Math 261-01: Calculus III

Thursday, May 6, 2010

Dave Richeson — Thu, 06 May 2010 20:43:17 +0000

Link of the day: the curse of dimensionality (This was what I was referring to in class today—that high dimensional spaces are difficult for statisticians to study.)

Sections to study for the final exam: 11.1, 11.2, 11.5, 13.1-13.6, 14.1-14.4, 15.1-15.8, 16.1-16.3, 16.6

Tuesday, May 4, 2010

Dave Richeson — Tue, 04 May 2010 20:36:36 +0000

Today’s topics:

Triple integration over a rectangular box
Triple integration over general regions
Volumes of hyperspheres

Homework:

Finish the handout from class
16.6 – 3, 9, 13, 14, 15, 19, 20

For next class:

Bring questions to class—review for final exam

Thursday, April 29, 2010

Dave Richeson — Thu, 29 Apr 2010 19:26:46 +0000

Quote of the day: “A mathematician is a device for turning coffee into theorems.” Attributed to Alfréd Rényi, and oft-repeated by Paul Erdős

Today’s topics:

Double integrals over non-rectangular regions
Using double integrals to compute area
Triple integration over a rectangular box

Homework:

16.3 – 3, 7, 8, 15, 20, 39, 40, 46, 47
16.6 – 1, 2

Read for next class:

16.6

Tuesday, April 27, 2010

Dave Richeson — Tue, 27 Apr 2010 19:58:23 +0000

Mathematical sculptor of the day: George Hart (I saw him give a talk this weekend—neat stuff!)

Today’s topics:

Double integrals over rectangular regions
Fubini’s theorem
Double integrals over non-rectangular regions

Homework:

16.2 – 3, 5, 10 (note: although it may not look like it at first glance, you can use formula 5 from this section to compute this integral), 15, 16, 27, 28
16.3 – 1

Read for next class:

16.3

Thursday, April 22, 2010

Dave Richeson — Thu, 22 Apr 2010 21:17:13 +0000

Quote of the day: Knowledge is knowing the tomato is a fruit. Wisdom is not putting it in your fruit salad.

Today’s topics:

The method of Lagrange multipliers
The definition of volume under a surface over a rectangle
Riemann sums for functions of two variables
How to compute volumes

Homework:

15.8 - 6 (you will get one point from the Lagrange multiplier method—is it a max or a min? Why?), 7, 8, 11, 25, 28
16.1 – 1, 2

Read for next class:

16.2

Tuesday, April 20, 2010

Dave Richeson — Thu, 22 Apr 2010 21:06:42 +0000

Exam today!

Thursday, April 15, 2010

Dave Richeson — Thu, 15 Apr 2010 20:33:01 +0000

Solution to Tuseday’s puzzle of the day: Solution 1.) turn the + into a 4: 5+545=550. Solution 2.) change the = into ≠: 5+5+5≠550.

Today’s topics:

Reviewed for the exam
The method of Lagrange multipliers

Homework:

Let’s plan not to have HW due next week. This assignment will be due 4/29
15.8 – 3, 4

Read for next Thursday’s class:

15.8

Exam 2:

Exam Tuesday, April 20
Topics on the exam: sections 11.5, 13.6, 15.1-15.7

Tuesday, April 13, 2010

Dave Richeson — Tue, 13 Apr 2010 20:29:41 +0000

Puzzle of the day: Add a single line segment to the following equation to make it true: 5+5+5=550 (there are two answers)

Today’s topics:

Max/min problems with a constraint equation
Extreme value theorem
Max/min problems on closed and bounded regions
The method of Lagrange multipliers

Homework:

15.7 – 30, 31, 34, 35, 43, 48
15.8 – 1

Read for next class:

15.8

Exam 2:

Exam next Tuesday, April 20
Bring any questions to class on Thursday. We can spend time reviewing for the exam.
Topics on the exam: sections 11.5, 13.6, 15.1-15.7

Thursday, April 8, 2010

Dave Richeson — Thu, 08 Apr 2010 18:35:32 +0000

Pictures of the day: Monkeys in saddles: 1 and 2

Today’s topics:

Max/min problem for functions of two variables
Critical points
Second derivative test

Homework:

15.7 – 1, 3, 5, 6, 7, 16, 19

Read for next class:

15.7

Tuesday, April 6, 2010

Dave Richeson — Tue, 06 Apr 2010 17:54:59 +0000

Video of the day: Nature by Numbers (no Calc III content, just a nice video)

Today’s topics:

Directional derivative
Gradient
Maximum/minimum directional derivatives
Gradient vector as normal vector

Homework:

15.6 – 11, 12, 21, 24, 25, 32, 33, 38, 41, 44, 47

Read for next class:

15.7