Analysis and Calculus

Somebody asked me if i knew what the Rule of conditional proof is and how is used in mathematics and particularly in analysis. can anyone help with respect to that??

I've always had a problem understanding the concept of equations that do not simply start with Y(x) = ...... This one for example: V(x+1) = V(x)+(g-(Cd/m)*v(x)^2)(ti+1-ti) is one that I have to make into a plot for this program called Matlab. (for computing stuff) Can someone explain this equation to me or enlighten me on the subject. How should I simplify this to make it more understandable?

I've yet to come across this despite the numerous references to Gamma functions in various places which I never gave notice. To what I am referring is integration of factorials which is now to my understanding a specific case of the gamma function. What are some of the finer points to be looked over when considering solutions? Where do these concepts lie in the greater scheme of mathematics?

As I worked on teaching my self calculus this summer I begin to wonder how to write a generic formula for the nth derivative of a equation of the form: [math]y=x^{a}[/math] [math]where: a\geq 1[/math] After thinking about it the pattern became obvious, but the proof took me a while to work out, in the end I came up with an inductive proof. Below is the proof I came up with. [math]Basis:[/math] [math]\frac{d^{n}y}{dx^{n}}=\left(\frac{a!}{(a-n)!}\right)x^{(a-n)}[/math] [math]Let: n=1[/math] [math]\frac{d^{1}y}{dx^{1}}=\left(\frac{a!}{(a-1)!}\right)x^{(a-1)}=ax^{(a-1)}[/math] This step is verified because I came to the form proven by the …

B(m,n)=gamma(m).gamma(n)/gamma(m+n) while changing the variables x to rcosz, y=rsinz and taking their differentials we tactly assume the terms containing (dz)^2 & (dr)^2 terms vanish. we only consider terms containing dzdr in the double integral in place of dxdy can somebody please explain why (dz)^2 & (dr)^2 terms vanish or not considered for the double integral?

I've hit a brick wall in trying to see how in a text book they went from:- T1xsin37deg + (1.33T1)(sin53deg) -100N = 0 straight to T1 = 60.1N Any help on the intervening steps would be appriciated. Thanks

well i didnt find it anywhere, please help me with sites where to find the proof if u wont like typing. well its easy to understand that if the rhs is true the lhs will be a periodic function for the lcm of the period remains same not the vice versa. plese give me the proof.

I'm taking a summer semester right now, with a REALLY tough math class. Here's an example of the kind of stuff I've got. Your watching a movie on a Youtube playlist with x videos. On the first video, you click the random button and click "play next" once to take you away from the first video, and click "play next" a second time to take you to another video that could be any one of the x number of videos, including the first one. After that, you watch x videos in a row without touching the keyboard or mouse. What are the odds that the entire movie will be played in perfect chronological order? Needless to say, my instructor is a big computer nerd. This is t…

I'm currently trying to find a way to perform a hyperbolic regression on a set of data I have as various transformations (i.e. logarithmic and reciprocal) can't linearise it. Having look through the literature it would appear that it can be described by a hyperbola, which is all well and good, but I need to use it as a standard curve for later on. The reason it is described by a hyperbola is because it is a the result of antibody binding and enzyme-substrate reactions which are themselves described by a hyperbola. I have an article which describes a derivation and a description of the requisite Python script that spits out the relevant coefficients which can then…

Hey all, I've been trying to learn second order differential equations with x and y' missing. I've been doing so with some material my math teacher gave me, and they give the following example: [math]y'' = -\frac {1}{y^3}, \ y \neq 0[/math] They go on to multiply both sides of the equation by [math]2y'[/math]: [math]2y'y'' = -2 \frac {y'}{y^3}[/math] Now here comes my problem. They rearrange the left side like so: [math](y'^{\ 2})'[/math] That is correct, when we use the chain rule the result is [math]2y'y''[/math]. However, it's the right side rearrangement that confuses me. From [math]-2 \frac {y'}{y^3}[/math] they somehow get [math]\left(\fr…

Correct me if i am wrong but isn't the fundamental Theorum of Calculus simply a formula to convert the energy of a system from x dimensions to either x+1 or x-1?

Hi everyone! This is my first post on this site so if I'm breaking any rules I appolgize in advance. For an opcoming physics entrance exam i'm repolishing my math skills but I just can't seem to solve this problem: Integrate: (e^x)/(1+e^(3x)) dx I've tried substituting with : u = e^x, u = e^3x and u= 1+e^3x, but nothing seems to work out. Maybe i'm just missing something very obvious but I'm just lost at this point thanks in advance!

