Analysis and Calculus

Guys, I have some homework and the answer itself matters less - I just can't figure out *how* to do these type of questions.. I figure it has to do with an elaborate chain rule, but.. I can't do it right. I would appreciate help in this. btw, sorry if this is in the wrong forum - I couldn't find the goold ol' "Homework Help" forum. The question is this: f(x) = 2^[3^(x^2)] find dy/dx. Again, I *have* a final answer, I just don't understand how to do the chain rule itself on this one.. it seems like a double chain rule? ergh. Anyone has some sort of method/trick for these type of questions? Thanks! ~moo

I was hoping someone can help me out here...... What is the Partial Derivative for the following fuctions: d^2/dx^2 (e^(-i (3x+2y)) ) d/dx √(x^2+y2) Any guidance would be much appreciated! Thanks

This has been bugging me so I would very much appreciate it if sum1 could clear up my difficulty ASAP. Suppose we have a general linear, homogenous ODE with constant coefficients as follows: [math]\sum_{i=0}^{n}Ai\frac{d^i}{dx^n}y(x) = 0[/math] We can propose a solution to the equation to be: [math]y=e^kx[/math] Whereby k can be one of the solutions of the resulting polynomial: [math]\sum_{i=0}^{n}Aik^n[/math] I know that if I have 2 repeated roots the independent solutions should be: [math]k=e^{lx}[/math] or [math]k=le^{lx}[/math] In my notes this is justified by saying that if we have 2 roots that are very close to each other e.g. [math]k=l[/math] and [math]k…

I took a LONG break from school and stopped at college algebra. I am taking Pre-cal during this summer, but they skipped over any trig in the book since its a short 6-week session. I have a choice in taking Cal next semester, or taking Trig. I know the very BASICS of trig, such as what sin/cos, etc are from a triangle, but none of the identities, circle units, etc. Some of my peers say that a trig course isnt needed, and that I can learn myself. Is this true? Right now I am undecided what is best for me. I had a hard time doing polar coordinated in precal because of the basic trig. Other than that, I have an A in the course(i have final next week). So..…

Here is something that popped into my head a few month ago that I would like to share with the community. This simple system allows one to solve the square roots of negative numbers without imaginary numbers. What it involves is using a tetrahedral coordinate system that has 4 axis a,b,c and d, instead of x,y and z. What this does is avoid the need for negative numbers since the negative of A can be expressed as positive values of b, c and d. It just takes movement between the two systems to get rid of those pesky negative square roots.

[math] \frac{H''}{H}+\frac{2}{r}\frac{H'}{H} = 0 [/math] when H is a function of r and H" is second derivative with respect to r solve for H please help me

Hey guys, Okay, so I had my summer utterly destroyed by a crashcourse in Calculus II (have to take it now so I can take Calculus III in the fall along with Physics and Engineering 203 which I wouldn't been able to take without it). The course is extremely fast moving, and I'm doing all the work and all that, but my teacher's running through material and I'm having some difficulty understanding a fundamental thing I thought, perhaps, maybe, pretty-please-oh-help-me-im-goin-insane, you bright fellows will help me out. What the heck is it with the Fundamental Theorem of Calculus!? I understand the second part of it (which is funny.. it's supposed to rely on the f…

Hi, everyone, I don't know how to type mathematics, but I have a scanner. I have a function L_A and it is an integral. I want to differentiate this function with respect to A. I already have the answer written but what I don't know is how it was obtained. Just by looking at the answer I can sort of see some sort of pattern, and I have written what I think is some sort of rule on the second half of this page, but I still don't really know what kind of differentiation rule is used here, so if any smart people here know it would greatly help me thanks!

If y=x + sin(xy) then dy/dx equals.... I don't understand how you take the derivative of sin(xy). I think you have to use the multiplication rule and get x dy/dx + y But what do you do from there?

I was reading a post on ar15.com, and thought it was a great discussion, ended up being 11 pages of math. so here is the question? X=.99999999999 repeating 10X = 9.9999999999 repeating 10X - X = 9X 9X = 9 X = 1 Therefore .9999999999 repeating = 1 So is this an example of limits?

Given that [math]I_n = \int_{0}^{\frac{\pi}{2}}x^n \sin(x)\cdot dx[/math] Show that, for [math]x \ge 2[/math]: [math]I_n = \left (\frac{\pi}{2} \right )-n(n-1)I_{n-2}[/math] Okay if that were an indefinite integral then I'd be happy to say that [math]I_n = -x^{n}\cos{x}-n I_{n-1}[/math] but processing just that as a definite integral, [math][-x^{n}\cos{x}-n I_{n-1}]_{0}^{\frac{\pi}{2}}[/math], causes the [math]I[/math] term to be canceled out and I am nowhere near what I am trying to prove. So what do I do?

