5, 7, 11, 13, 15, 19 (factor!), 21, 23 (do you need partial fractions?), 35, 39. Ifyou're up for a challenge, try #52. Read section 8.6 (we won't cover this material, but it is useful to know. Pay particular attentionto pgs 597-600 as this is the modern way).
Homework 16 pg 592 # 44. On the same page, just before the problems, is an account of the substitution z= tan theta/2 we discussed in class.
pg 637 # 151, 155, 179, 181, 182, 190, 194, 208, 211. Note that on pgs 634-636 there are loads of integrals to try if you feel like you need more practice.
Read section 8.7 pgs 603-605, example 2.
Homework 17 Read pgs 607-611. pg. 613 # 3, 12, 21 (Just use the trapezoid rule and calculate its error, ignore the Simpson's rule parts to the problems)
Integrals: pg. 591 # 19, 23, pg. 635 # 85, 107, 119, pg. 638 # 5
Homework 18 For Friday, Feb 23.Read pages 619-625 of section 8.8. Section 8.7 # 19, 23, 25 (both trapezoid and Simpson's), 33.
Integrals:pg 635 # 83, 109, 121, 196 pg. 639 read tabular integration, do #41, 43 on pg 640.
Homework 19 For Monday Feb. 26: Review problems On Monday a solution sheet will be handed out in class.
Homework 20 For Wednesday Feb. 28: Study for second mid-term. I would suggest the practice exercises on pages 634-638. Make sure
to review how to compute the number of sub-intervals necessary for a given accuracy when using the trapezoid rule and Simpson's rule.
Homework 21 For Monday, March 12. Re-read section 8.8
Homework 22 For Wednesday, March 14. Section 8.8 #1, 7, 11, 15, 17, 25, 39, 42, 43, 51, 55, 57, 58, 62, 65, 74
Homework 23 For Friday, March 16. A few more improper integrals: Section 8.8 # 14, 24, 31, 33, 47, 53, 54. Carefullyread section 11.2. Use the formula in the box on page 764 to do Section 11.2 # 7, 9, 11.
Homework 24 For Monday, March 19. section 11.2 # 1, 5, 15, 18, 19, 23, 27, 29, 35, 38, 41, 43, 77, Section 11.3 #6, 9, 16, 21 (look back at the inverse trig functions)
Homework 25 For Wednesday, March 21. section 11.3 section 11.3 (Integral test again) 22, 23, 25
section 11.1 27, 31, 37, 45, 49, 52, 55, 59, 62, 63, 68, 73, 78, 81, 88
Homework 26 For Friday, March 23. Read section 11.5, section 11.4 (Comparison and limit comparison tests) 2, 3, 5, 7, 9, 11, 15, 17, 25, 27, 33, 35, 38, 40
Homework 27 For Monday, March 26. Section 11.5 # 1, 2, 3, 5, 9, 12, 14, 19, 20, 23, 29, 36 (tricky), 41, 44
Homework 28 For Wednesday, March 28. Section 11.6 # 5, 10, 15, 19, 21, 25, 26, 29, 36, 39, 45, 51, 61, 62
Homework 29 For Friday, March 30. Section 11.7 # 3, 6, 7, 10, 11, 15, 21, 23, 27, 29, 35
Homework 30 For Monday, April 2. Read section 11.8, pg. 805-809!!! problems # 1, 5, 9, 11, 13, 17, 19, 23, 27
REVIEW FOR THIRD MID-TERM: pg. 804-805 39, 42, 43 (this is practice for what we discussed today). pg 840 - 841 (I realize this is a lot, but try to do some from each section. We'll cover as much as we can on Wednesday)Sequences # 7, 11, 14, 18
Improper Integrals pg. 637 # 138, 139, 146
Series # 19, 24, 30, 33, 34, 36, 40
Power Series # 43, 44, 45, 47
Taylor Series (don't find these by taking derivatives!) # 57, 61, 64, 78. Now use derivatives to find the Taylor series at a = 0 for f(x) = (1 + x)^{-1/2}.
Extras # 89, 92, 95, 100
Homework 31 For Wednesday April 11. Read section 11.10. Pay special attention to pgs 824-827. pg 832 # 43, 44, 46 (don't worry about the error of magnitude, find the Taylor series instead!), 47, 51, 53, 55. Look at page 831 for a list of useful Taylor series.
Homework 32 For Friday April 13. There are examples on pgs 824-827. pg 832 # 17, 19, 21, 23, 27
Homework 33 For Monday April 16. A few more problems about Taylor series. pg 831-833 3, 5, 7, 69, pg. 820 41, 45. Read sections 10.5, 10.6.
Homework 33 For Wednesday April 18. Section 10.6 # 1, 5, 7, 9, 21, 23, 45, 46
Homework 35 For Friday April 20. Section 10.7 # 1, 3, 5, 7, 13, 18, 19, 21
Review: There is no homework for this weekend! On Monday we will review chapters 6 and 7. The material for the final will comefrom
Sections 6.1 - 6.3, 7.1 - 7.7, 8.1 - 8.5, 8.8, 10.6-10.7, 11.1 - 11.10
A few topics will not appear: numerical integration and hyperbolic functions, for example. A good way to review is to lookat the old
mid-terms and understand every problem, then move on to the review sections at the end of each chapter.
Note: On Wednesday we will cover 6.1 - 6.3 as well as the techniques of chapter 8. You should learn the formulas insections 6.1 -6.3, but you should also understand how they arise.
Note #2: The math department maintains some old finals at math department website, sample finals . While there is no sample for this course, you should be able to do eveything on the sample final for math 133. The questions on your exam will be similar in form, but will also include some harder questions.