Analysis and Calculus

I found a cone shaped seashell on the beach that had been eroded away so three of the sprirals were cut in half. It looked cool so I took it home, and then I thought of Fibonacci numbers. So I measured the three spirals at their widest points, getting 10 mm, 17 mm and 27 mm. The first two add up to give the last one, and the ratio between the first two is 1.700, between the second two is 1.588. These are pretty close to the golden mean of about 1.618, especially since I was using a dodgy plastic ruler. Ok so it's not ground breaking mathematical work, but it's probably the closest I'll ever get.

Hi, How do I integrate Sqrt( 1+(1/x) )? Thanks.

Here's the problem: Find the length of an arc of a the curve y = ln x between the points where x=1 and x=2. (To carry out the integration rationalise the numerator.) So: y=ln x, y'=1/x Length = I(sqrt(1+( 1/x^2) )dx (I for integral...how do you get math symbols?) "...rationalise the numerator...": sqrt(1+( 1/x^2)) = x^2 + 1 -------------------- x sqrt(x^2 + 1 ) or x^2 + 1 --------------------- sqrt(x^4 + x^2 ) Answer: sqrt(5)-sqrt(2) + ln ( ( sqrt(5) - 1 ) / 2(sqtr(2) - 1) ) How do you integrate it? Is there a standard form? From the answer it looks like they used: I(sqrt(u^2 + a^2)du = 1/2 u sqrt(u^2…

There was no thread on cryptology, so I decided that the highest level math forum would do. Has anyone here taken any cryptology courses, and if so, could you please tell me which books you used if you remember? thank you.

Dear all Before I say anything, I must congratulate you on this fantastic website...so there really ARE other people who almost 'enjoy' maths too! My problem is as followed... Determine all the values of the real number c for which the following integral converges: (the integral from infinity to zero of) (x^c) / sqrt (x^4 + x) dx My first step was to split the ingral into two components A and B... A= (the integral from 1 to zero) (x^c) / sqrt (x^4 + x) dx B= (the integral from infinity to 1) (x^c) / sqrt (x^4 + x) dx Is this the logical thing to do? So that then you can work out which real values each integral is smaller or eq…

Hi, I'm just starting to do differential equations and I'm stuck on this one: (y^2 - x^2)dy - 2xydx = 0 Ans: x^2 +y^2 - cy = 0 How do I separate the variables? What's the intergrating factor? Thanks!

Hi, I've spent a week on this problem, and I think the answer in the book is wrong. Here it is: A rectangle is inscribed in a circle of radius 5 inches. If the length of the rectangle is decreasing at the rate of 2 inches per second, how fast is the area changing at the instant when the length is 6 inches. HINT: A diagonal of the rectangle is the diameter of the circle. The answer given is -7 sq in/sec. It is not clear whether you are to find the rate of change of the area of the circle or the rectangle. First consider the rectangle: The width is 8 making the area 48. After 1.5 seconds the length is 3, width is 4 and area is 12. So the answer given of -7 in/sec…

Can someone please help me solve this problem? dy/dx - [ycos(x)/1+2y^2] = 0 y(0) =1 Is this a combination of a differential equation and implicit differentiation? I'd appreciate any replies. Thanks

Just a little food for thought kinda thread here; what ways are there to find the numerical value of "e", that is, the natural base. There's 2 I learned this semester: 1. 1/1! + 2/2! + 3/3! + ... n/n!, as n-->infinity where n is an element of natural numbers Or something like that and 2. The fundamental limit of calculus, that is: lim x-->infinity for (1 + 1/x)^x

Im in high school and I am in a honors pre-calculus class. Anyway, we dont learn anything that in depth in that class and I am extremely interested in physics. However, in order to understand physics and its derivations you need to learn calculus. I was wondering if anyone knows a good way to learn calculus through any books or websites you have> i know it will take a long time to learn but i want to know how to understand physics. Next year I am going to take AP Calculus so i will learn some stuff there but i know it will not be all that i want to learn. I was just looking for some suggestions since people on these forums seem to know a lot.

