Calc III HW

The calendar below includes your exams, homework (HW) due dates and a list of your daily HW exercises. I will probably adjust some dates and content from time to time, but will also announce any major changes in class. If I need to post class news [moving an exam, hurricane news, etc] I will do it here first. You can print this page out, but be sure to check it regularly for updates. The HW lists are intended to bethe minimum required to get by. You should do at least 50 per cent more.

How to read the tables: As you can see from the first two tables below, I expect to cover Ch 11 in the first 5 lectures, from 8/24 to 9/7. Homework 1 is due on Thursday 9/9/10, on the assigned problems in Chs 11.1 thru 11.7 (so HW 2 starts with 11.8). Exam 1 is on 9/16/10. The rest is similar. As always, please contact me if you don't understand anything, or if you see a mistake.

You should be reading Ch 11 and doing HW 1, which is listed below. Look over Ch 10.1 - 10.3, to make sure you learned most of it (maybe not polar arc length, or polar tangent lines, for example) in MAC 2312. Look over this website including the syllabus, my policies and the exam page. If you need special treatment - such as a certified disability, a religious holiday conflict, etc - see me ASAP. If you can't be in class at normal times, see me.

Day	Date	I give you	You give me	Lecture topics	HW
1	T 8/24	web site		11.1 R^3 11.2 Vectors	odds 1-15, all 19-22, 29, 35 odds 1-15, all 17-20, 21, 25, 27, 31
2	R 8/26			11.3 Dot prod	odds 1-15, 22, 28-31, 34
3	T 8/31			11.4 Cross product 11.5 Param eqns	1, 3, 9, 11, 13-16, 17, 25 odds 1-9, all 11-14, 18, 29, 59
4	R 9/2			11.6 Planes	odds 1-15, all 21-24, 28, 43

Before Exam 1, read Ch 11, at least, and practice some True-False. You might also check my exam page. Look over the review problems on pages 838-839. Review HW 1, which I should return to you on 9/14. If you do not feel you have mastered the material, do more problems as needed. Main proofs to know for Exam I -

Exam I is mainly related to HW 1 [thru 11.7], but it may have an easy question from other recent sections [from approx 11.8 to 12.2], to check that you are keeping up. If you have attended the lectures and are reading the book, I don't expect you to have to study for this for Exam 1. These "recent sections" will also be on Exam 2, when I will expect more skill. This pattern repeats; Exam 2 and 3 will also overlap a little.

For now, I have no online help pages specificly for MAC 2313, but you can look at my MAC 2312 help pages for info on tutoring and links to helpful websites (you might also try the math dept page, which is probably more up to date). I often give a little extra credit for catching website errors, or for making some similar contribution to our world. Just email me, or stop by DM 419B.

Note: FIU [usually] has a Math Club that meets weekly. We often enter a team in the annual Putnam Exam. We have a certificate program in actuarial studies and often have job openings for graders and Learning Assistants. Please contact me if you are interested in any of this.

Remarks after grading HW 1: I graded 11.1.1 and 11.5.18 fairly carefully [about 30 points each] and spot-checked the rest for organization, completeness etc [about 40 points]. On the whole, the HW was good, but some HW packages were poorly organized [not in order, not stapled, not well-labelled]. Next time, if you label the top of each page with the current section number, I can find your work and give you the credit you deserve [this time, I tried...]. Do not copy from the back, or from anywhere else.

Day	Date	I give you	You give me	Lecture topics	HW
5	T 9/7			11.7 Q. surfaces 11.8 C/S coords	11.7 - odds 1-9, all 11-14, 16, 27 11.8 - odds 1-9, all 15-18, 23, 30, 37, 52
6	R 9 /9		HW 1 thru 11.7	12.1 Vec funcs 12.2 Vec Calculus	12.1 - odds 1-11, 17, 21, 24, 31-34, 37, 47 12.2 - odds 1-11, 19, 23, 29, 36, 41-45
7	T 9/14	Checked HW 1		12.3 Length 12.4 T and N, + review	12.3: odds 1-13, all 17-21, 25, 26, 34, 43 12.4: odds 1-13, 15, 19, all 21-24
8	R 9/16	Exam 1 on Ch.11

I will be giving a talk in the Math Dept about my work on Sept 20, and you are welcome to attend. Most of it will be aimed at the level of beginning graduate students, but I'll be trying to say some very simple things too. Check the Math Dept web site for the announcement.

