Functions Definition and 1000 Threads

In our complex variables course we were told that an analytic function of an analytic function is itself analytic. i.e. For ##h(z)=g(f(z))## ##h(z)## is analytic. I was wondering is this is just a fact, or if it is possible to prove this statement. I did some googling and the best response I...

I noticed the graphs of ##y=\cos^{-1}x## and ##y=\cosh^{-1}x## are similar in the sense that the real part of one is the imaginary part of the other. This is true except when ##x<-1## where the imaginary part of ##y=\cos^{-1}x## is negative but the real part of ##y=\cosh^{-1}x## is positive. I...

Homework Statement δ(z*-z0*)δ(z+z0)=? δ(z*+z0*)δ(z-z0)=? where 'z' is a complex variable 'z0' is a complex number Formula is just enough, derivation is not needed.

Homework Statement What is the product of two Dirac delta functions δ(Real(z-c))δ(Img(z-c))=? 'z' and 'c' are complex numbers. This is not a problem, But I just need to use this formula in a derivation that I am currently doing. I just want the product of these two Dirac delta functions as a...

Homework Statement Homework EquationsThe Attempt at a Solution So far I have a solution for a) as For b) I formulate the equation as and so far for c) I have My main idea at the moment is that as the Lagrangian was not time dependent, the Hamiltonian will not be. Following on maybe...

Homework Statement We are required to find the no. of ordered pairs ##(x,y)## satisfying the equation ##13+12[tan^{-1}x]=24[ln x]+8[e^x]+6[cos^{-1}y]##. (##[.]## is the greatest integer function, e.g. ##[2.3]=2##, ##[5.6]=5##, ##[-2.5]=-3## etc)Homework EquationsThe Attempt at a Solution The...

Well I was reading this paper http://inspirehep.net/record/1409825 and came across this comment: My question is basically a statistical one... how can you make several fits using only 2 fitting functions? Or do they mean something like fitting with func1 in some ranges [a,b] with a,b varying...

g(t)=½( f(t)+f(-t) ) h(t)=½( f(t)-f(-t) ) show its 2π periodic so: g(t+2π) = ½( f(t+2π)+f(t-2π) ) why does -t become t-2π ? ½( f(t)+f(-t) ) = g(t) h(t+2π)=½( f(t+2π)-f(t-2π) ) ½( f(t)-f(-t) ) = h(t) is this correct? can...

Homework Statement Homework Equations no equations required The Attempt at a Solution [/B] a) The number of hours of daylight is a periodic relationship, because it repeats the same wave-like pattern over the course of 1-2 years. b) the period is the amount of time it takes for one cycle...

Homework Statement Homework Equations none The Attempt at a Solution Is this correct? Thanks.

Homework Statement 2. Homework Equations The Attempt at a Solution a) [/B]f(x) = -5x2 + 20x + 2 y = -5x2 + 20x + 2 Factor -5 from the first two terms: y = -5x2 + 20x + 2 = -5 (x2 – 4x) +2 Complete the square in the bracket: (1/2 b)2 = [1/2 (-4)]2 = (-2)2 = 4 Group the perfect...

Please guide why answers are different in following two cases and which one is correct? Case 1. sin-1 ( – 1/2 ) – sin-1 (– 1) = 7π/6 – 3π/2 = – π/3 Case 2. sin-1 ( – 1/2 ) – sin-1 (– 1) = – sin-1 ( 1/2 ) + sin-1 (1)...

Homework Statement Let σ : Z_11 → Z_11 be given by σ([a]) = [5a + 3]). Prove that σ is bijective. Homework EquationsThe Attempt at a Solution I am just wondering if I can treat σ as a normal function and prove that is bijective by using the definitions of one to one and onto.

Homework Statement check for linear dependecy[/B] f(x) = cosx and g(x) = xcosx 2 functions from R to R Homework EquationsThe Attempt at a Solution Why this is wrong: if i take the scalar a1 = 3, a2 = 1 i can do that since 3 is real, and a1 is in R. so 3f(3) + -1g(3) = 0 there for we have none...

Functions f,g from R to R. f(x) = xcosx, g(x) = cosx for x = 0, we get f(x) = 0, g(x) = 1. so for scalar t in R t(f(x)) + 0 * g(x) = 0 . ==> f(x) and g(x) are linearly idepenent. Is that right? if so in functions we search for an x that makes the function dependent?

Homework Statement What is the fundamental period of the expression sinx/sinx.can you guys please illustrate how to make its graph? Homework Equations Okay I know drawing graph can give me the period.Can the period be found by any other method? The Attempt at a Solution I'm told that the...