Hi, I've finished "Teach Yourself Calculus" (in only 11 months!) and I feel like I've got a good foundation (Equivalent to Calculus 2, I think) for what's next. So...what's next? I'd like to get to Stochastic Calculus for Finance and Game Theory. I'm tempted to get a book on differential equations and/or partial derivatives. I think I'm lacking a big picture outlook of what's out there, how it's related, and where to go next. Thank you in advance for any advice.

I'm just messing around with some computer graphics and I got a little over my head in the math. I need to find the normal to this plane which I'm using to model water splashes. 0=(sin sqrt(x^2 + z^2))/(x^2 + z^2)-y

http://www.claymath.org/Millennium_Prize_Problems/Hodge_Conjecture/_objects/Official_Problem_Description.pdf Work on that for a bit, I'll tell you if you get it right ;)

:pi:/2 :int: sin(4x)dx 0 :int: sin(ax)dx = -1/a cos(ax) right? so . . . . . . . . . :pi:/2 -1/4 cos(4x) | . . . . . . . . . 0 [(-1/4) cos 4:pi:/2] - [-1/4(cos 4(0))] (-1/4) - (-1/4) 0 ?? where did I go wrong

Despite a lengthy and intensive period in the education system, I am one of many thousands of people who was never introduced to Mr Calculus. If someone could make a "Calculus for Dummies" style thread, it would be most appreciated. I'd be very interested in learning about the method and application of this theory.

since i'm once again bored, I thought I'd share a problem with you. Solve :int: sqrt(1+sin(2x))dx I've seen a very nice way of doing this that made me kick myself after I'd seen it, so i'll let you all have a look at it before before spoiling the fun have fun.

can anyone think of a clever way to find the determinant of the following matrix, preferably by row reduction and laplace development: |cos:lctheta: 1 0| | 1 2cos:lctheta: 1| | 0 1 2cos:lctheta:| I know the answer, that isn't the problem, but I hate multiplying out entire matrices.

Since the maths forums have been fairly inactive over the past week or so (I think I've only seen three or four posts), I've decided to see if people would like some weekly (or fortnightly) maths challenges that they can solve. The idea runs something like this: 1) The problem is posted in the appropriate forum for the challenge. 2) People send me their solutions. 3) At the end of the week, I say who "won" and post a solution. It's all a bit of fun really, but I think it would put a bit more life into the maths forums here. Another rule (to make it a bit fairer) is that nobody can win twice in a row. I'd also like to see people submitting their own problems …

Anyone have any particularly effective strategies for solving calculus word problems? Neither my book or my teacher provided any. I get confused just reading the problem. Are there strategies??

I am stuck in the eigth circle of hell, also known as Pre-calc. I got some calc books (& Organic Chem ) books from the library, but I wanted to know if anyone has used any good year-1 calc books or knows the ones they use at prestigious universities. The one I have now is the one that MIT uses for its year-1 calc students. Thank you

How do I solve ©? Also, can someone post the derivative, just to check my answer?

Hi, Here's the problem: dy/dx = y/a The answer is y=ce^(x/a) I can get to : x = a ln |y| + c and I know that x=ln y is the same as y = e^x but I can't make the connection to the answer. Thanks.

question: y= x^x "solve using logarithmic differentiation" ln y = ln (x^x) ln y = x ln (x) 1/y dy/dx = (1)(ln(x)) + x(1/x) 1/y dy/dx = lnx + 1 dy/dx = y [ln (x) + 1] is this right?

In some area of math there is a capital PI which denotes something which I don't know. Can anyone help? and it's not pi(n)= all primes under n....

In short, can some one show me how this works: the difference eqn is: y(t+1)-2y(t)=1 therefore y(t)=2^t-1 what i don't understand is the step to get the exponent (t) on the right side of the eqn....what happened to the y(t+1)? any help would be nice. I'm going to go to my tech on Mon. to ask...but if I could get it before hand it'd be nice...