From my maths notes, I have come to a point in the section concerning paremtric differentiation on curves and have a query concerning it. I will label the change in x, y or z using a vector quantity [math]\vec{r}[/math] Basically the tangent of any curve can be represented using the following equation: [math]T=d\vec{r}/dt[/math] With which we can define a "unit tangent" whereby: [math]\hat{T}=|d\vec{r}/dt[/math] But another quantity is established: [math]ds=|d\vec{r}|=(dx^2+dy^2+dz^2)[/math] The following equality is then established: [math]ds/dt=|d\vec{r}/dt|[/math] Although it seems highly suggestible, the final statement still erks me a little. Can anyone show …

Hi everybody, this is a question that popped into my head while revising some maths. I have just covered the section describing stationary points for multple variable functions. So for example if we have a function of 2 variables we can imagine in 3 dimensional cartesian axes that the variables are described by the x and y axes and the value of the function is represented by the z axes. The subsequent stationary points for the resulting shape can be found when the partial derivatives for both variables equal zero. All this is fairly trivial, but we have been told that the 3 types of stationary points possible for this kind of function. These are maxima, minima an…

I'm not sure if this is the right section of the math area to post this but I was hoping to get some help any way. Just recently I downloaded a calculator that has the capibility to graph 3D functions which has been fun experimenting with to see what I can get to come out but to be honest I dont really understand it. I know all about 2D graphs and reading them but untill now I never had an interest in 3D so what I am asking is if sombody here could explaing how 3D graphs work, kinda like how 2D graphs use the general formula y=mx+b, but in 3D terms with an explanation. Keep in mind I am still in high school math (AP calc which Im finding now isnt that high a math to study…

I have heard that they can be found online with answers but no explanations. I can only find free response questions. Help please...

I'm stuck with this 2 questions ... q1) Using laplace transforms, solve: y" + 4y = r(t), where r(t) = {3sint, 0<t<pi, -3sint, t>pi y(0)=0, y'(0)=3. this is what i get after rewriting for the step function: 3sint [1-u(t-pi)] + (-3sint)u(t-pi) ... im lost from then on. q2) Using the method of seperation of variables, solve the following partial differential equations: a)yux(subscript)-xuy(subscript)=0 b)ux(subscript)=yuy(subscript) i'm really at my wits end ... need to submit shortly afterwards. thanks a lot for the help.

what were your thoughts on the test? Difficult? Easy in any way? How does one study for such a test?

Hi everyone, I have to do some coursework, and I am studying independant of school - so I have no tutor. I am doing some coursework on sequences of fractions. I'm just wondering, after finding the formula for the nth number, what else can you do with sequences? Here is what I have to do: 1/1 1/2 1/3 1/4 1/5 1/6 ... ... the difference from above is 1/2 1/6 1/12 1/20 1/30 ... ... the difference from above is 1/3 1/12 ... ... ... 'invesigate further' I'm not sure how to investigate further! I can find the formula, but then what? How can I investigate this further?

Hi, I need urgent help with these 3 integrals problems ... been stuck on the questions and the deadline is Friday. Thanks a lot ! 1) For the green's theorem, I got the answer : 27.552. Not sure whether it is correct. Please kindly explain in steps so I know where I went wrong. 2) I'm totally unsure about finding the surface integral. How do I know the shape of the surface ? 3) and finding the curl function f All I know is, it has something to do with curl. Something like F = grad f. How do I find the function ? Thanks again !

In class today, we had a problem in which we needed to integrate a function following the form [math] \int{\sqrt{u^2 \pm a^2}\,du} [/math] and it said to refer to the appendices which gave that integral was equal to [math] \frac{1}{2}(u\sqrt{u^2+a^2}\pm a^2\ln{|u+\sqrt{u^2+a^2}}|) [/math]. I tried to do this (using [math]+[/math] for the [math]\pm[/math]) and I first did some rationalizing [math] \int{\sqrt{u^2 \pm a^2}} \frac{\sqrt{u^2 \pm a^2}}{\sqrt{u^2 \pm a^2}}\,du [/math] as to split it into [math] \int{\frac{u^2+a^2}{\sqrt{u^2+a^2}}du} = \int{\frac{u^2}{\sqrt{u^2+a^2}}du} + \int{\frac{a^2}{\sqrt{u^2+a^2}}du} [/math] and th…

Well, this isn't a homework problem or anything, but we're incorporating factorials into our Calc II now..and I hate them to be honest I was just wondering what would be 4!!!! or if it's even possible to calculate. I did 3!!! which made my head hurt

I am trying to calculate a convolution integral in Fourier transform, and still struggling with my fear of convolution. In the inhomogneous field of my photon model the source term of current involves [math][-\lambda^2 + a^2(y^2 + z^2)]A[/math] , where the vector potential was constructed as a Gaussian wave packet of cylindric symmetry. I'd welcome comments to help me see my way clear here; these expressions in k-space can be awkward. Is there an easy generalizable statement, given that I have written the transform of [math] A_y= A_o cos(kX-\omega t)e^{-a^2(X^2+y^2+z^2)}[/math]?

I would like to ask you the following question: When we calculate the power spectrum of a N*M matrix, the result is also an N*M matrix, right? In which cases the result is an 2N*2M matrix? This question arises from the paper "TEXTURE CHARACTERIZATION USING ROBUST STATISTICS" (Russell Muzzolini etc.) page 122 (see picture). It looks like the fft is expanded and in the negative frequencies too. Thank you very much!

If ln© = b*ln(x) + ln[x^1-a + y^1-a], what is dln©/dln(x) (partial derivative of natural log of c with respect to natural log of x)

hello everyone, fundamental theorem of calculus is just one of the smallest parts of calculus so why we make it sound like differential equations (or even more than that)? What is so fundamental about it (if there's something)? also, can someone please explain how do we derive to this theorem.... I am just reluctant to accept something I don't really understand/know? thx