poirot
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 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