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Name: Christopher
Date: July 13, 2003 (13:20)
Comment: What is the mathmatical name for the gradient function?

Name: Harry
Date: January 02, 2003 (15:45)
Comment: I want that can i get a free copy of "Differential Equations with boundry value problems" by : Dennis G.Zill, Michael R.Cullen I need a Soft copy in some good format.

Name: Sarah
Date: October 15, 2002 (08:37)
Comment: When was Mathmatical Function first used?

Name: Sarah
Date: October 15, 2002 (08:36)
Comment: When was Mathmatical Function first used?

Name: NADINE
Date: April 25, 2002 (07:35)
Comment: 1 - * 6 6

Name: Anonymous
Date: April 17, 2002 (20:23)
Comment: how do you solve vectors

Name: RUNE
Date: November 24, 2001 (05:18)
Comment: m*dv/dt=mg-kv^2 v=?

Name: Anonymous
Date: March 20, 2001 (19:31)
Comment: I can't prove the tangent reduction formula. I've been searching in the internet for help but there isn't any.

Name: Anonymous
Date: March 20, 2001 (19:31)
Comment: I can't prove the tangent reduction formula. I've been searching in the internet for help but there isn't any.

Name: Anonymous
Date: December 12, 2000 (22:24)
Comment: Just wanted to say I am from Indiana I have a 3 year old son named Brayton Lee we named him after Scott Brayton the Indy driver that was killed 5 or so years ago.. Beautiful name... Bye

Name: Anonymous
Date: November 06, 2000 (23:27)
Comment: what is the sum of a mathmatical equation

Name: Anonymous
Date: January 03, 2000 (19:33)
Comment: Best of luck to the newcomers of this class!

Name: Anonymous
Date: December 07, 1999 (11:25)
Comment: does this mean that we can find out our scores now?

Name: TRS
Date: December 07, 1999 (08:31)
Comment: You can Blitz for your score

Name: Anonymous
Date: December 06, 1999 (09:33)
Comment: How will be able to find our scores on Wednesday? By blitzing our professor or actually seeing him?

Name: TRS
Date: December 06, 1999 (07:46)
Comment: Final Exams are not returned to you (for a term), but you may look at your exam in your professor's office anytime next term.

Scores will proably be available Wednesday


Name: Anonymous
Date: December 06, 1999 (00:45)
Comment: MATH IS OVER!!!! WOO HOO!!!

Name: Anonymous
Date: December 05, 1999 (19:13)
Comment: On the same note, will we be able to get our final exams returned to us?

Name: Anonymous
Date: December 05, 1999 (18:17)
Comment: When will the results for the final exam be distributed?

Name: Anonymous
Date: December 04, 1999 (21:46)
Comment: Dear Anonymous, A mastery of the calculus of one and several variables will put you back on the road to health. -Dr. Anonymous

Name: Anonymous
Date: December 04, 1999 (21:45)
Comment: Dear Anonymous, A mastery of the calculus of one and several variables will put you back on the road to health. -Dr. Anonymous

Name: Anonymous
Date: December 04, 1999 (21:16)
Comment: I am having digestive problems. Can math help me?

Name: Anonymous
Date: December 04, 1999 (21:14)
Comment: Professor Shemanske- If you had to guess what the answer to question 1 would be, what would you guess?

Name: Anonymous
Date: December 04, 1999 (21:09)
Comment: Is this test going to be hard?

Name: Anonymous
Date: December 04, 1999 (20:35)
Comment: On page 778, #7, why can't y=(2n+1)*pi/2? Why is it limited to n*pi/2?

Name: Jessica Sharkness
Date: December 04, 1999 (20:29)
Comment: What is this "percieved rate" you speak of? we did not learn that in arkowitz's section...

Name: Anonymous
Date: December 04, 1999 (20:18)
Comment: Should we know Hooke's Law for the final exam? Will simple harmonic motion be on it? Or partial fractions? Are there concepts we came across, such as these, which were just supportive and not actually to be tested?

Name: Anonymous
Date: December 04, 1999 (19:48)
Comment: On page 778, #7, why can't y=(2n+1)*pi/2? Why is it limited to n*pi/2?

Name: TRS
Date: December 04, 1999 (13:22)
Comment: No concerns about 2nd partials, or testing for differentiability.