Hi, mathematicians. In the following link, there are Euler's articles and books coded as E1, E2, E3,.... I wonder in which article he introduces his special number which we now know as the number "e". http://www.math.dartmouth.edu/~euler/

Hey again guys, I was in a study session today with classmates, and we had a hard time answering a question that involved the dirac delta. But the difficulty wasn't so much the method (we have that in the book and as equations online), but rather with the concept. What is the meaning of the dirac delta, specifically in 3D?? If you need to "imagine" it in 3D - how would you describe it? How does it look? What's the point of it? If anyone can help with this, it'll be greatly appreciated.. we can plug in numbers into equations, but if we don't understand what the concept is, we have no clue what we're doing. Thanks in advance ~moo

[math] \int \frac{\sqrt{x}}{\sqrt{1-x}} dx [/math] From 0 to .5 How would you go about solving this without the use of a calculator?

Hi guys. I play now a bit with EM fields and I have encountered some problems connected with Dirac delta. By coincidence I visited this forum and I thought I could find some help in here. Surely i have read these topics: http://www.scienceforums.net/forum/showthread.php?t=35186&highlight=dirac+delta http://www.scienceforums.net/forum/showthread.php?t=35132&highlight=dirac+delta That gave me a lot but i still do not feel it. The problem is that in order to get a potential in some point from a single charge you need to just solve such thing: [math]\square \phi = - \frac{ \rho}{\epsilon} [/math] and there by the way you need to use such equation: [math]\nabla…

Ah, I used to be able to do this easily but I really have forgot by now... Say you have a sphere with radius 10, you are drilling out a hole along the diameter with a radius of 3 inches... Find the volume of what's left of the sphere... So the way I thought to do it was just y = sqrt(100-x^2) in range y>3 rotated around x axis, but I really did forget how to write this... It was something like [math]pi \int^{10}_{3}(100-x^2)[/math]? Merged post follows: Consecutive posts mergedActually, sorry for wasting your time, that seems to be about right.

i have a problems,i hope that u can help me to solve it the question ask to find the volume using integrate find the volume of the solids that results when the region enclosed by y=squareroot x , y=0 and x=9 is revolved about the line x=9

First off, mornin' ladies and gentlemen of Science Forums. I'm currently an AP Calculus student, and I've noticed that the College Board curriculum for calculus is kept strictly to real numbers. So that got me wondering: can you have imaginary calculus? I would guess that the answer is yes; if so, are the rules the same as real calculus? I did some messing around with f(z) = (z + zi). I haven't done anything with imaginary numbers for a while, but I think the graph of this would be a vector with a constant slope i? (Can you take slopes on the imaginary plane like a linear function?) I tried to find a derivative of z+zi that equaled i and found that if I took the d…

I think this is one of the things that calculus screws my train of thought on. I think I understand what a limit is. Why would you have to define a limit? Is there ever a situation where not defining a limit would change the outcome?

IM SO CONFUSED (and it doesn't help that my teacher barely knows what she is talking about). I don't know when an object that is rotated around either axis is a washer or when it is a shell. If the problem says "do volume by shell" or "do volume by washer" I can get it right. I can't tell on my own though. http://img297.imageshack.us/my.php?image=ahhcalculus.png For example, get that in #1 it is a disk when rotated around the x axis In #2 though, when you rotate that shaded part, formed by the equation x^3 and some other equation that intersects it at the origin and in the first quadrant somewhere, around the x-axis which one is it? What about around th…

I am interesting in teaching myself calculus and so far have been using a book which briefly covers the very basics of the subject. I am wish to go deeper into the subject and so have been doing some research trying to find a text book. Some people I have discussed this with suggest getting Ron Larsons Calculus text book, but it comes in different versions: Calculus of Single Variables: Early Transcendental Functions Calculus with Analytical Geometry I am not sure what the difference is between each course and am not sure which is the best to start out with. Or what other textbooks might people recommend. I know that people have suggested using online sourc…

Hey all, I just need someone to check the following: [math]F_a= G \frac{m_a \cdot m_b}{r^2}[/math] [math]a_a(t)= \frac{F_a}{m_a}[/math] [math]v_a(t)= \int G \cdot \frac{m_b}{r^2} \,dt = G \cdot \frac{m_b}{r^2} \cdot t + v_0[/math] [math]s_a(t)=\int G \cdot \frac{m_b}{r^2} \cdot t + v_0 \,dt = G \cdot \frac{m_b}{2 \cdot r^2} \cdot t^2 + v_0 \cdot t + s_0[/math] Cheers, Gabe

I have absolutely no idea what calculus is please could someone explain the basics of calculus or at least say what it means

(This would ordinarily be in Homework Help, but we are not actually graded on homework and it fits better here.) I have a problem which looks like this: Find all values of x for which the series converges. For these values of x, write the sum of the series as a function of x. [math]\sum^{\infty}_{n = 1} \frac{x^n}{2^n}[/math] I don't really know where to start. Intuition tells me I could just declare x < 2, but I do not know how to go about finding the actual sum of the series or proving that my intuition is actually correct. I'd imagine I am supposed to create a sequence of partial sums and see if the sequence converges (via a limit), but how would…