# Tom Morley's 1508 Archive Winter 1998

### Who is this Integrator?

Hello.

Welcome to Mathematics 1508, Winter quarter 1998. My office hours are MWF 9:30-11, Skiles 263 or Skiles 237 (Math Lounge).

Updated 9 March

Quizlet of the Week

Previous quizlet results can be found here.
A substantial number of people answering last weeks quizlet said that we were going too fast. OK. I'll slow down. Please let me know when I am going too fast or too slow. -- tdm

Course Outline for Math 1508
Topic Sections Appoximate Days
The Integral 4.1-4.8 6
Applications of the Definite Integral 5.1-5.6 5
Areas in Polar Coordinates 8.7 1
Transcendental Functions and Their Inverses 6.1,6.3-6.8 6
Techniques of Integration 7.1-3,6,7,9 5
Ordinary Differential Equations 16.1-16.5 5

A final from this course, last year Solutions contain MANY errors -- Be careful.

Problems from chapter 16. ODE's

• Section 16.2, page 1039: # 1,2,3,4,5
• Section 16.3, page 1049, # 1,2,3,5,6,7,8,9,10
• Section 16.4, page 1-57 #1 through 20
• Section 16.5, page 1063, #1,2,3,4,5,6,7,8,10,11,12,17, 19

A list of sections and topics that you may have forgoten about, but which are in the sylabus, and therefore possibly on the final:

• The definition of the integral, and how to use it. See Section 4.4.
• Numerical integration, trapaziod and simpson's rule. Section 7.9
• Section 7.3
• Power and energy. See 5.4

SUGGESTED PROBLEMS FOR FINAL EXAM STUDYING:

• Section 4.4 Page 290 -- 1,4,5,7,9,11,23
• Section 4.4 Page 290 -- 1,4,5,7,9,11,23
• Section 4.5, Page 306 - 1, 5, 8, 31,33,35
• Section 4.6, Page 318 -- 3, 10, 15, 16, 25, 27, 35, 37
• Section 4.2, page 274 -- 1, 3, 10, 20, 23, 26, 27, 28, 29
• Section 4.7, page 326 -- 11. 12. 13. 19, 22, 23, 25, 29, 26, 27
• Section 5.1, Page 229 -- 1,3,5,7,15,17,19,25,29,31
• Section 5.2, Page 5.2 --1.3.5.19.20,22,23,24
• Section 4.2, page 274 -- 1, 3, 10, 20, 23, 26, 27, 28, 29
• Section 4.7, page 326 -- 11. 12. 13. 19, 22, 23, 25, 29, 26, 27
• Section 4.2, page 274 -- 23,25,27,29,31
• Chapter Review, Chapter 4, page 332, 1,3,11,13,15,18,19-24, page 333, # 5,6 (For the computer literate)
• Center of Gravity, etc, Section 5.6, page 376 -- 1,3,5,7,9,11,13
• Section 5.4, page 364: 1,3,5,7,13,15,21,24
• Section 5.6, page 376: 1,3,5,7,13,14,15,19
• Section 1: page 395 -- 18,19,20,21
• Section 2: page 406 -- 9,11,13,33,34,35,36,48.49
• ** Section 3: page 408 -- 1,3,5,7,7,9,11,19,41,43
• ** Section 4: page 430 -- 1,3,5,23,25,27,29,31,49,50
• Section 5: 19,21,23,25,27,28
• ** Section 6, page 450 -- 1,3,5,7,8,10,14,17
• ** Section 6.8, page 463 -- 19,21,23,25,29,31,25,27,39
• Page 450: (Section 6.6) 1,3,5,7,9,11,13,19 (Covered Wed/Fri).
• Page 364: 1,3,5,7,11,13,14,15,16,21,22,23,24
• Page 376: 1,3,5,7,8,9
• Page 376: 5,7,8,9,10
• Page 418: (Section 6.3) 1,3,5,6,7,11,13,14,15,,2122,23,25,27,31,32,33
• Page 430: (Section 6.4) 1,3,5,11,2,13,17,18,19,23,25,27,28,29,30
• Page 437: (Section 6.5) VI, 1,2,3,4,5,9,10,11,19,21,23,24,28,29,30,31
• Page 450: (Section 6.6) 1,3,5,7,9,11,13,19 (Covered Fri/Mon).
• The derivatives of arcsin, arccos, arctan, and how to derive them Page 463: 19,21,22,24,25,26,27,30,31,32.
• Page 463 35,36,37,38,42,43,44,45,47,49/
• > Page 463: 10,12,12,13,14,15,16,18.
• Integration by Parts: Page 485: 1,2,3,4,6,8,10,12,13,14,15,17,21,22,23.
• Integrals of certain trig functions: Page 490: 3,4,5,7,8,9,11,13,14,15, 20,21,23,24,25. YUK I hate these!!!!