The limit (as (x,y) -> (0,0))of sqrt(x^2 + y^2) does exist and equals zero. Note that the function is simply the distance of the point (x,y) from the origin, so as (x,y) -> (0,0), the distance goes to zero.

Generally you should understand all of the hiker problem including perceived rates.


Name: Anonymous
Date: December 04, 1999 (12:57)
Comment: What do we need to know about partial derivatives for the final exam (like what parts of the hiker on the mountain problems do we need to know)? Do we need to know rates perceived by a moving observer?

Name: Anonymous
Date: December 04, 1999 (12:54)
Comment: How come the limit (x,y) --> (0,0) of the square root of (x squared + y squared) does not exist?

Name: Anonymous
Date: December 03, 1999 (17:48)
Comment: Should we be responsible for testing the differentiability of a point on a function or second partial derivatives with chain rule?

Name: TRS
Date: December 03, 1999 (13:15)
Comment: Don't worry about the heat, wave or Laplace's equation

Name: Bonnie Tice
Date: December 02, 1999 (20:05)
Comment: Will we need to know Laplace's equation, the wave equation, or the real Newton's Law equation for the final exam? By real Newton's I mean: du/dt = the second partial of u wrt x + the second partial of u wrt y + the second partial of u wrt z, when u(x,y,z,t) = temp at pt (x,y,z) at time t

Name: Anonymous
Date: December 01, 1999 (15:43)
Comment: On question 5 of the last homework, could grad f be thought of as <2,1,-2>? I did this and got the same answer as the method used in class... I was thinking that it was the vector from (2,1,-2) to the origin. THen using the Lagrange method i got the same answer. THe reason I ask this is because I am not sure if this is a method that I could used on, for example, the final , and not lose credit... I hope lynx doesn't garble me message

Name: TRS
Date: November 29, 1999 (09:47)
Comment: The final exam is worth 150 points. Appriximately 100 of those points will cover material since the last exam; the other 50 will cover material from the first two exams.

Name: Andy Fisher
Date: November 28, 1999 (23:52)
Comment: I'm willing to do review sessions this week

Name: Alexis McGuinness
Date: November 28, 1999 (20:30)
Comment: Is anyone interested in doing multiple group review sessions during the week of Nov. 29?

Name: Anonymous
Date: November 28, 1999 (19:48)
Comment: Does the final exam cover all material from the term or only the material started after the second exam?

Name: Anonymous
Date: November 28, 1999 (17:53)
Comment: Could someone explain how to do the hypotenuse of a triangular boundry for these 3D graphs...I have the notes..but they don't seem to make sense after so much turkey...

Name: Anonymous
Date: November 28, 1999 (17:47)
Comment: Could someone explain how to do the hypotenuse of a triangular boundry for these 3D graphs...I have the notes..but they don't seem to make sense after so much turkey...

Name: clueless
Date: November 28, 1999 (13:12)
Comment: Does anyone know what the final exam covers? Is it everything we've covered during this entire term or are there specific assignments like all the other exams?

Name: Anonymous
Date: November 22, 1999 (13:49)
Comment: Has anyone else in Arkowitz's class, who's last name begins with C, been getting homework back lately? I'm missing four or five or so...

Name: slim shady
Date: November 19, 1999 (16:09)
Comment: how can i use maple to find partial derivatives. keep in mind i have never used maple before

Name: TRS
Date: November 19, 1999 (08:40)
Comment: #23 on pg 750 I get their answer.

Consider the function f(x,y) = x^2y^3. You are asked to find the path of an object orthogonal to the level curves of f(x,y), that is parallel to the gradient.

So if grad(f) = , you want dy/dx = f_2/f_1.


Name: Kurt
Date: November 18, 1999 (13:48)
Comment: I'm having trouble with #23 on pg 750. Should I start by taking the gradient or by implicit differentiation? Either way I don't seem to be getting the right answer...

Name: Anonymous
Date: November 16, 1999 (12:20)
Comment: I have no clue how to do 21e. Did we do something like this in class?

Name: TRS
Date: November 16, 1999 (08:48)
Comment: Tutorials: will meet this week as normal through Sunday. There will be no tutorial next Tuesday or Thursday, but tutorials will resume on Sunday Nov 28. They will end on 30 November.

