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The schedule below assumes we will meet on campus from Jan 11 to mid April. It includes your exams, some tentative quiz dates, homework (HW) due dates and a list of your daily HW exercises. The HW lists below are intended to be the minimum required to get by. You should normally do at least 50 per cent more, or until you feel you have mastered each topic. I may adjust some dates and content from time to time, but will also announce any major changes here and in class. I may post class news items here. You can print this page out, but be sure to check it regularly for updates.

How to read the tables: As you can see from the first table below, I expect to cover Ch 12 in the first 5 lectures, from 1/11 to 1/27. HW 1 is due on 1/25, on the assigned problems in Chs 12.1 thru 12.4 (and HW2 covers 12.5 thru 13.3). The midterm exams are 100 minutes each, all on Wednesdays, including Exam 1 on 2/10. I have included notes below on Exam I and I will probably update them a few days before the exam. The other tables are similar. Notice that Exam 1 and Exam 2 topics overlap. As always, please contact me if you don't understand, or if you see a mistake.

Weeks 1 - 5 and Exam I

There will be a diagnostic quiz ("Quiz 0") on Wed 1/13 partly for us to learn how well-prepared you are. You may want to review Calc I and II skills, such as 

Simple derivative or antiderivative calculations like the derivative of ln(3x).
Basic trig identities such as the double-angle formula (or "half-angle formula").
Using symmetry, for example integrate tan x  on [-1,1] and simplify.
Solve a simple 2x2 system (used with Partial Fractions in 2312).
Find the extreme values of f(x) on [a,b] or (a,b) - if they exist.
Understand domain and range.
Find the equation of the tangent line to y = x^2 +3x +1 at x=2. Then approximate f(2.1).
Relations between rectangular and polar coordinates.

Then, start reading Ch 12 and doing HW 1, which is listed below. Review Ch 11 if needed  (perhaps excluding polar arc length, polar tangent lines, and Ch.11.7). 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. FIU may require me to report on attendance in the first weeks. If you can't be in class at normal times, see me.  

HW is due at the start of  class, 11am. Write it on paper, scan it into a single file, and send it to Melissa by email. Or you can give your paper to me before class, but the grading and the return may take longer. Your grade may include neatness and organization. You should, for example, label the top of each page with the current section number, so we can find your work easily, and give you the credit you deserve. Do not copy from an answer key, etc. Show all your work !

Check that you are registered for this course. If you registered late, after 1/13/21, contact me about Quiz 0 and getting into the PC building.

You should be able to access the MyLabsPlus software without my help; see the syllabus. For now, this is optional, except that you may need it to access the texbook. You can also try http://www.wolframalpha.com, which is free and easy. For example, type "plot z=x^2 +4y^2" and wait a few seconds. 

Before Exam 1, read Ch 12.1 thru 13.5  and practice with True-False. If needed, you can surf online for that, or use my exam page. Look over the textbook review problems for Chs 12 and 13. Review HW 1 and 2, to make sure you learned enough from them. If you do not feel you have mastered the material, do more problems as needed, preferably alone with book closed. See Melissa. Learn these proofs (including words!) for Exam I. I usually prefer the versions given in my lectures, if there is any difference, but I usually accept either. 

• Thm 1 of Ch 12.3 [p.728] with the angle.
• The component eqn of a plane [p. 746]
• The equation in Fig 12.35 [pg 740, V=TSP]
• 13.1 Equation 4 about ||r(t)||=C [pg 769]

The most common mistake with exam proofs is just not preparing for them. With some luck you should do OK preparing well for just 2 or 3. You can look over my old exams and answer keys for the question-types to expect.

Exam I may also have an easy question on "recent lecture topics" (already covered in a lecture, but not yet on graded HW) to check that you are keeping up. These topics will also be on Exam 2, and then I will expect greater skill. For Exam I, I expect these topics will be Ch. 13.4 and 13.5. 

Remember to check back here a few days before the Exam for possible updates. If you need help, you should normally see me or the TA. Or,  our dept site lists some other options. 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.

Learning Assistant [LA]: Melissa Venedicto, mvene010@fiu.edu.
Mondays: 1:00pm - 2:00pm, https://fiu.zoom.us/j/92783121081
Fridays: 12:30pm - 2:00pm, https://fiu.zoom.us/j/98868206787

Review Sessions: I do not expect to have much class time for review. In general you should ask our LA about doing this with Zoom, roughly a week ahead of each exam. Otherwise attend the LA's normal contact hours. If you have time conflicts with Melissa's hours you might try the shared sessions below.

Shared sessions: The department is organizing an online math help room for ODE and Cal 3 courses.  These are MTWR from noon to 3pm, starting Jan 19, manned by two graduate students at a time. The schedule and zoom links are

MW  12-3, led by Luis and Jose via https://fiu.zoom.us/j/96680693920  

TuTh 12-3, led by Alex and Ginelle via https://fiu.zoom.us/j/92497643673?pwd=T2NSS2JyTWlhazRZNTVFUTF3ajY4Zz09  

Other sessions: [a new link] The CAS at FIU offers a Calc 3 Study Hall. I am not very familiar with it but I think it is more free tutoring.