Current Problems: Some problems:
• Page 510: 1,3,5,6,7,8,19,20,21,23
• Page 518: 1,3,5,6,7,8,9,,11,13,14,27

Extra credit: Find the integral of Square root of tangent x. To recieve credit on this you need to EMAIL me a detailed explination of the individual steps in computing this integral. I am NOT interested in just getting the answer, which is easy to do in maple or mathematica.

Quiz 3 solutions
Quiz 4 solutions

New! Improved! The calculus editable web pages (CoWeb pages) are here . Add what you like. I will give 1-3 points extra credit for substantial contributions to these pages. A substantial contribution is something that would prove useful to other students in this class and other students in calculus.

REMINDER: The student honor code:

Students are expected to act according to the highest ethical standards. The immediate objective of an Honor Code is to prevent any student from gaining an unfair advantage over any other student through academic misconduct. The following clarification of academic misconduct is taken from Section XIX, Student Conduct Code, of the Rules and Regulations section of the Georgia Tech General Catalog:<

• Possessing, using, or exchanging improperly acquired written or verbal information in the preparation of any essay, laboratory report, examination, or other assignment included in an academic course;
• Substitution for, or unauthorized collaboration with, a student in the commission of academic requirements;
• Submission of material that is wholly or substantially identical to that created or published by another person or persons, without adequate credit notations indicating authorship (plagiarism);
• False claims of performance or work that has been submitted by the claimant;

The easy way to do symbolic integrals: The Mathematica Integrator. This can also be used to check you own answers.
General Information

Class (at Tech) is at 11:00 am MWF in Skiles 256. On TTh, it is at 1:00 pm in the same place. The TA for 1508A is S. Manay

The quiz grades will be scaled and added together, and count for 55% of the grades. Computer Projects 10%, Homework 10%, and Final exam 25%.

All tests and quizes will be open book and notes. Calculators allowed.

Help stamp out meaningless symbolic manipulation
If you are taking MATH 1507, 1508, 1509, 1518, 1709, 1711, 1712, 1713, and 2507, please note that the Math Lab is open on M - Th from 11 to 4 in Skiles 257. It is staffed by teaching assistants. It is free and is open to Georgia Tech students taking the above classes.

Previous stuff from this quarter

Stupid Puzzle of the Day #6:

Note: As of yet (Feb 11) No one has answered this puzzle correctly. If you tried before, try again.

At the trial of Nat Chafee, who was accused of steeling a Calculus book, there were three witnesses, Ted Hill, Carl Spruill, and Dan Klain. These three came forth and made the following statements:

• (Ted Hill) Chaffee has committed over a dozen roberies in the past.
• (Carl Spruill) That is not true
• (Dan Klain) He (Chafee) has certainly committed at least one!
It turned out that exactly one of the witnesses told the truth. Did Chafee steel the Calculus book or not?

Solution by Ryan Cantor: Chafee did not still the book. Since Hill's and Spruill's contradict one of them is lying and the other is telling the truth. That means Klain is also lying. Therefore Chafee has stolen less than one book.
- Ryan Cantor

New puzzle to appear soon.

• Puzzle #1: Ryan Cantor
• Puzzle #2: Matthew Nugent.
• Puzzle #4: Nick Mazzolini
• Puzzle #5: Chris Young

Previous Stupid Puzzles with answers can be found here

Next quiz ... Next Thursday.... Suggested Problems:
• Page 450: (Section 6.6) 1,3,5,7,9,11,13,19 (Covered Wed/Fri).
• Stuff on inverse trig functions to know: (Note that I have written the inverse trig functions as arcsin, etc., instead of sin^-1, which is hard to do without superscripts...)
• The derivatives of arcsin, arccos, arctan, and how to derive them Page 463: 19,21,22,24,25,26,27,30,31,32.
• Integral that you can now do -- Those involving 1/sqrt(1 - x^2) and 1/(1 + x^2), and integrals that reduce to these by substitutions. There are a bunch of these at the end of the section... Page 463 35,36,37,38,42,43,44,45,47,49/
• trig functions of inverse trig functions. Problems like cos(arcsin(4/5) = Page 463: 10,12,12,13,14,15,16,18.
• Chapter 7
• Integration by Parts: Page 485: 1,2,3,4,6,8,10,12,13,14,15,17,21,22,23.
• Integrals of certain trig functions: Page 490: 3,4,5,7,8,9,11,13,14,15, 20,21,23,24,25. YUK I hate these!!!!