Name: TRS
Date: November 16, 1999 (08:45)
Comment: Rebecca and Erin: Yes you should be able to draw these; they are just hyperbolas.

Name: Anonymous
Date: November 15, 1999 (22:22)
Comment: How will the Math tutorial that is normally held on Sun, Tues and Thurs operate over Thanksgiving break and the reading week? Is it just the night before an assignment is due?

Name: Rebecca and Erin
Date: November 15, 1999 (16:11)
Comment: For 21 a) on Monday's homework are we expected to be able to plot the graph without using Maple?

Name: TRS
Date: November 12, 1999 (17:03)
Comment: For Friday's assignment on chain rule, you need not worry about higher order derivatives, homogeneous functions, or Laplace's equations in polar coordinates.

Sheesh! What's left for you to do?!


Name: TRS
Date: November 12, 1999 (08:40)
Comment: Robinson: Sure, use:
plot3d({f(x,y),g(x,y)},x=-5..5,y=-5..5);

Name: John Robinson
Date: November 11, 1999 (21:24)
Comment: Is there a way to make Maple put two different 3D plots in one frame?

Name: JP
Date: November 11, 1999 (15:07)
Comment: Is there anything MAPLE can't do?

Name: Anonymous
Date: November 11, 1999 (01:40)
Comment: HI :0)

Name: Anonymous
Date: November 09, 1999 (18:00)
Comment: Is there going to be a curve on the test?

Name: Anonymous
Date: November 09, 1999 (17:16)
Comment: Definition 5 is found on page 708. It involves taking the limit rather than using the chain rule. If you have Shemanske there's an example of this towards the end of your class notes from Monday.

Name: Anonymous
Date: November 09, 1999 (11:18)
Comment: what/where is the "definition 5" referred to in problem 11 on page 714?

Name: Anonymous
Date: November 09, 1999 (09:44)
Comment: rediculous ==> ridiculous

Name: Anonymous
Date: November 09, 1999 (00:07)
Comment: are math quesions sopposed to be rediculous?

Name: Anonymous
Date: November 09, 1999 (00:02)
Comment: i like quesions

Name: Anonymous
Date: November 08, 1999 (19:05)
Comment: RE:Anonymous: FIRST MESSAGE POSTED HERE AT 17:41 HEY YOU!!! HAHAHAHA!!!! YOU MISREAD THE QUESTION!!!!! Boy are you foolish! The question WAS do the 3 points lie on a LINE!! HAHAHA!!! Maybe next time you should try READING the question before you come up with such frivolity! HA! You are in math 8? Maybe you should try taking an English 1 Placement exam next time!!!!!

Name: Anonymous
Date: November 08, 1999 (17:41)
Comment: I thought that question 3e on the exam is rediculous. Do the three points P, Q, and R lie on the same plane, and why? How are you sopposed to prove that. The answer given, that the vectors they form are not scalar multiples of each other, does not answer the quesion. Even if the vectors formed were multiples, the points would still lie on the same plane. The question is similar, by analogy, to asking do two points P and Q lie on the same line. How do you prove that?

Name: bob
Date: November 07, 1999 (18:07)
Comment: at exactly what point in our notes does the material pertinent to this exam(11/8) begin and end? (aka, whats it on, where to where?)

Name: Esther Warshauer-Baker
Date: November 07, 1999 (17:23)
Comment: Would it be possible for you to post the answers to the online homework assignments? It would be really helpful while studying for the exams. (especially for the students who have not gotten homework returned to them)

Name: TRS
Date: November 07, 1999 (16:28)
Comment: Error estimates are on the test

Name: Anonymous
Date: November 07, 1999 (12:51)
Comment: For exam 2, do we need to be able to find a value for N such that the error term is less than a given value?

Name: TRS
Date: November 07, 1999 (10:32)
Comment: Brown: Try reloading the page. The practice materials have been available for a couple of days.

Jeff: You need not know how to test to see whether the endpoints are in the interval of convergence, simply what the endpoints are.

As the review sheet, I have no knowledge of anything like this for the first exam, and no there is nothing like that for the second exam.


Name: Jeff
Date: November 06, 1999 (17:30)
Comment: Question #1: Should we know how to test if endpoints are included in the interval of convergence in a power series? (This question is in reference to #2 on the practice exam.) Question #2: Did we receive a review sheet for this test similar to the one given out for the first test? The first one included subjects to review and suggested problems from the book.

