MATH 253a - Accelerated Calculus III

Click here for latest version of the Syllabus

Current Office Hours:

Tuesday 11:30-2:00 walk-in (other times by appointment)


Date: Assignment(s): Handouts
Aug 20 Class: go over syllabus, start vectors.


Read: 11.1-11.3

Problems: (not to be turned in; quiz Friday):
11.1/35, 37, 41, 51
11.2/3-39 odd mult of 3; 31, 41, 49
HW will be discussed Wednesday;
Quiz Friday on these two sections

Slides from lecture:

Vectors 1


I would like everyone to try the first assignment, which is called "Demo", before 11:00PM this Friday, August 24 (but preferably before class so you can ask questions in class if you have problems). These are some simple problems you should all be able to do, but will give you practice working the interface. I am not counting your score on this one, but I want to see that you've at least tried a selection of the problems.

The second assignment, "Vectors1", will open at 08/22/2018 at 05:00pm (so after Wednesday's class), and is not due until Monday, 08/27/2018 at 10:00pm, but for full credit you should have tried most of the problems by midnight Friday, 8/24.

VIDEO TUTORIAL (best viewed in fullscreen mode; use controls to pause or single step):

(Note: no sound in these videos, sorry. Also, it was created for another class, but the "Demo" assignment is essentially the same)

To log in to WebWork, go to

Your login should be either your UH email address, or the part of that address before the @ sign. For example, if your UH email is, your login should be myname

Your initial password is your 8 digit UH ID number.

This is a FREE FOR YOU online homework system. As discussed in the syllabus and in class, I will be giving some assignments using it. It isn't hard to use, and will even let you check correctness of your answers before submitting them.


Aug 21 Class: Dot products, applications, start cross product


Read 11.4

HW will be discussed Friday

Slides from lecture:

Vectors 2 (dot products)

Aug 22 Class: Continue dot products, start cross products (?)

Discuss HW from 11.1-2

Vectors 3 (cross products)

Aug 24


Aug 27 If UH is open:

Projections of vectors

Start cross products

Aug 28 Class: Finish cross products; start lines and planes

Discuss 11.3 HW

11.3/13, 18, 21 (compare to 19!), 28, 43 (these are additional problems that will not be covered on tomorrow's quiz, but might show up in an extra credit context)

11.4/7, 15, 17, 21, 23, 27,28, 29, 30abc,31,33 (27-31 should go quickly!), 35, 39, 43
(WebWork exercises on cross products coming soon!)

Aug 29 Class: Finish cross products; start lines and planes

Quiz on 11.1-3 (long, as it combines 2 quizzes)

Lines and Planes
Aug 31 Class: Continue lines and planes

11.5/3,9, 10, 23,25,26,27,31,35,41,45,59,61,65,67

On all of these problems if the answer is a line then give the equation in all three forms: vector, parametric, *and* Cartesian

Sep 3 Labor Day - no class
Sep 4 Class: Finish lines and planes

Start Ch 12(?)

Discuss 11.4 HW

Sep 5 Continue Ch 12

Discuss 11.5 HW

No Quiz Today!

Vector Functions 1

Vector Functions 2

Sep 7 Quiz on 11.4, 11.5
Sep 10

12.1/3, 7,8, 9, 13, 21,23,25,27,28,29b,34
12.2/2, 3, 5,9, 27ab,29

Note: projectile motion will not be on the first exam (but you could look at 12.2/17,18)

Sep 11

Examples from 12.1,2

Start 12.3

Sep 12 Discuss HW from 12.1, 12.2

Continue 12.3


Sep 14 Quiz on 12.1,2

Finish 12.3, start 12.4 (Well, that didn't happen!)

12.3/3,5,7,13, 15; look at 18, 19 (which is easier than it looks, and combines ideas we've been doing), and 20 should be easy for you using the answer to 19!

Sep 17 Finish 12.3, start 12.4

Here are some supplemental arclenth problems

Sep 18
Sep 19 Exam review

Solution to 12.3#19,20 (sorry I forgot to post this last night)

Sep 21 Midterm I

Covers 11.1-11.5, 12.1-12.3

You will NOT be allowed: calculator, text
You WILL be allowed: one page of notes (one side of one 8x11 sheet of paper, you can write anything you like on the page)


(I will NOT be posting solutions!)

Sep 24

Finish 12.4; start 12.5

12.4/1,5bc,6ab,7ab,9,11, 23,26; look at 17 (for the graphs in 23, 26 feel free to use a computer)

Sep 25

Finish 12.5; start Ch 13

(12.6 will be done outside of regular class with a video on Kepler's laws)

12.5/1,3,5 (see text example 1), 7,11,13,23. (See Figure 12.27 for 7-13; I only care about the normal and osculating planes, not the rectifying plane) Think about 17-19!

Sep 26 Discuss HW from 12.4

Continue Ch. 13

13.1/13-18,21,27,39 (I might add more to these!)

Cylinders and Quadric surfaces

You should be able to graph cylinders quickly using the fact that they are cylinders (even non-round ones)

As for quadric surfaces, I don't expect you to be able to name them, but you should hone your graphing skills to the point where you can graph relatively easy ones and can match equations to their graphs. You should also be able to recognize when an equation is the equation of such a surface.

