Thursday, May 6, 2010

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

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

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

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

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

Exam today!

Thursday, April 15, 2010

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