Name: katie brown
Date: November 06, 1999 (15:43)
Comment: where is the practice exam for exam 2??? the website is not allowing me to access it--i can only get exam 1, not 2

Name: ryan
Date: November 06, 1999 (00:03)
Comment: when is our final exam?

Name: TRS
Date: November 05, 1999 (07:42)
Comment: No, but I think one of the practice problems talks about that stuff as part of a larger problem.

Name: Anonymous
Date: November 05, 1999 (01:12)
Comment: Will the material we covered on wed. (ie. column spaces and show all b's are solvable) be on this test?

Name: TRS
Date: November 03, 1999 (13:15)
Comment: Question: If we are told that Ax=y, and that R is the row reduced form of A, does Rx = y? It seems to me that it would not.

Answer: Correct! You would need to row reduce the augmented matrix (A|y) -> (R|y'), and consider Rx = y'.

No class Novmber 23, see homework page for details

No linear algebra books on reserve. Happy to talk about these things in office hours or tutorials.


Name: Chaz
Date: November 03, 1999 (08:39)
Comment: are there any linear algebra books on reserve for this class?

Name: ryan
Date: November 02, 1999 (17:14)
Comment: do we have class on nov. 23?

Name: Anonymous
Date: November 02, 1999 (16:47)
Comment: If we are told that Ax=y, and that R is the row reduced form of A, does Rx = y? It seems to me that it would not.

Name: trs
Date: November 02, 1999 (08:09)
Comment: Not sure what discriminant means in this context. Perhaps you meant dterminant. In any case, the zero matrix is simply the matrix all of whose entries are zero.

Name: Anonymous
Date: November 01, 1999 (16:31)
Comment: Is the zero matrix defined as when the discriminant =0?

Name: TRS
Date: October 28, 1999 (17:53)
Comment: Since the first exam; the final will be cummulative

Name: Anonymous
Date: October 28, 1999 (13:05)
Comment: Will the second one hour exam cover all the material we have gone over in the course or just the material we picked up after the first exam?

Name: TRS
Date: October 27, 1999 (07:40)
Comment: HW As discussed in class, homework assigned:
1. Monday is due before class on Wednesday
2. Tuesday is due by class time on Friday (that is, you walk over to your classroom building, and turn in the homework even though you do not have class.)
3. Wednesday is due before class on Monday.

In other words, you turn them in the same days as always.


Name: Anonymous
Date: October 26, 1999 (09:44)
Comment: Since there's no class on Fri. this week, when do we turn in Wednesday's assignment? Do we turn in both Wed. and Fri. homework on Mon.?

Name: TRS
Date: October 26, 1999 (08:15)
Comment: Angle between lines: Each line as a direction vector. The dot product will allow you to find the angle between those two direction vectors. This is the angle between the lines.

Name: Anonymous
Date: October 25, 1999 (20:34)
Comment: Orthongnal means perpendicular.

Name: Anonymous
Date: October 25, 1999 (19:34)
Comment: Is there an equation for finding the angle between two lines given in the form of r=<...>, such as is the case in number 4 of the homework? It wasn't covered in class, and I can't find an example in the book.

Name: The Greastest Person Ever
Date: October 25, 1999 (17:42)
Comment: What does orthogonal mean?

Name: Anonymous
Date: October 24, 1999 (21:43)
Comment: On #6 of the homework, does anyone understand how +k component would affect the problem. After all, isn't that what the + or - part of the problem compensates for at the end?

Name: TRS
Date: October 23, 1999 (14:32)
Comment: My current guess is that there will be class in the xhour on Tuesday, and no class Wednesday

Name: Anonymous
Date: October 22, 1999 (17:15)
Comment: How are classes going to be scheduled for Thanksgiving week since Wednesday, Nov. 24 is a shortened day?

Name: TRS
Date: October 22, 1999 (13:20)
Comment: Advanced warning: Next week, October 25 - 29, Shemanske's section will meet M, Tu, W and not Friday because of Harvard weekend.

In particular, we shall meet in the x-hour on Tuesday 12 - 12:50.

Arkowitz's schedule will also be affected, but I am not sure how he will proceed.


Name: TRS
Date: October 19, 1999 (08:31)
Comment: The exams (for both sections) have been graded and are back in your respective homowork boxes.

