Analysis and Calculus

Can anybody explain how to and solve the equation: d2005y/dx2005 - y = 0 for y? I have tried ancillary equs but are there complex roots. I know the ans it y=exp(x) but need to be able to show it.

How would you figure out if this converges or diverges: 1/((n)(lnn)^2)

hey guys i was just wondering if anyone knew any functions that are equal to their own derivative other than e^x?

cos(theta)= (A.B)/(lAllBl) OR cos(theta)=(lA.Bl)/(lAllBl) ---->my teacher insist this one is right and other one is wrong

Hi. Too many years since left university, cannot think on how to create the equation. An 8 feet long string, (or rod, or sheet) forming a parabola. The shape will be somewhat like a flattened U. I want the focus at the center between the upper ends of the U. (Or, at the lower tip of the accent on this letter Ú ) How do I come up with the equation? -It's to build a reflector with a 8'x4' sheet and be able to mechanically support the focus between its ends- Miguel

In order to promote the interest, welfare, and enjoyment of calculus I propose we start a random calculus problem thread. Just answer the previous question and provide a new one, however easy/hard you want (hopefully someone can answer it.) Have fun I'll start with [math]\int{\sec{x}^3dx}[/math] (I think this one is fun and different)

integrate (1+x^2)^(1/2) I used trig substitution and gotten integrate sec(theta)^3 but no clue what to do ....

Okay my school's bit peculiar in a way that it spends two years in AB Calc. Anyway, I think this is a waste of my time so I'm going to self-prep extra materials for BC Calc as well and take AP BC Calc if I can. How hard are they compared to each other? Is it possible to get 5/5 on BC by self-prep on additional materials like Taylor's Series and stuffs?

here is the official ICM press release http://www.icm2006.org/press/releases/ INFORMATION EMBARGOED UNTIL TUESDAY AUGUST 22ND, 12:00 AM, CENTRAL EUROPEAN TIME) Fields Medal Grigory Perelman CITATION: "For his contributions to geometry and his revolutionary insights into the analytical and geometric structure of the Ricci flow" The name of Grigory Perelman is practically a household word among the scientifically interested public. His work from 2002-2003 brought groundbreaking insights into the study of evolution equations and their singularities. Most significantly, his results provide a way of resolving two outstanding problems in topology:…

I would appreciate if anyone cares to take a look here http://icm2006.org/v_f/web_fr.php?PagIni=1pl then click "PRIZES" over on the lefthand sidebar menu this will say if Grisha won the Fields medal they have not announced yet. I suppose they will announce Tuesday sometime, but i will be turning in and going to bed while it is tuesday morning in Madrid. I really think Grisha deserves to win, and I hope very much he does.

Grisha is a 40-year old recluse living in St. Petersburg with his mother. His proof of the Poincaré conjecture is the greatest mathematical achievement of recent times. They want to give him the maths equivalent of the Nobel prize (the Fields medal) but he so far declines to come to Madrid to receive it. Telegraph.co has this profile, with a couple of snapshots. He looks like a nice modest person, perhaps a bit shy. http://www.telegraph.co.uk/news/main.jhtml?xml=/news/2006/08/20/nmaths20.xml The New Yorker is rumored to be coming out with a long piece on Grisha written by the author of "A Beautiful Mind" (Sylvia Nasar, she obviously has a thing about mathema…

Apt title... hehe Anyways, I was trying to do some calculations based on the "Tunnel Through Earth" thread. I wanted to actually find out how fast an object, that was dropped from earths surface to the center, would be going. This involves Physics, but its more math intensive, so I put it in Math. If that rubs anyone the wrong way, then move it Earths Radius: 6378100 m Earth Mass: 5.9742 x 10^24 kg Object (Sphere with app. human mass): 70 kg Now, I'm thinking that throughout the fall the force of gravity is constantly changing. [math]F_g = \frac{G*m_e*m_o}{{r_e}^2}[/math] So I need to find out what [math]\frac{dF_g}{dt}[/math] is. (Force of …

this is a good article it gives lots of mental imagery to help understand the significance of the Poinc conj and how a series of minds succeeded to prove it http://www.nytimes.com/2006/08/15/science/15math.html?8dpc=&_r=2&pagewanted=print it's by Dennis Overbye, who is the top NYT science writer at least for physics and math. This link has the pictures http://www.nytimes.com/2006/08/15/science/15math.html?pagewanted=1&8dpc&_r=2