11.6/ 1-12; 15, 19, 23, 35

Sep 28 Discuss HW from 12.5

Quiz on 12.4

Oct 1 Continue Ch 13 Differentiation of functions of several variables
Oct 3 Limits and continuity for functions of n variables

Derivatives in R^n

(Discuss on Tuesday)

Oct 5 Quiz on 11.6, 13.1

13.5/7, 13, 19, 21, 25, 29, 35

Oct 12 Quiz on 13.2,3,5

13.4/3,9-23 odd,27, 29, 30, 41, 45, 47
13.6/3,5,9,15,17; optional 21,41

Lecture Notes on Min/Max
Oct 15 13.7/ 31, 33, 34, 35, 37 (These are covered for the exam!)

13.7/ 3,7,17,27, 29, 39, 41, 45, 47,51, 55; (Not covered on this exam)

Oct 18 Informal review session, 4-5, room TBA
Oct 19 Midterm Exam II

Covers: 12.3-5, 11.6, 13.1-6, 13.7 (slightly)

You will NOT be allowed: calculator, text
You WILL be allowed: one page of notes (one side of one 8x11 sheet of paper, you can write anything you like on the page)


(I will NOT be posting solutions!)

For 13.7, the problem(s) will be just like one right out of the HW assignment.

Oct 22 LaGrange multipliers

Taylor series n dimensions

13.8/5,9,13,19,23,29 <= 1-constraint LaGrange problems
13.8/31,37 <= 2-constraint LaGrange problems
13.8/43 <= just an interesting problem; try it!


Handout on LaGrange multipliers
Oct 23 Multiple integrals Lecture notes on multiple integrals
Oct 24 14.1/3,7,13,15,23

14.2/3,5,11,15, 19,32,35,37,41,51. 54 is pretty interesting.

Oct 26 There will be no quiz today.


Polar Coordinates Review

If you haven't seen polar coordinates, you might want to look at these videos before we get to 14.4 (soon!)

1. What are Polar Coordinates?

2. Polar graphs, and Area in Polar Coordinates

Some exercises to try:

10.1/1-21 odd multiples of 3; 23,27,29,33,40,45 (these shouldn't take you more than a few minutes each

I will not be quizzing or examining you on these; you are supposed to know how to do these already before taking Math 253a!

14.5/9, 15, 21, 23, 29, 35, 41,47 Do #13 without actually integrating
Nov 2 Quiz on 14.1,2,3,5

14.4/9, 13, 22, 27
14.6/3, 5, 9, 19, 33

Nov 5 Finish 14.7; start 14.8 (?)

14.7/3, 7, 11, 17, 21, 37
14.7/51-75 odd multiples of 3; at least set them up

Nov 6 No class - election day - go vote!
Nov 7 Finish 14.8

By request: solution (setup) to number 33


Some slides from today's class:
  1. First spherical integral example.
  2. Second example. (Note that the integral I set up was correct after all, my description of the region in the board was wrong, which is what led to the confusion.)
  3. The volume element for spherical coordinates using the COV formula
  4. Diagram justifying the COV formula for R^2
  5. COV in R^n examples
Nov 9 Section 15.1 (line integrals)

Quiz on 14.4,6

SOLUTION TO QUIZ 7 (last week's)

You should be able to do the following even just from lecture today:


(I will add to these)

Nov 13 15.1/25, 30
15.2/3, 5, 7, 9, 13

The material through here, including problems like these, will be covered on Midterm III

Nov 14
Nov 16
Nov 19 Midterm Exam III

Covers: 13.7-13.9, 14.1-14.8, 15.1-2

See an approximate points breakdown

You will NOT be allowed: calculator, text
You WILL be allowed: one page of notes (one side of one 8x11 sheet of paper, you can write anything you like on the page)

I will provide a table of integrals.

Sample exam

Nov 20 Line integrals of gradients

15.3/3, 5, 9, 13, 19, 27, 32, 33

Nov 21 Start Green's Theorem

Slides on Green's Theorem, div, grad, curl
Nov 26 Finish Green's Theorem

15.4/5, 7, 11, 23, 26, 27, 33

Nov 27 Start Surface Integrals Surface integral slides
Grade estimation webpage.
Nov 30 Finish surface integrals

15.5/17, 21, 37
15.6/7, 13,15,17,33

Kepler's Laws.

Now that you've been using polar coordinates again, you are ready for this derivation, which is also a nice review of the material from the end of Chapter 12. You might need to review the equations of conic sections (especially the ellipse) in polar form, see Section 10.5 in the text.

You should watch this short (~15 minutes) video...
...and answer the questions on this problem sheet.

This is due by the day of the final exam. You may watch it and work on it with a classmate, but turn in your own answers.

(If you have trouble with the video, try this version.)

Dec 10 I will have some extended office hours, probably 11:00 - 2:00 (I will be giving an exam to my other class 2:15-4:15). If you can't make these and want to see me after 4:15, let me know ASAP.
Dec 12 Final Exam, 12-2, Keller 404.


Practice Final Exam 1
Practice Final Exam 2
Practice Final Exam 3
Practice Final Exam 4


The scores ranged from well under 100 to over 200. If you want to see your exam, you can look it over in my office (probably next semester). Please please please check that the grades I have for your midterms are correct, it is far easier for me to make changes now than after I file semester grades with the registrar.

I will not be posting semester grades, you will be able look them up on MyUH.