Analysis and Calculus

I am trying to teach myself numerical analysis, and I have come to numerical differentiation. I understand how this works have only one independent variable. Now suppose I have functions of two or more variables. How can I calculate the partial derivatives and the gradient numerically?

I have written the following MATLAB code h = 10e-12; f = @(x)cos(2*pi*x); x = 0:.01:pi; fd = (f(x+h)-f(x-h))/(2*h); hold on plot(x,f(x)) plot(x,fd, 'r') The result is quite surprising. fd, which is the derivative of f evaluated numerically, has an amplitude roughly 6 times larger than what the real derivative is. Can anyone explain how this comes to happen?

Can anyone help in finding the integrating factor of (ydx-xdy)=0 According Schaum's outline of differential equations 3rd edition it's integrating factor are (-1/x^2), (-1/(x^2+y^2)). plz help me. May God bless those who will help me.

I once gave fractional calculus a brief look to see if it could help solve a problem of mine. Since it didn't apply (as far as I could tell), I moved on. Still, it's a cool idea. So, does anyone know of any "practical" applications of fractional calculus, or is it only a mathematical curiosity?

Okay. So for my research project this year I've used the DFT/FFT algorithm to calculate amplitudes of harmonics in various waveforms. These waveforms had been played to various subjects as they took spatial-reasoning tests to see which waveform enhanced concentration the most (based on the hypothetical claim that "music improves learning"). So right now I have 14 graphs I acquired from running FFTs, and I am at a loss of how to find a connection between them. Why are the waveforms on top more beneficial than the ones on the bottom? Absence of 3rd harmonic? High 2nd harmonic? The results are so inconsistent I'm totally lost. So my question is, what would be the mos…

Hi, I'm new and I'm wondering if anybody here is familiar with the Saxon mathematics curriculum, which I am currently using on a self-education endeavor that I have embarked on five years too late. If you are familiar with the Saxon math series, do you agree with its pedagogy? And if so, why? And if not, why? I am mastering John Saxon's first three books with great success, and will soon begin his Calculus text, but I fear that I am not truly absorbing the beauty of mathematics -- you know, the one mathematicians and physicists wax lyrical about. The excessive repetition and tedious multiplication and division problems he throws at the student give the i…

I have a tough problem for my calculus class I was hoping to get help for: A person meets new people at a rate of about 100 every day. After 7 days, he remembers the names of 600 of the 700 people he met. The rate of change of the # of names he remembers (dR/dt) equals 100 minus an amount that is directly proportional to R. a) write an equation expressing the assumptions above assuming at t=0 he knew no names. _________________________________________________________________________________ What I've come up with so far is dR/dt=100-kR, where k is the constant of proportionality. I'm not sure where to go from here...I think the next step would be to get the d…

I am currently taking calc 2 because I am lazy and wanted to hold off taking calc 2 because calc one gave me some trouble. I am a mechanical engineering student and I need some help with this one problem. So far I got 18 out of the 19 questions correct, this one is just killing me and I think its just a silly mistake. Thank you

I'd like to initiate a kind of Integral Marathon. This is simple, person who solves a problem must receive a confirmation whether the answer is correct or not. In case where the answer is correct, solver may post the next integral. (Of course, indefinite & finite integrals are allowed.) Let's start with an easy one: Solve [math]\int {\frac{1} {{x\sqrt {x^2 - x} }}\,dx}[/math].

hi, i have the answer to this problem, but can't figure out how they did it. find the total area of the region bounded by the graph of y=x[(1-x^2)^(1/2)] and the x axis.

Hey everyone, I am trying to solve the following indefinite integral: [math]\int \frac{dx}{x\sqrt{4x^2-9}} [/math] And I have got 2Arcsecx+c... but I am afraid it could be wrong... can anyone please check it...