First Computer Project: is here . It is a maple file. You are to do the exercies is groups of two or three, including text so that the file is readable. Also you are to contribute (as a group) a web page on the editible CoWeb about this project, or about similar problems. This will be due on or about Febuary 22. More information to come on the CoWeb section of the project.

Directions for the Computer Project:

• Work the project in groups of two or three
• Hand in a printed copy of the worked project o n the Due Date.
• Include in the printed version lots of English Text explaining what you are doing and why.
• Create of CoWeb page detailing your group's experience, trials, tribulations, and suggestions. To do this:
• Go to the 1508 web page
• GO to the CoWeb link here.
• Go to the Math1508 Computer Project 1 link
• Edit that page by adding your group's name between #'s. Like #Maria Calas, Birgit Neilson and J. Sutherland#
• After you do that, hit save.
• The page will now have a link that looks like Maria Calas, Birgit Neilson and J. Sutherland?
• Go to this link, and your CoWewb page will be created.
• Edit there. Flat text if fine.
• Your CoWeb page should contain:
• A description of the problem in English
• The mathods that you used to solve the problem.
• Any problems (computer problems, maple problems, group problems, etc...) that you encountered in working the project.
• Any useful hint you have for others.
• Anything else you want to add.

The due date is Febuary 22.

Wed. Feb 3 we start work and centroids. Feb 8 we did centroids, center of mass, and started logs. On Wed 9 and Fri 11 we fishished covering sections 6.3 and 6.4, and basically covered 6.5. As of now (Friday afternoon) the quiz on Tues will cover though 6.5.
Suggested Problems:
• Page 364: 1,3,5,7,11,13,14,15,16,21,22,23,24
• Page 376: 1,3,5,7,8,9
• Page 376: 5,7,8,9,10
• Page 418: (Section 6.3) 1,3,5,6,7,11,13,14,15,,2122,23,25,27,31,32,33
• Page 430: (Section 6.4) 1,3,5,11,2,13,17,18,19,23,25,27,28,29,30
• Page 437: (Section 6.5) VI, 1,2,3,4,5,9,10,11,19,21,23,24,28,29,30,31
• Page 450: (Section 6.6) 1,3,5,7,9,11,13,19 (Covered Fri/Mon).
Quiz Feb 16
Feb 16.... Will cover at least through 6.5.

There will be a review sesion on Monday from 5:30pm to about 6:30 pm.

Solutions to quiz 2 . Note: There was error in the solution to problem #2 that was corrected at 4:32 pm Tuesday. Many thanks to John Foss (+2 points on this test!) for pointing this out.
General Information

Class (at Tech) is at 8:05 am in The Paul Weber Space Science and Technology Building on MWF. On TTh, it is in Skiles 146. The TA for 1508A is Dr. Eric Boczko

Suggested Problems - Chapter 6 Quiz -- Feb 26

• Section 1: page 395 -- 18,19,20,21
• Section 2: page 406 -- 9,11,13,33,34,35,36,48.49
• ** Section 3: page 408 -- 1,3,5,7,7,9,11,19,41,43
• ** Section 4: page 430 -- 1,3,5,23,25,27,29,31,49,50
• Section 5: 19,21,23,25,27,28
• ** Section 6, page 450 -- 1,3,5,7,8,10,14,17
• ** Section 6.8, page 463 -- 19,21,23,25,29,31,25,27,39
Sections one and two and five are primarily "review".

The quiz will consist of one growth and decay problem, and then a buch of shorter [roblems involving derivatives and integrals involving logs, exponentials, trig functions and inverse trig functions.

Current Problems - Chapter 6 Qu
• Section 1: page 395 -- 18,19,20,21
• Section 2: page 406 -- 9,11,13,33,34,35,36,48.49
• Section 3: page 408 -- 1,3,5,7,7,9,11,19,41,43
• Section 4: page 430 -- 1,3,5,23,25,27,29,31,]49,50
Sections one and two are primarily "review"
Last Week Computer project: Due Feb 18. To be done in groups of Three Text Version , Maple Version , Mathematica 3.x version . Mathematica 2.x version available Wed.

Problems from Recent Lectures:

• Center of Gravity, etc, Section 5.6, page 376 -- 1,3,5,7,9,11,13
• Section 5.4, page 364: 1,3,5,7,13,15,21,24
• Section 5.6, page 376: 1,3,5,7,13,14,15,19
• What is the centroid of Georgia, What county is it in?