Exam and Quiz Rules:  If you bring any electronic devices (such as cell phones, airbuds, calculators, etc), you must leave them with me before the exam. Keep your eyes and hands on your desk at all times. Barring freaky weather, no hats, hoodies or long sleeves are allowed. Seats may be assigned. No bathroom breaks. Arrive early if possible so we can settle and start on time. If you do not follow these rules you will get a zero. You may also face charges of academic misconduct and/or cheating. If you cannot follow these rules contact me at least 24 hours in advance to discuss.

 I will post an answer key on the Exam page a few days later, probably including a more accurate (but unofficial) grading scale than the one on the syllabus. I may also post keys for quizzes and worksheets if time permits.

Quizzes, a relatively new feature, should help you keep up and give you more feedback. I expect to give approx 4, but the number and the dates given are tentative. I plan to discuss these a bit more in class and may also post some quiz remarks on this page. Quiz 0 is mainly a review of Calc I and II,  and Quiz I covers the Ch 12 HW, roughly. It should help you prepare for Exam I. I may also occasionally give you worksheets to solve in class. I do not expect to grade those, but I might eventually decide to treat them like quizzes. I would announce that in advance. 

 Weeks 6-9 and Exam II

Math at FIU - Check out the FIU Math Club. We usually enter a student team in the prestigious Putnam Exam, held every December. We have a certificate program in actuarial studies, a great career choice. We often have job openings for graders and Learning Assistants. If you are interested in becoming a McNair Fellow, click here. Most of these options are linked to the dept web site, or you can always see me.

Quiz 2 will be 3/1 thru Ch 14.5 [HW 3 and half of HW 4].

Mainly, Exam 2 will cover topics from HW 3 and 4 [Chs.13.5 thru 14.7]. Also, review Ch. 14.8 and the homework there. My remarks for Exam I above, about overlap, proofs, TF, review sessions, etc, also apply to Exam II. Know the main formulas used in class or HW. Know vocabulary such as domain, range, boundary point, interior point, relative extrema, osculating plane and Lagrange's method (but not necessarily the definition of differentiable). Prepare for these proofs -

• 14.5.9 about D_u and the gradient. The proof includes equations (2) and (3) above the theorem. Either notation for D_u is OK.
• Fig 14.31 in Ch.14.5 (Know the middle third of page 849).
• Any HW proofs [For example 14.2 ex.41]

Weeks 10-14 and Exam 3

Check the FIU Calendar about the Drop deadline (I think it is 3/22). I will post the current scale for the semester on the answer key to Exam II by approx 3/15. 

Fubini found a counterexample to reversing the order of integration, when f is not bounded. It is a bit involved, but if you are interested, the clearest explanation I can find is the picture on page 2 of this web page http://www.math.ubc.ca/~feldman/m226/fubini.pdf .

Section 15.5 may require visualization in 3D. If this seems hard, practice the easier exercises and work up. It may also help to draw traces or 2D cross sections. You are not expected to use software to graph any of these surfaces, but if you need help with that while getting started, you can try MyLabsPLus, Mathematica, MATLAB, wolframalpha.com, etc.

Quiz 3 is scheduled for 3/29  through Ch.15.7.

Exam 3 will cover HW 5 and HW 6 topics and the lectures/reading thru 3/31. On the topics after HW 6, know the vocabulary and prepare for exercises like 16.3.1 to 5, 16.4.1 and 16.4.11.

Proof list for Exam 3.

• Eqn (3) of Ch.14.6, page 855. The proof on page 854 is based on Eqn (1).

• Explain  "r dr dTheta". See Fig. 15.23 + equations + the box on pages 915-917 [or the lecture version]. Don't use the det formula for this.

Except for the final, everything is due by 4/12. This include requests to review grading, any medical excuses for missed work, etc. You don't have to hand in HW beyond Ch.16.2, but practice the listed problems before the final

The final will be Wednesday, 4/21/21, from 9:45AM to 11:45AM in PC 213.  It counts 25 points and cannot be dropped, even with a medical excuse. Almost half of it will be on recent material (like an "Exam 4") and the rest will be review. See the policy page about this, about incompletes, etc.  The best review is to work a variety of exercises similar to past homework.

Textbook Proofs for the Final:

• Thm 1 of Ch 12.3 [p.728] with  the angle "theta", or the version in the lectures.
• Fig 14.31 in Ch.14.5, page 849 [include the equations and box beside this].
• Exercise 16.8.32 (done in class). This replaces Green's thm which we did not do.

Review the 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, the major definitions (differentiable, curvature, limit, continuous), area of a surface. 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), but not all the proofs, and the simplifications (for replacing dS, etc). Practice enough exercises with these, that you can do simple ones with confidence. These topics will probably be emphasized at least as much as older ones. The exercises after HW 7, or similar problems, will form a large part of the final. Review your exams, especially any problems identified as weak spots on the answer keys, though it is unlikely that identical questions will appear on the final.

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