HW2: I graded 11.8.15-18 [30pts] , 12.2.1 [20pts] , 12.6.32 [20pts] , and completeness / general [30pts]. If you missed 12.6.32 for whatever reason, I graded 12.5.29 instead, but deducted 5 points from your completeness grade. The resulting average was about 80%.

Day	Date	I give you	You give me	Lecture topics	HW
9	T 9/21			12.5 Curvature 12.6 Motion	12.5: odds 1-9, all 19-22, 23, 25, 29, 58 12.6: odds 1-9, 17, 25, 31, 32, 39, 43 all 47-50
10	R 9/23			13.1 f(x,y)	odds 1-11, 14, 17, 19, 25-28, 39, 42, 61
11	T 9/28		HW 2 (11.8-12.6)	13.2 Limits	odds 1-15, 24, 27, 29-32
12	R 9/30			13.3 Partial Ds	odds 1-11, all 13-16, 29, 35, 39, 47

HW3 - I graded 13.1-7, 13.2-24 and 13.4-27 to 30. Notes: a) the book asks you to explain the TF; b) 13.4.28 is false [if f is not continuous]; c) if you attached 12.6 from HW2, in a very clear manner, I added up to 10pts; d) several unstapled HWs came apart ... I will deduct more points for this next time; e) you need L'Hopital for 13.2.24.

Exam 2 will cover mostly topics from HW 2 and 3 [Ch.11.8 thru Ch.13.4] and the lectures thru R 10/7 [thru approx Ch 13.6]. Remember to practice with True-False, and pay attention to special examples in the reading. Know the main formulas used in class or HW (such as the top of page 834, misc formulas in blue in Sections 12.2-12.6, and 13.2 to 13.4). Prepare for these proofs :

Day	Date	I give you	You give me	Lecture topics	HW
13	T 10/5			13.4 On Derivs 13.5 Chain Rule	13.4 - 1, 7, 9, 11, 13, 21, 23, all 27-30, 33, 49 13.5 - odds 1-7, 17, 23, 29, all 35-38, 40, 43, 55
14	R 10/7		HW 3 (-13.4)	13.6 Gradients	13.6 - 1, 3, 9, 19, 21, 23, 25, 29, 39, 41, 45, 47, 55, 61-64
15	T 10/12			13.7 T Planes + review	13.7 - odds 1-7, 11, 13, all 17-20, 27
16	R 10/14	Exam 2

Now, HW4 goes thru 13.7, so HW 5 starts with 13.8. For HW 4, I graded 13.5-55a [not many correct] [30pts] and 13.7 TF [40pts], and general [30pts]. I've posted some hints for the 13.8 HW problems on my help page.

The Drop deadline is 10/15/10 [but check this!]. To estimate your semester grade, average your two exam scores and use the scale for Exam 1 [Exam 2 is the same]. You can find the scale on the answer key. If you don't understand this, see me.

Sections 14.4, 14.5, etc require visualization in 3D. If you find this hard, practice additional exercises until you are more comfortable. It may also help to draw 2D traces of the solids (see Ch 11.7). You are not expected to use software to graph any of these surfaces, but if you feel you need to do that, MathGV is freeware, and easy to learn.

Day	Date	I give you	You give me	Lecture topics	HW
17	T 10/19			13.8 Max Min 13.9 Lagrange	13.8 - 1, 3, 7, 9, 13, 23-26, 27, 31, 35, 43 13.9 - 1, 5, 9, 13-16, 29
18	R 10/21		HW 4 (thru 13.7)	14.1 Double Ints 14.2 More general	14.1 - 1, 5, 10, 13, 17, 23-26, 29, 35 14.2 - 1, 5, 9, 11, 13, 16, 19, 29, 33-36, 47, 61
19	T 10/26			14.3 in polar coords	14.3 - 1, 5, 7, 11, 13, 17, 23, 30, 35-38
20	R 10/28			14.4 Surface Area 14.5 Triples	14.4 - 2, 5, 11, 13, 19, 39, 47-50 14.5 - 1, 4, 9, 15, 19, 25, 27-30, 39

If you are interested in becoming a McNair Fellow, click here, and / or see me. If enough of you are interested [let me know!], we can invite Dr Banjoko to give us a presentation. In my opinion, this is a good opportunity for almost any math /sci /eng major.