We will talk about grades and questions about grading in class on Wednesday.


Name: TRS
Date: October 18, 1999 (07:35)
Comment: You should know that double angle formula to help with sin^2 x and tan^{-1}x would be done by parts; you're not expected to remember its antiderivative. As to Harvard weekend, we will meet MTW next week, using the xhour, and not have class on Friday.

Name: Anonymous
Date: October 17, 1999 (18:17)
Comment: Will we have to know the anti derivatives of trig funtions, such as the square of sin (x), the inverse of tan (x) or others ?

Name: Anonymous
Date: October 17, 1999 (13:53)
Comment: Do we have class on Friday, Oct. 29? (Harvard Weekend)

Name: TRS
Date: October 17, 1999 (09:08)
Comment: Response to various:

It's hard to judge what you did wrong in your geometric series problem since there many typos in your question. You are correct that a = (2e)^3 and r = 2/e. This yields (after some trivial algebra), the answer in the book.

There will be NO formulas supplied to you, nor may you bring any such list into the exam. We try to keep the number of things you need to memorize to a minimum, but there are simply things you must remember: It is far easier to remember that the derivative of sin x is cos x, rather than deriving it...


Name: Anonymous
Date: October 16, 1999 (16:47)
Comment: The info on the calculator policy is located in the First Hour Exam Information at the bottom of the homework assignment page.

Name: Anonymous
Date: October 16, 1999 (16:41)
Comment: will we be supplied with any formulas?

Name: Anonymous
Date: October 16, 1999 (16:02)
Comment: What is going to be the calculator policy for the exam on monday? When we asked in class, we were told to refer to the web site, but i'm having difficulty locating that information.

Name: Anonymous
Date: October 16, 1999 (15:40)
Comment: P. 533 #7. I rearranged the sum notation to produce (2e^3)(2/e)^k a=(2e)^3 r=2/e using a/(1-r), I came up with 2e^3/(1-(2/3)). However, the book states the answer as 8e^4/(e-2). What did I do wrong?

Name: TRS
Date: October 15, 1999 (09:39)
Comment: We shall assume you know the form of a Taylor polynomial (w/o proof). The solution to something like Newton's law of cooling is a little more subtle. If you are not explicitly asked to derive such an answer, you may state the form of a solution without proof, but of course if you misstate it without any proof, you are (shall we say) hosed. That is partial credit is awarded only if there is some correct work which substantiates an answer.

Name: TRS
Date: October 15, 1999 (08:30)
Comment: Fisher: A little unclear about your question. Clearly the center is a = -2.

You could also think of #3 as sum (1/n)* (1/2^n)* (x+2)^n

Perhaps that helps


Name: TRS
Date: October 15, 1999 (08:27)
Comment: Try evalf(Pi, 50); The constant pi is stored in the variable "Pi" (case sensitive). Maple thinks "pi" is your own variable, not the constant. The 50 indicates that you would like to see 50 places of accuracy.

Name: TRS
Date: October 15, 1999 (08:25)
Comment: Math 8 Final Exam: Sunday, Dec 5, 4 - 6 pm

Name: Anonymous
Date: October 15, 1999 (00:56)
Comment: For the exam, will we have to prove or derive such formulas as the Taylor poly. or Newton's law of cooling, or will we be allowed to simply use the formulas like a+be^kt?

Name: Andy Fisher
Date: October 14, 1999 (21:53)
Comment: On #3, can you use(x+2)/2 as the function, or do you need to split them up to actually get x-a?

Name: Kurt Peters
Date: October 14, 1999 (18:06)
Comment: When I use the evalf command in Maple and the expression includes pi, the result still includes pi as a symbol. How do I get Maple to give me a single number result?

Name: Anonymous
Date: October 14, 1999 (15:45)
Comment: when will they post the schedule for final exams?

Name: TRS
Date: October 13, 1999 (07:30)
Comment: Read the general information page.

Name: Anonymous
Date: October 12, 1999 (21:40)
Comment: When is the final exam (before winter break)?

Name: TRS
Date: October 12, 1999 (08:52)
Comment: The last two questions are addressed in the homework or general information web pages

Name: Anonymous
Date: October 11, 1999 (00:38)
Comment: will we be allowed to use calculators on exams?