hmm so my new vector calc book essentially uses linear approximation and derivative interchangably, this seems entirely contrary to everything I've ever known about derivatives and everything else. is this the way I should be thinking about them or am I being led astray? I'm a bit nervous about it all as some of the "derivatives" seem like they would hold true in general however others seem a bit hodgepodge take this for example. what is the derivative of the mapping of a matrix A to... [MATH] (AA^t+A^t)^-1 [/math] now I struggled with this one for a while and apparently went way off track. the solution manual says that the problem should work …

http://www.lehigh.edu/~dmd1/pc724 the Wall Street Journal can be good on getting across the essentials of some dramatic science or math news. this article is by Sharon Begley. It gives a good idea of the basic situation surrounding Perelman's proof of the Poincaré conjecture, without getting at all technical. it is a great event of our time and is playing out in a curious eccentric slightly funnyt way, I hope that a lot of us know about it at least what is in this Sharon Begley article thanks to John Baez for this link----it has more than the abridged version that went out on AP.

this is a wierd limit, its the first time I've ever seen a limit of a function involving a function of a series I think it diverges to infinity, but I don't know how to get that mathmatically, so if someone could tell me how to take the limit of a function such as this it would be greatly appreciated. heres the function [MATH]\lim_{n\rightarrow \infty}\frac{n}{\sqrt{\sum_{n=1}^{\infty} n^2}}[/MATH]

What did you all get on your AP calculus exams? I got a 5 on BC and 5 on AB subscore. You just gotta love calculus eh? Hard studying pays off for sure!

I am having a bit of problem with finding the particular function for linear difference equations. The method of finding the particular function is similar to the method for finding the particular integral in linear differiational equations. Can anybody help?

I have just looked at the gamma function and am wondering what it tells us and what is the point in the function?

2,20,?,110,182 336,210,120,?,24,6,0 5,?,61,122,213,340,509 24,6,18,9,36,9,24 9,18,10,27,11,?,12 17:48::101:? 74,63,54,45,? 3/2,2,5,6,12,18,26,54,? -3^1/3,-1,1,3,? find the missing number in the coloum 25 15 40 8 65 25 90 ? 45 15 60 12

Hi, I just wanted to ask someone for urgent help as I am doing a computing degree which has a mathematics part to it. The question im stuck with is in regards to complex differentiation and integration. Ive tried asking mathematic teachers locally etc etc but no-one seems to be able to help so i got reccomended here so this is my first post. Below is a link to the pdf with the questions. Im fine on question 5 but im having trouble with question 4 and 6. Thanks in advance for any help in explaining it or helping with workings so i understand it. http://www.geocities.com/joebloggs7654/this.pdf

Hey, I'd like to get brush up on my math skills a bit. I actually used to tutor calculus at my college and got extremely good at it but its been about a year since Ive even looked at it and could use some work. Im going off to finish my BA in engineering in a month and would like to refresh my mind a bit but I packed up all my books already and have them stored so if anyone knows a good site with plenty of practice problems with solutions and some brief lectures as well (basically an online textbook of sorts) that would be great! P.S. Im interested mostly in the various intergration techniques, multi-variable calculus, and infinite series. Thanks.

I'm establishing this thread to ask all the questions that I'm having problem with, or to make sure my answer is correct. The practice exam is at http://www.math.unb.ca/~maureen/UMRA/Test2005.pdf and it don't provide the answers to the questions. So the sole purpose of this thread is to make sure my answers are correct, or I need some help with some of the questions. NOTE: NO CALCULATORS! The limit of [math]\frac{n+1}{n^2 + 2n + 1}[/math] is undefined. Is this correct? What is the limit of [math]\sum^{n}_{k=0}(\frac{1}{3})^k[/math]? How do I sketch a graph that satisfies the equation of [math]2^y = x[/math]? How do I put it in y form? These are some of the…

I just got back from taking the final exam for my Calc 1 class. I did pretty well on it. The only question I wasn't sure about was the last one. It was a trapezoidal rule problem. I completely spaced how to do it. I drew the graph and divided it into sections. I drew the trapezoids. I then broke the trapezoids into triangles and rectangles. I found the areas of all triangles and rectangles then added them togather. It was y=x2 from 0 to 2 with 4 trapezoids and I got 2.688(i think). I think I ended up doing it the right way, but in a longer form. When i got home, I derived the formula for what I did. [math]\frac{b-a}{n}(f(x_1)+f(x_2)+f(x_3)+{\frac{1}{2}}f(b))[/math] w…

By using the def of e^x ( series function) and considering the sequence of partial sums, how can you prove that f(x) = e^x is differentiable on R and that (e^x)' = e^x?