I was reading the wikipedia article on Lithium and noticed that it says: Trace amounts of lithium are present in all organisms. The element serves no apparent vital biological function, since animals and plants survive in good health without it, though non-vital functions have not been ruled...

I have two questions related Gamma functions 1. Finding ##\Gamma## analytically. Is that possible only for integers and halfintegers? Or is it possible mayble for some other numbers? For example is it possible to find analytically ##\Gamma(\frac{3}{4})##? 2. Integral...

Homework Statement Assume a particle with a wave function ##\psi(x)## such that ##-\infty < x < \infty##, that move under some potential ##V(x)##. Show that: a) two wave functions with same energies can only differ by a complex phase; b) if the potential is real, then you can choose the wave...

hello, in the task of finding the optimal phase covariant cloning machine, i have to maximize two functions of six variables :f1=a.C+b.D and f2=a.B+c.D , they are many constraints, but I've already used them to get to those expressions in the first place, the variables are real scalars and vary...

Hello, i am studying calculus and I am looking for a book or website that covers the following topics: -Real functions with vectorial variables (limits, domains, continuity, derivatives, directional derivatives, gradients) -Vectorial functions with vectorial variables (derivatives and...

Homework Statement So I want to prove that the expression 20Cr×0.1r 0.9(20-r) reaches maximum value for r=(0.1)×20=2 Homework EquationsThe Attempt at a Solution I can prove it by trial and error but can't differentiate the expression because nCr isn't continuous.

Homework Statement Prove $$T\int_c^d f(x,y)dy = \int_{c}^dTf(x,y)dy$$ where $$T:\mathcal{C}[a,b] \to \mathcal{C}[a,b]$$ is linear and continuous in L^1 norm on the set of continuous functions on [a,b] and $$f:[a,b]\times [c,d]$$ is continuous. Homework EquationsThe Attempt at a Solution [/B]...

Homework Statement Write three functions int get_hour(int timestamp), int get_min(int timestamp), int get_second(int timestamp) which will respectively return the hour of the day, the minute of the hour, and the second of the minute from a value given as parameter which is in milliseconds...

Consider a two-point function $$f(\mathbf{r}_{1},\mathbf{r}_{2})$$ If one requires homogeneity, then this implies that for a constant vector ##\mathbf{a}## we must have $$f(\mathbf{r}_{1},\mathbf{r}_{2})=f(\mathbf{r}_{1}+\mathbf{a},\mathbf{r}_{2}+\mathbf{a})$$ How does one show that if this is...

I read about quark distribution functions in the nucleon that are chiral-odd or chiral-even functions (Sivers function, Boer-Mulders function and other distribution function related to nucleon transversity). What is the definition of chirality for functions? Does this mean they are odd or even...

I have the following code creating an object on a web page: My question is if the function(event) { // var id=myid; unbind(event, this); } part of the code below results in a unique instantiated function per anchor or will all anchors point to the...

The question says find apex, low point and the monotonic properties of the functions. a) b) c)... To find intervals, I use the abc-formula. Example: f(x) = 3x^3 - 3x d/dx * f(x) = 3 * 3x^2 - 3, here a=3*3, b= -3 and c=0 (because there is none) x1 = ( -b + sqrt(b^2 + 4*ac) ) / 2a x2 = ( -b -...

Homework Statement im trying to understand how an electric generator works Homework Equations no equations required The Attempt at a Solution here is a diagram of an electric generator, and a small section of what my lesson was trying to explain: [/B] so this was the explanation from my...

hi, and thanks for come in, sorry for bad english :frown: I was watching a proof of euler to the basilean problem, and a part of the proof he did this sin(x) = x ( x + π ) ( x - π ) ( x + 2π ) ( x - 2π ) ( x + 3π ) ( x - 3π) ... i understand why, but i wanted to know what not polynomial...

Hello, I got the following diagram, shown below, and I have to derive its transfer function. I think I have a general misunderstanding about the transfer functions. What I think it is, is: output/input basically. As input is the whole block of things that affect the output. This is the system...

For ordinary differential equation y''(x)+V(x)y(x)+const y(x)=0 for which ##\lim_{x \to \pm \infty}=0## if we have that in some point ##x_0## the following statement is true ##y(x_0)=y'(x_0)=0## is then function ##y(x)=0## everywhere?

Homework Statement Prove functions f and g are continuous in ℝ. It's known that: i) lim g(x)=1, when x approaches 0 ii)g(x-y)=g(x)g(y)+f(x)f(y) iii)f2(x)+g2(x)=1 The Attempt at a Solution [/B] g(0) has to be equal to 1 because it's known that lim g(x)=1, when x approaches 0. Otherwise g won't...

