Reputation
4,014
Top tag
Next privilege 5,000 Rep.
Approve tag wiki edits
Badges
10 34
Impact
~179k people reached

Oct
26
comment How to think of a function as a vector?
I finally found something that made intuitive sense to me linking the traditionally taught idea of a vector to these vectors as functions. I could never quite understand where the integral product $\langle\cdot,\cdot\rangle=\int_0^1 f(x)g(x)dx$ came from. I was always told it was just defined that way, but the lecturers never explained why this might be the case... eng.fsu.edu/~dommelen/quantum/style_a/funcvec.html. Seems that a suitably well-behaved function defined over a finite interval $[0,1]$ can represent an infinite dimensional vector. Makes sense now.
Oct
26
comment Sketch $\{z^2|\text{Re}(z)>0\}$. Having troubles with finding what points are or aren't in the graph.
@Omnomnomnom I'd not considered the image/codomain difference before, so thanks for your comment. However, it was not clear to me. The OP mentions graph in the title which means to me the set of ordered pairs $(z,z^2)$, both elements being complex numbers. But yes, the sketching statement clears that up. Apologies.
Oct
26
comment Sketch $\{z^2|\text{Re}(z)>0\}$. Having troubles with finding what points are or aren't in the graph.
So what you actually want to do is plot the image of the function, i.e. the codomain.
Oct
26
comment Sketch $\{z^2|\text{Re}(z)>0\}$. Having troubles with finding what points are or aren't in the graph.
You are attempting to plot 4-dimensional data since $z=x+iy$ (two dimensions), and $z^2=u+iv$ (a further two dimensions). One way to plot this is using a vector field, but that's probably not what you're after. Another way would be to plot $|z^2|$ in a three-dimensional space. Also, you say your expressions are too hard - maybe you will need to numerically evaluate your expressions.
Oct
26
revised Prove trigonometric identity $\frac{\sin^6x}{1 - \tan^2x} + \frac{\cos^6x}{1-\cot^2x} = - \sin^2x \cdot \cos^2x$
[Edit removed during grace period]; added 143 characters in body
Oct
26
revised Prove trigonometric identity $\frac{\sin^6x}{1 - \tan^2x} + \frac{\cos^6x}{1-\cot^2x} = - \sin^2x \cdot \cos^2x$
[Edit removed during grace period]
Oct
25
answered Prove trigonometric identity $\frac{\sin^6x}{1 - \tan^2x} + \frac{\cos^6x}{1-\cot^2x} = - \sin^2x \cdot \cos^2x$
Oct
21
revised elementary vectors addition
deleted 1 character in body
Oct
21
revised elementary vectors addition
added 462 characters in body
Oct
21
answered elementary vectors addition
Oct
20
comment An easy way to remember PEMDAS
Maybe you find BEDMAS easier to remember? Brackets, Exponentiation, Division, Multiplication, Addition, Subtraction. (I changed that from BODMAS [Brackets Off ...] to contain your inclusion of Exponentiation)
Oct
20
revised Complex integration using singularities
deleted 8 characters in body
Oct
20
comment Complex integration using singularities
Yes, you can only use the theorem if its conditions are met, so any restrictions are perfectly acceptable. Later on you will be able to state the correct value of the integral for your special case ($|w|=1$) once you know how to compute it using the residue theorem. I suspect your lecturer will not expect you to consider the special case, but if you do know how to use the residue theorem then just evaluate that special case as well and put that in your answer ! Make sure to follow the instructions of the question carefully though - maybe they don't want you to consider that special case...
Oct
20
revised Complex integration using singularities
added 27 characters in body
Oct
20
answered Complex integration using singularities
Oct
20
comment Complex integration using singularities
Sorry, I read your question incorrectly by forgetting your initial sentence after reading the last, which lead my thoughts down the wrong path !
Oct
19
comment Complex integration using singularities
Cauchy's Residue Theorem: en.wikipedia.org/wiki/Residue_theorem
Oct
15
comment Confused about Euclidean Norm
That's why I made this community wiki. Just though it might give some background. And exercise my little grey cells !
Oct
15
revised Confused about Euclidean Norm
deleted 3 characters in body
Oct
14
revised Confused about Euclidean Norm
added 283 characters in body