Math 121: Calculus II Fall 2013
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Math 121: Calculus II Fall 2013 |
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Prof. Rafe Jones
MW 8:30-9:40, F 8:30-9:30 in CMC 206 (Section 01) MW 11:10-12:20, F 12:00-1:00 in CMC 319 (Section 02)
Textbook: Calculus: early transcendentals, 2nd edition, by Jon Rogawski. |
There were three fine entrants in the all-important Best Sloth category. In the first one, the sloth is infatuated with Euler's formula, and seems unfazed by the brilliantly-colored formulas all around:
And now we have the Largest Formula award, with a hint of (ravenous) sloths to come:
Finally, we have a sloth that came out slightly more rotund than expected:
This one wins an award for Most Inventive New Holiday, with an equally inventive depiction of Euler's formula:
The next one wins the Modern Art award, with its undulous orange lines creating unexpected islands:
This one also has a cool design, with red arrows flaring up against the formulas:
Here's the winner in the Best Hitchhiker's Guide References category:
This one wins for Most Eye-Scorchingly Pink:
The next one takes the Smallest Writing prize, along with having remarkably straight lines and right angles, making the jagged line at the bottom stand out all the more:
Finally, this one featured the coolest geometric design occurring in just one region, a kind of geometric black hole:
Review session: Friday 10-12 in CMC 206.
Extra office hour: Sunday 2-3.
The final will be approximately twice as long as the midterms, though you'll have 2.5 hours in which to do it. It will cover everything we've done in the class. The material since the second midterm (Sections 10.3, 10.4, 10.5, 10.6, and 10.7) will account for between one-third and one-half the exam. That's why these sections are over-represented on the review problems below.
From the things we have studied since the second midterm, here are some that will definitely be on the final: finding the interval of convergence of a power series; the comparison and integral tests for convergence; finding Taylor series starting from known series; integrating Taylor series; the alternating series test and the alternating series error estimate.
You will be allowed to have one side of one 8.5 by 11 sheet of notes for the exam. All sheets must be handwritten. You can write anything you like on the sheet -- formulas, examples, mnemonics, your personal calculus mantra, etc. No magnifying devices allowed. For those who would like to decorate their sheets or otherwise artistically arrange them: I will post my favorite ones on the course website after the exam.
Review tips:
Review Problems:
The second midterm is Wednesday, November 6, in class. It will cover Sections 7.8 (you don't need to memorize the error bound, though you should be able to use the formula), 8.4 (you don't need to memorize the formula, but you should be able to use it), 9.1, 9.4, other material we've done on differential equations, and Sections 10.1 and 10.2, including the nth term divergence test. You should know what the solution is to the logistic differential equation, but you can use it as a formula without re-doing all the steps we did in class to solve it.
As with the first midterm, this one will consist of 5-7 problems that are similar in format to the homework problems. Good ways to review for the exam include working the review problems below, reworking any homework problems that you lost points on or feel you didn't fully understand, and reviewing your class notes.
Here are some review problems:
Chapter 7 Review Exercises (p. 465) #98, 103.
Chapter 8 Review Exercises (pp. 500-501) #23, 25, 27, 30
Chapter 9 Review Exercises (pp. 534-536) #2, 3, 5, 6, 7, 9, 25, 41, 43.
Section 10.2, #17, 19, 21.
Chapter 10 Review Exercises (pp. 603-605) #10, 11, 13, 15, 19, 21, 28, 29, 31, 75, 77.
For a few additional problems to work (numbered A1, A2, A3, A4, A5, and A6), click here. Included are solutions to the homework problems on Differential equations involving Chloe the canoeist. The problems on this sheet are important -- make sure you have time to get to them!
In order to simulate the actual exam, set aside 70 minutes and do the following problems: Ch. 8 Review Exercises #23, Ch. 9 Review Exercises #3, 6, 41, Ch. 10 Review Exercises #13, 15, 29, 77.
The first midterm is Monday, October 14, in class. It will cover Sections 7.1, 7.2, 7.3, 7.5, 7.6, and 8.1.
You should know how to find the integrals of sin^2(x) and cos^2(x) using integration by parts,
but you don't need to memorize any of the trig integral formulas on p.410. You also don't need to memorize the formulas for arc length or the surface area of a surface of revolution. Apart from these cases, the general rule is that the formulas and identities you need to know are those that you have used on the homework problems or that have appeared in class.
The exam will consist of 5-7 problems, each of which is similar in format to one of the homework exercises. You'll have the full 60 minutes on class on Friday to complete the exam. I've posted a bunch of review problems below. They won't be collected, but you should attach to them the same importance as a homework assignment, as they'll be quite useful for the exam.
Good ways to review for the exam include working the review problems, reworking any homework problems that you lost points on or feel you didn't fully understand, and reviewing your class notes.
Here are some review problems:
Chapter 7 Review Exercises (pp. 464-466) #13, 15, 17, 19, 21, 22, 23, 27, 29, 35, 37, 41, 43, 44, 48, 49, 53, 54, 56, 57, 75, 77, 79, 81, 82, 87, 90, 103, 104, 105.
For a few more review problems, which we'll discuss in class on Friday, click here.
In order to simulate the actual exam, set aside 70 minutes and do the following problems: Ch. 7 Review Exercises #13, 29, 35, 57, 79, 86. For comments and solutions to these problems, click here.
Friday's class will consist largely of review, and we'll go over some of the above problems.
| EXAMS |
Midterm Exam 2: Wednesday, November 6, in class Final Exam: |