Recent content by CGandC

Ah, I see that now, in our case, the linear map is the differentiation operator over vector space of smooth functions over reals? ( because we wish to find such a smooth general solution )

I find a solution in math.exchange site: https://math.stackexchange.com/questions/3100237/find-general-solution-given-two-particular-solutions The way I thought about solving the problem is to somehow use the two particular solutions to generate a homogeneous solution, I couldn't figure out how...

Thank you sir! I understand now

This was a question from some past exam, I found online a solution but it uses Frobenius method which wasn't taught in the course. I would approach the solution by attempting to find a solution to the homogeneuous DE ##\left(t^2-1\right) \ddot{y}-6 y=0##, but that by itself is quite tricky...

Well, thinking about it the question of how to define something as "dead" can quickly fall into the realm of skepticism and the answer's difficult since there isn't any scientific consensus for it - should the question viewed microscopically , i.e. if there's still cellular activity after the...

I meant my simulation of a spider, though I want it to be as close as possible to the "real thing" and based on true biological axioms and principals of animal behavior ( I don't want to just simulate a simple AI using A* algorithm as that's a "fix" )

I’m interested in this because consider simulating a neural network with 100,000 neurons, let’s say you want to simulate the behavior of a wandering spider ( and suppose you have the computer power and memory to do so ); how is his a-priori knowledge which sets a basis to his entire behavior...

What about male bowerbirds creating highly articulated, bewildering nests? maybe on the hand the offspring learn from others of their kind to some degree and extemporize based on what they learned, whilst on the other hand maybe that knowledge is entrenched within their minds from birth? this is...

Very clever indeed. Thank you. I understand perfectly now, very insightful, thank you. I agree with you, finding the first point of intersection of the ray with the square and then checking which edge/line it belongs to ( this is done by checking inequalities for different edges similar to...

I understand, thank you so much! thank you so much, I just a have question regarding this method, I hope you can help me because I want to understand: The equation of a normal vector ## (x,y) ## to the vector ## r=(r_x,r_y) ## will be ## f(x,y) := x\cdot r_x + y\cdot r_y = 0##, is this the...

Consider some ray ## \bar{r} ## that starts at point ## A=(a_x,a_y) ## and faces some direction and consider an upright square ( i.e. it's not rotated ) at some location: Question: if we let the ray continue until hitting the square, how can we detect which face of the square was hit? is there...

Thanks for help! I understand now.

Relevant equations ( a quote from the book A Concise Introduction to Numerical Analysis by A. C. Faul explaining what is floating point representation ): __________________________________________________________________________________________________________ I've been reading A Concise...

Understood, thanks!. I missed the result at the site, sorry, my bad.

I've started reading A concise introduction to numerical analysis, A.C. Foul and on the first page there's the following paragraph about how a floating point in fixed point precision can be represented: I don't understand the example where it says " ##\beta=2## and ##p=20##, the decimal number...