Recent content by occh

In two semesters or so, i will be taking a numerical analysis course as part of an Applied Mathematics major. In the course description it says that you should have knowledge of at least one programming language, but i cannot find any more information about this. What do you all think would be...

use the cauchy-riemann conditions along with the laplace equation

Okay this yields the correct answer, for both the integrals, with the real part being for ##cos(x^2)## and (the same thing) for ##sin(x^2)## in the imaginary. Thank you very much! I guess i just needed to brush up on my manipulation of complex numbers.

well this problem gives you the integrals: ##\int_0^{\infty} cos(x^2) dx ## and ##\int_0^{\infty} sin(x^2) dx## and suggested proceeding in this manner to find the values of both of them by extracting the real and imaginary parts at the end after you solve the gaussian integral. This is where I...

So i am trying to find the ##\int_{0}^{\infty} cos(x^2) dx##. I used Eulers identity to get ##\int_{0}^{\infty} cos(x^2) - isin(x^2) dx = \int_{0}^{\infty} e^{-i(x^2)} dx##. I squared this integral, changed to polar and evaluated and at the end of this process i got the result of ##\frac{1}{2}...

Great, thanks!

Adrian Banner's Princeton lecture series on Calc I and Calc II was especially good, free on youtube. I know this stretches into post-sec mathematics, but it walks through basically all of single-variable calculus in a very precise way. Also, there is a cheap supplementary book by Adrian ~$20...

People would always sit in my Pre-Calculus class and constantly complain "When will I ever use this". They maintained these feelings throughout first semester Calculus as well, however beyond calculus 1, I've noticed that a lot of manipulation techniques learned in precalculus begin to...

Basically anything by Feynman would be good to pick up. I started with some of his "conceptual" books and then just ended up grabbing his 3 volume Lectures on Physics. These are available free online if you want, they do use calculus but they have been a beneficial source for the exact reason...

Yeah definitely multiplied, but I'm nearly positive that the RHS bottom limits are 0. Regardless, my question still holds, where does this identity come from (in whatever form it actually has)

In the proof of the closed form of the Gaussian Integral the expression$${(\int_{-\infty}^\infty f(x)dx)}^2= \int_0^\infty f(x)dx+\int_0^\infty f(y)dy $$ appears. I have seen it multiple places and understand this step is justified, but I cannot find a theorem for it anywhere. Can anybody...

The problem with most mathematics courses is that they are taught theoretically with elementary or no applications. In order to get an intuitive understanding of the underlying concepts, I usually do research on the physical applications of the topic to have a mental picture of what it...

Thanks very much for both of your replies, i think i am going to take the course. I feel like I'm one of the few freshman physics majors at my university that is in love with the math AND the physics, not just the concepts of physics.

I am a second-semester undergraduate in Physics and I have been looking to do some extra course work in my major beyond the intro course sequence. I took what was basically the equivalent of AP physics in high school, but the program at my university STRONGLY recommends that all physics majors...