I have a few questions, one concerning a basic integral that I'm having trouble working out, one about notation, and lastly about graphing a two dimensional function in R^3. This is the integral I'm having trouble with: [math] \int e^{2x} sin(3x) dx [/math] I'm pretty sure I have to start off by using u-substitution, and then use integration by parts. I think the u-substitution is what's giving me trouble. If I let [math] z= 3x [/math] then [math] dz= 3 dx [/math] and therefore [math] \frac{1}{3}dz = dx [/math]. If [math] z= 3x [/math] then [math] x= \frac{z}{3}[/math]. Then I would have [math] \frac{1}{3}\int e^{\frac{2z}{3}} sin(z) dz [/math] Is …

I can't integrate dx/(1-x^2)^1/2 inverse sinx

I was possibly thinking about teaching myself calculus and I was wondering what book(s) I could buy that are user friendly and have good explanations. I'm not a math whiz and I'm currently taking analytical geometry, but I want to get ahead before next year. I looked on amazon.com and almost every calc book on there has horrible reviews. So I was wondering what everyone on here thought. Thanks

Does calculus involve any physics problems that might relate to architecture? I've seen some calc problems about some physics-related problems but I was wondering if they involve something like shapes. Also, if you know the difference between calculus Ab and calculus BC, should I take Ab or BC (I'm going into my senior year in high school). I've already taken half of calc Ab because of my pre-calc class I'm taking right now so yeah, if you know what it's like.......

There is a method to apply derivation in computer, but I dont know. What method is this?

Hi. I am trying to figure out what the Maclaurin series of the error function looks like. I use the reference from Wikipedia to check my results, but I cannot seem to get it right. with [math] f(x) = \int_0^x e^{-\frac1{2} t^2}~dt[/math] I would expect [math]f(0) = 0[/math] and [math]f'(0)=-\frac1{2}[/math] and thus the first two terms of the Maclaurin series to be [math]\frac1{1!}x + \left(-\frac1{2}\right) \frac1{2!} x^2[/math] but this does not seem to be correct. What am I doing wrong? Anyone?

Could anyone explain to me how you do this. It says to complete the segmented function so that it is continuous. y={ (x^2-11)/(x+(sqrt11)) ---- if x = ----- Thanks

What is differentiation used for?

How would I go about showing that the function defined by f(x)=exp(-1/x^2) for x<>0 and f(x)=0 for x=0 has derivatives of all orders and the value of all the derivatives at x=0 is 0? It seem obvious that f is infinitely many times differentiable for x not equal to 0, but I don't know how I would write down a proof. Taylor series come to mind, but nothing in the book deals with that, so there should be another way. I've shown f'(0)=0 by writing down the limit and using L'Hospital. But how would I show it for higher order derivatives without explicitly calculating the derivatives and evaluating the limits? Would induction work? I've thought of letting g(x)=-…

does anyone of you know any online calculus exams? please, if you do know one, put the website or URL. its summer here and i can't go inside our school library cause i'm not yet a "registered" student. and i can't go to our public library since i still have a standing balance there. heehhe!! please help. i tried google and i did not find what i was looking for.

I know that the cdf of the normal distribution can not be evaluated analytically, since e^(-t/2) has no antiderivative. Why is that?

The function y= (3x^3-2x+1)/(2x^2) has me confused. I am trying to figure out why this function has a horizontal asymptote when the degree of the numerator is larger than the denominator, which I thought was supposed to mean it has no horizontal asymptote? Thanks

I was hoping someone could help me out with this question..... what is d^2/dx^2((2ax^2-1)(e^-(ax^2)/2)) where a is constant Any guidance would be great thanks

consider the function [math]\frac{1}{\epsilon^2 + z^2}[/math] So we know that there are two poles, one at [math]z = i \epsilon[/math], one at [math]z = - i \epsilon[/math]. So when this function never hits 0 on the real line, how do the singularities affect its behavior on the line? Okay, so poles are a subclass of singularities. I think that [math]z = i \epsilon[/math] and [math]z = - i \epsilon[/math] are poles - I may be wrong here. The question is - how do complex singularities (complex poles in this case) affect a function's behavior when the function is plotted on the real line?