Name: Anonymous
Date: October 10, 1999 (21:12)
Comment: where and when are the tutorials held again? and also- when will the practice exams be available online?

Name: TRS
Date: October 07, 1999 (15:30)
Comment: Osgood: You ought to look at problem 21 again. That is not the correct auxiliary equation

Name: TRS
Date: October 07, 1999 (15:28)
Comment: re: papers. Homework papers are supposed to be returned by the next class period. If they are not please tell me.

We have had HUGE problems with the grader for S-Z. The claim is that he will have them all back on Friday.


Name: Brayton Osgood
Date: October 07, 1999 (11:40)
Comment: Is there some trick required for number 21 on page 1015? I can't figure out how to find the roots of r^3+2r+1=0.

Name: Anonymous
Date: October 06, 1999 (21:43)
Comment: I have a question regarding the return of homework: I haven't gotten several of my homework assignments back, and I was wondering how long it generally takes for homework to be returned.

Name: Amanda Plagge
Date: September 30, 1999 (13:41)
Comment: Are we permitted to use calculators on the exams?

Name: TRS
Date: September 30, 1999 (08:26)
Comment: Exams are closed book and notes. We will not require you to know "obscure" integration formulas, but certainly would expect you to know antiderivatives of standard functions (exponential, logs, trig and inverse trig) as well as general methods (substitution and parts).

More likely, we would ask you to derive an integration formula like int(sin(x)^n,x) than memorize it


Name: TRS
Date: September 30, 1999 (08:23)
Comment: Augello: yes,... I believe those words are part of the question.

Name: TRS
Date: September 30, 1999 (08:22)
Comment: Richardson: One needs no calculus to determine the terminal velocity (as the book intimated), however to derive the velocity function one does need to solve the differential equation.

Name: TRS
Date: September 30, 1999 (08:19)
Comment: Regarding the grading of late homework:
http://www.math.dartmouth.edu/~m8f99/general.html#hw

Name: Anonymous
Date: September 30, 1999 (01:01)
Comment: When it is time for the exams, are we going to have to memorize all of the (uncommon) integration formulas, or will be able to use a sheet with them on it?

Name: Evan Richardson
Date: September 30, 1999 (00:06)
Comment: Cant you solve # 11 without any integration at all? m(dV/dT)=mg-kV @ t=infinity, dV/dT=0 (just like it does when one solves for the maximum of a function using the derrivitive). substitute 0 for V' 0=mg-kV mg=kV V=(mg)/k this is V @ infinity, and thus the limit as t goes to infinity. Is this correct, or am I missing something? if it's correct, then why bother with separable or linear methods of integration?

Name: Charles Augello
Date: September 29, 1999 (21:14)
Comment: for tonight's problem that wasn't in the book, the one about the brine solution,if the solx flows in at twice the rate that it flows out, won't it overflow?

Name: Anonymous
Date: September 29, 1999 (18:14)
Comment: If I turn in my assignment late, will someone still grade it? I'm not concerned about receiving credit, but I'd just like to see if I'm doing things correctly.

Name: TRS
Date: September 29, 1999 (17:09)
Comment: Generally, if you are away for a College sponsored event, you can arrange with your instructor to take the exam in advance of your trip.

The key here is to talk to your instructor in advance.


Name: Anonymous
Date: September 29, 1999 (10:43)
Comment: Is there any way to take one of the exams at a different time? Looking at the schedule I know I have an away game on October 18th. Unfortunately, I don't know how to handle this situation. What is your policy? Thanks.

Name: Amanda Plagge
Date: September 28, 1999 (23:44)
Comment: I am stuck again, too. Apparently you are supposed to find Isub0-Isub3 and then find IsubN by integration of parts. It gets pretty messy, though.

Name: Anonymous
Date: September 28, 1999 (23:26)
Comment: Anyone have any tips for the reduction problem? I have been trying to solve it and keep getting stuck. It's problem # 34 if anyone cares to share ideas.

Name: Andy Fisher
Date: September 28, 1999 (22:50)
Comment: Is anyone else having problems with the reduction formula? I don't quite understand the process myself.