Are the Eigenspectra (a spectrum of eigenvalues) and the Empirical Orthogonal Functions (EOFs) the same? I have known that both can be calculated through the Singular Value Decomposition (SVD) method. Thank you in advance.

With basic fractions, the limits of 1/x as x approaches infinity or zero is easily determine: For example, \begin{equation} \lim_{x\to\infty} \frac{1}{x} = 0 \end{equation} \begin{equation} \lim_{x\to 0} \frac{1}{x} = \infty \end{equation} But, we with a operation like ##\frac{f(x)}{g(x)}##...

"If a function can be differentiated, it is a continuous function" By contraposition: "If a function is not continuous, it cannot be differentiated" Here comes the question: Is the following statement true? "If a function is not right(left) continuous in a certain point a, then the function...

Homework Statement I am trying to determine whether $$f(x)g(x')\delta (x-x') = f(x)g(x)\delta (x-x') = f(x')g(x')\delta(x-x')$$ where \delta(x-x') is the Dirac delta function and f,g are some arbitrary (reasonably nice?) functions. Homework Equations The defining equation of a delta function...

i have a question, why is the plot of r2(Ψ2p)2 not a good representation of the probability of finding an electron at a distance r from the nucleus in a 2p orbital

Homework Statement If f: [0,1] \rightarrow \mathbb{R} is continuous, show that (n+1) \int_0^1 x^n f(x) \mathrm{d}x is in the range of f Homework Equations (n+1) \int_0^1 x^n f(x) \mathrm{d}x=\int_0^1 (x^{n+1})' f(x) \mathrm{d}x The Attempt at a Solution I tried integration by parts, but that...

Sorry for the terribly vague title; I just can't think of a better name for the thread. I'm interested in functions ##f:[0,1]^2\to\mathbb{R}## which solve the DE, ##\tfrac{\partial}{\partial y} f(y, x) = -\tfrac{\partial}{\partial x} f(x,y) ##. I know this is a huge collection of functions...

Hi! I'm looking at some piece-wise function right now and I can't help but wonder what all these parts are called. I'm learning to use and write this type of functions now and I think I have a pretty good understanding of how they work. I even took the extra step of learning some "set builder...

My Calculus 2 teacher's lecture slides say: Many of the functions that arise in mathematical physics and chemistry, such as Bessel functions, are defined as sums of series. I was just wondering how this was different from the basic functions that we've already worked with. Are they not...

Homework Statement Find the domain of this function and check with your graphing calculator: f(x)=(1+cosx)/(1-cos2x) Homework EquationsThe Attempt at a Solution i get to (1+cosx)/(1+cosx)(1-cosx) which is factored. so then setting each one to zero one at a time i figure out that cosx = -1 and...

Why is the triplet state space wave function ΨT1=[1σ*(r1)1σ(r2)-1σ(r1)1σ*(r2)] (ie. subtractive)? How does it relate to its antisymmetric nature? Also, why is this opposite for the spin wave function α(1)β(2)+β(1)α(2) (ie. additive)? And why is this one symmetric even though it describes the...

Homework Statement Suppose that f has an inverse and f(-4)=2, f '(-4)=2/5. If G= (1/f-1) what is g '(2) ? If it helps the answer is (-5/32) Homework Equations [/B] f-1'(b)=1/(f')(a) The Attempt at a Solution Im not really sure how to start this problem. I am familiar with how to use the...

On the paper I'm reading the arctan of 35 over 65 is approx. 28.30degrees. When I use the Google calculator "arctan(35/65)" gives me 0.493941369 rad. What am I doing wrong?

I am trying to find the field lines of the 3D vector function F(x, y, z) = yi − xj +k. I began by finding dx/dt =y, dy/dt = -x, dz/dt = 1. From here I computed dy/dx = -x/y, and hence y^2 + x^2 = c. For dz/dt = 1, I found that z = t + C, where C is a constant. I am unsure where to go from...

My question regards finding the field lines of the 3D vector function F(x,y,z) = yzi + zxj + xyk. I was able to compute them to be at the curves x^2 - y^2 = C and x^2 -z^2 = D, where C and D are constants. From my understanding the field lines will occur at the intersection of these two...

Hi All, In teaching the basics of quantum mechanics, one has often to introduce potential functions such as the step, the barrier and the well. When I try to get some example of the physical environment of a particle that could correspond to a step function, for instance, what comes out is...

So, it is known and easy to prove that if you have f : D -> G and g : G -> B then -if both f and g have the same monotony => fοg is increasing -if f and g have different monotony => fοg is decreasing But the reciprocal of this is not always true (easy to prove with a contradicting example)...