HW 5 only goes through Ch 14.6 - problem 9 [because my 11/2 lecture didn't get very far into that section]. The rest of 14.6 will be part of HW6. Nov 6: I graded 13.9-9 and 14.1-10 [30pts each] and overall [40pts].

Exam 3 will cover mostly HW 4-5 topics. I suggest giving extra attention to Ch. 13.9: 5-12, Ch.14.2: 15-18, E5 (Example 5, pg 982) and E4 (pg 1055). And, of course, any problems in HW 4-5 you are still not sure about. I won't ask anything very hard from 14.7, but be ready for something straightforward, such as E2 (pg 1064).

We have not done many real proofs lately, but I might ask you to explain a formula, such as

* Thm 13.6.6 (see the explanation above the Theorem on page 965 and put it in your own words).

If you have questions before Tuesday, please email me, hudsons AT fiu DOT edu. Or, try the usual resources, such as the Learning Center in the library.

Day	Date	I give you	You give me	Lecture topics	HW
21	T 11/2			14.6 in C/S coords	14.6 - 1, 5, 9
22	R 11/4		HW 5 (thru 11/2/10)	14.6 [more] 14.7 Jacobians	14.6 - 13, 17, 21-24, 27 14.7 - 1, 5, 9, 13-16, 17, 21, 31, 32
	T 11/9			14.8 C of Gravity 15.1 vec fields	14.8 - 2, 5, 9-12, 13, 15, 17, 23, 37 15.1 - 1, 3, 4, 7, 11-14, 15, 17, 23, 34, 41
23	R 11/11	Vet Day	No Class		na
24	T 11/16	Exam 3			na

Except for the final, all work is due on 11/30. This includes HW6, any late HW, any requests to review grading, any medical excuses for missed work, etc. I have moved HW 6 to Tues Nov 30 and included section 15.3. You don't have to hand in HW from 15.4 to 15.8 but practice those before the final. We are not supposed to cover Ch 15.6, but it might be helpful to scan it, especially if you want to understand the physical meaning behind certain examples in Chs 15.7 and 15.8.

Day	Date	I give you	You give me	Lecture topics	HW
25	R 11/18			15.2 Line Ints	1, 3, 11-14, 15, 19, 29, 33, 41
26	T 11/23			15.3 Indep of Path 15.4 Green's Thm	15.3 - 1, 5, 9, 15, 19-22 15.4 - 1, 7, 13, 15-18, 29
	R 11/25	T Day
27	T 11/30		HW 6 (-15.3) + any late HW + excuses	15.5 Surface Ints 15.7 Div Thm	15.5 - 1, 3, 5, 9-12 15.7 - 1, 5, 6, 9
28	R 12/2	Checked HW		15.8 Stokes + review	15. 8 - 1, 5, 13, 14

The final counts 40 points - at least half will be on recent material (like an "Exam 4") and the rest will be review. It cannot be dropped; see the policy page about this, about incompletes, etc. Be sure to do the listed HW problems from Chs 15.4-15.8, even though I won't collect them. The best review is to work a variety of exercises like the past homework.

Important examples, possible weak spots, etc: basic geometric questions (distance to a plane or line, using projections, angles between vectors, intersections of planes, etc), Directional derivatives (see Exam 3; Prob 1), the major definitions (differentiable, curvature, limit, continuous, etc; see Exam 2; Prob 8), area of a surface (see Exam 3 Prob 7). Review the various types of integrals we've seen to be sure you know the differences (eg along curves and surfaces; of scalar functions, vector fields, etc). It goes without saying that other topics are likely too (max-min, center of gravity, potentials, approximations by tangent planes, etc).

Very recent topics: memorize the main theorems (Green's, Div, Stoke's) and the simplifications (for replacing dS, etc). Practice enough exercises with these, that you can do simple ones with confidence and don't get them confused.

Remember that the exercises after HW 5, or similar problems, will form a large part of the final.