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**

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

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

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.

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. **

Previous stuff from this quarter

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!

** 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.

Email the answer: morley@math.gatech.edu

List of first currect answerers:

Previous Stupid Puzzles with answers can be found here

- 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.**

- The derivatives of arcsin, arccos, arctan, and how to derive
them
- 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!!!!**

- Integration by Parts:

Directions for the Computer Project:

- Download the maple projet on the 1508 web page.
- 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.

- 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

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).

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.

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

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

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?

- 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)

** **

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

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

- Work problems by yourself
- Work problems with others (more fun than 1)
- Ask questions of me in classs on Wed.
- Ask question of the TA (Boczo or Lewis) in class on Tues or the first half of class on Thurs.
- See me during office hours (MWF 9:30-11, Skiles 263 or 237) -- other times by arrangement.
- See the TA during office hours.
- 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:

- The grade is recorded twice in the spreadsheet. OR
- The two halfs of the quiz are graded seperately, and recorded seperately .

center>

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

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

- 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

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.

If you do not have Mathematica, you can read the following files with Math Reader , downloadable from Wolfram Research

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

A Reiman Sum Java Aplet by Bill Ziemer at Long Beach

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