Name: Anonymous
Date: September 28, 1999 (22:03)
Comment: re: Karla Leavens For question #22, (homework due Wednesday) I believe it may be easier to use substitution for the square root of x and then doing the integration by parts. Say that the square root of x =y (substituting) and y^2 = x, then 2y dy= dx and then the integral from 0 to 4 is y* e^y * 2y dy or 2y^2* e^y dy. Using u= 2y^2 and dv= e^y the answer comes out to about 4e^2 -4 or 25.55.

Name: Anonymous
Date: September 28, 1999 (21:13)
Comment: re: Karla Leavens 2*[e^(x^.5)]*[(x^.5)-1]

Name: Karla Leavens
Date: September 28, 1999 (11:29)
Comment: I'm so close on this one problem, but can someone help me out? What is the antiderivative of e^X^1/2? Thank you.

Name: TRS
Date: September 28, 1999 (10:16)
Comment: Problem 9 on page 351 will result in an integral which I believe is accessible only through techniques not to be covered in this course, so don't worry about taking it past the first integration by parts.

Name: TRS
Date: September 27, 1999 (14:56)
Comment: We're getting pretty close here. Periodicity is indeed the issue, but with the tangent and not the arctangent(which is not periodic). Said another way, it has to do with the principal values of the arctangent.


If tan(y) = 1, then since the tangent has period pi, y = ...,-3*pi/4, pi/4, 5*pi/4, ..., that is pi/4 + n*pi. The arctangent and tangent are inverse functions only on a restricted interval (principal values)


This is a subtle point over which we glossed during class. No worries.


Name: Anonymous
Date: September 27, 1999 (13:19)
Comment: I think that n*pi has something to do with the period of the arctan. The graph is a one basic curve repeated every n*pi, for n an integer. I don't think I would have come up with it on my own, but I can justify it now that I see it. I think. Anyone have any other suggestions?

Name: mike mothner
Date: September 27, 1999 (10:28)
Comment: i too was confused by the n*pi in the answer -- other than that my work was identicle. where did this come from?

Name: TRS
Date: September 27, 1999 (07:50)
Comment: re: Zilioli: Nobody has an opinion on this? Curious...

Name: erica zilioli
Date: September 26, 1999 (15:54)
Comment: On our homework for Monday...#13: I don't understand why the answer has n*pi as part of the answer. Does anyone know why?

Name: TRS
Date: September 26, 1999 (09:46)
Comment: We are meeting in the regular class periods next week, and will not be using the Tuesday x-hour next week.

I will give you advance warning of any use of the x-hour.


Name: song han
Date: September 25, 1999 (19:36)
Comment: oh never mind the last comment, but are we having an X-period on Tuesday?

Name: TRS
Date: September 23, 1999 (08:34)
Comment: Homework page: You probably should "reload" the homework page whenever you access it. It changes frequently, and often your browser will not reload automatically.

I have also changed the address slightly, so you if you have bookmarked it, you may want to go to the homepage and rebookmark it. Your old link won't break, but on the new link I have been able to add a line at the bottom which indicates when the page was last reloaded.


Name: TRS
Date: September 23, 1999 (07:47)
Comment: re: Piermont. This is a little strange unless you are connecting via windows from off-campus. On the other hand you will need an account on ADAMS in order to print from your machine. You should contact Kiewit.

You should also carefully read the documents in the download section of the m8 web page. Several are devoted to using key-served applications and obtaining an account on ADAMS.


Name: John Piermont
Date: September 22, 1999 (17:32)
Comment: When i try to open the Adams directory, my computer asks me for a password to connect and I don't have one

Name: TRS
Date: September 22, 1999 (17:01)
Comment: re: Torrey. We will use Maple for a variety of tasks. Certainly drawing graphs of functions will be paramount. The graphs in the first part of the term will be functions of one variable; towards the end of the term functions of several variables. We will also use it for differential equations, Taylor polynomials, perhaps matrices as well.

You need not be overly concerned. The point of the demos I put on the web is to give you prototypes of things you might want to look at. Of course, this is only a starting point. Feel free to explore. The ? command is very powerful.


Name: Lisa Torrey
Date: September 22, 1999 (16:31)
Comment: What exactly are we going to be using Maple for, just so I have an idea of what kinds of aspects to get used to in the program? Thanks

Name: TRS
Date: September 06, 1999 (11:45)
Comment: This is a test of the comments and FAQ page. Questions and comments posted here can be answered by anyone.

Please be aware that comments made here cannot be removed except by me...