Math 104 - Lecture 2 Notes Thursday, September 15, 2011

Week 2 Material: Chapter 6 - Applications of integration

• Basic integrals; integration by substitution; fundamental theorem of calculus
• Integrals to find area, volume, velocity, position, average value, etc.

• Chapter 5 -- sections 5.4, 5.5 and 5.6
• Chapter 6 -- where the course begins -- sections 6.1 and 6.2

Maple - This week, get acquainted with it - commands to pay attention to this week are "solve", "plot", "limit", "diff" and "int".

Second Homework Assignment - due at lecture on Thursday, September 22.

1. Reading: Read sections 5.4, 5.5, 4.6 6.1 and 6.2.
2. More reading: In the Maple/Calculus Lab Manual, read the sections of the manual on "solve", "plot", "limit" "diff" and "int".
3. Textbook assignment: (submit nothing) Make certain you can do the following problems from the textbook:
• Section 5.4, page 333, # 15, 25, 51, 61, 73
• Section 5.5, page 342, # 17, 29, 39, 51, 71
• Section 5.6, page 350, # 17, 29, 39, 47, 55, 75, 101, 107
• Section 6.1, page 371, # 3, 9, 17, 23, 33, 41, 53, 57
• Section 6.2, page 379, # 3, 9, 17, 33, 41
4. Textbook assignment: Submit answers to the following textbook problems in lecture on Thursday, September 22:
• Section 5.4, page 333, # 16, 20, 52, 62, 78, 84
• Section 5.5, page 342, # 24, 36, 54, 78
• Section 5.6, page 350, # 30, 40, 48, 58, 68, 80, 98
• Section 6.1, page 371, # 2, 6, 16, 22, 32, 44, 52, 56
• Section 6.2, page 379, # 4, 10, 18, 32, 48

BONUS PROBLEM!!

Bonus problem #2: Consider a square with side length L. Let R be the region inside the square consisiting of all points that are closer to the center of the square than to any side of the square. What is the area of R ?

This is an interesting problem -- the hard part is to draw a good picture of the region and get equations for its (curved) sides. (Can you do it with Maple?)

For full credit, you must be as specific as you possibly can! When you have solved it, either write up the solution by hand and give it to me, or else send the solution to

deturck@math.upenn.edu

by electronic mail - extra credit for the first complete solution I receive.