Week of Feb 2-6
Quiz This Thursday!
Covers:
• Volumes, including shells. (problems as before)
• The length of arcs and curves: 5.3 page 355, # 1,3,5,7,9,11,13,15

Current Problems:
• Lecture #7, 8 (January 23, 26)
• Section 5.1, Page 229 -- 1,3,5,7,15,17,19,25,29,31
• Section 5.2, Page 5.2 --1.3.5.19.20,22,23,24
• Lecure #5 (January 16)
• Section 4.2, page 274 -- 1, 3, 10, 20, 23, 26, 27, 28, 29
• Section 4.7, page 326 -- 11. 12. 13. 19, 22, 23, 25, 29, 26, 27
• Lecture #6 (January 21)
• Section 4.2, page 274 -- 23,25,27,29,31
• Chapter Review, Chapter 4, page 332, 1,3,11,13,15,18,19-24, page 333, # 5,6 (For the computer literate)

(Hour) quiz January 29.
Covers through 5.2 (not including shells, but including disc and surfaces revolved arround the x-axis.). Problems to work for the test are as follows:

Copy of quiz #1, with answers: Mathematica 3.0 Document , Postscript (printable) file .

Quiz on Thursday
Covers 4.4, 4.5,4.6

Suggested Problems:

• Section 4.4 Page 290 -- 1,4,5,7,9,11,23
• Section 4.5, Page 306 - 1, 5, 8, 31,33,35
• Section 4.6, Page 318 -- 3, 10, 15, 16, 25, 27, 35, 37
How to prepare for the quiz:
1. Work problems by yourself
2. Work problems with others (more fun than 1)
3. Ask questions of me in classs on Wed.
4. Ask question of the TA (Boczo or Lewis) in class on Tues or the first half of class on Thurs.
5. See me during office hours (MWF 9:30-11, Skiles 263 or 237) -- other times by arrangement.
6. See the TA during office hours.
7. Math-Lab (see below...) Skiles 257, MTuWTh 11-4 ... free

The hour test on thursday counts as two quizes. There are two alternative ways to handle this:

2. The two halfs of the quiz are graded seperately, and recorded seperately .
Which do you want? Let me know: email: morley@math.gatech.edu

center>
Course Outline for Math 1508
Topic Sections Appoximate Days
The Integral 4.1-4.8 6
Applications of the Definite Integral 5.1-5.6 5
Areas in Polar Coordinates 8.7 1
Transcendental Functions and Their Inverses 6.1,6.3-6.8 6
Techniques of Integration 7.1-3,6,7,9 5
Ordinary Differential Equations 16.1-16.5 5

The grade will be based on

• Appoximately 5 or 6 half hour quizes.
• Appoximetely one hour test. This will count as two quizes.
• Computer Projects.
• Homework
• Final Exam
The quiz grades and hour test grades will be added together, with one quiz (whoch could be 1/2 of the hour test) dropped. They are then ageraged together, and count for 55% of the grades. Computer Projects 10%, Homework 10%, and Final exam 25%.

All tests and quizes will be open bok and notes. Calculators allowed.

Stuggested Problems
• Lecture #1 (Jan 7)
• Section 4.4 Page 290 -- 1,4,5,7,9,11,23
• Lecture #2 (January 9)
• Section 4.5, Page 306 - 1, 5, 8, 31,33,35
• Lecture #3 (January 12)
• Section 4.6, Page 318 -- 3, 10, 15, 16, 25, 27, 35, 37
• Lecture # 4 (January 14) -- Review For Quiz
• Lecure #5 (January 16)
• Section 4.2, page 274 -- 1, 3, 10, 20, 23, 26, 27, 28, 29
• Section 4.7, page 326 -- 11. 12. 13. 19, 22, 23, 25, 29, 26, 27

Mathematica Information

I will sometimes post Matheamtica Documents on the web.

Note: If you have access to Mathematica on your machine, you may want to set Netscape preferences so that file extensions "ma" and "nb"points to Mathematica. This can be found under "helper apps". Note however, that you need a lot of RAM to do this.

Need to do an integral? Try this. Brought to you by Wolfram Research

A Reiman Sum Java Aplet by Bill Ziemer at Long Beach

Help stamp out meaningless symbolic manipulation
If you are taking MATH 1507, 1508, 1509, 1518, 1709, 1711, 1712, 1713, and 2507, please note that the Math Lab is open on M - Th from 11 to 4 in Skiles 257. It is staffed by teaching assistants. It is free and is open to Georgia Tech students taking the above classes.