Domain Definition and 743 Threads

  1. R

    Understanding Electromagnetic/X-Ray Pulse in Time and Frequency Domain

    Dear All, Suppose we have a electromagnetic/x-ray pulse with fixed energy with finite line width. I want to know the schematic of a plot how it looks in time- and frequency-domain? I think I understand in time domain: there will a straight vertical line on plotting intensity vs time in x-axis...
  2. J

    Is there physics knowledge hidden to public domain?

    I was wondering if our governments hide us some knowledge. Military industry for sure, but What about physics? Is all the knowledge public? I include in my question biology. I am sure that the richest people in this planet are investing right now hundreds or thousands of billions researching...
  3. M

    Find the Domain and Range of Functions with Given Domain and Range Values

    Homework Statement Suppose f is a function with domain [-2,10] and range [5,10]. Find the domain and range of the following functions. (a) f(2x+4) (b) 2f(x)+4 The Attempt at a Solution [/B] Would I just substitute the in the domain and range values to find the answer?
  4. R

    A Domain Wall Geometries: Continuous Coordinates, Discontinuous Metric

    Hi all, I need some help regarding domain wall geometries, essentially a bubble of some spacetime (say deSiiter or flat) inside another kind, say anti-deSitter. For simplicity it is spherical symmetric situation and we are intent on using Schwarzschild like static coordinates. So now I am used...
  5. T

    MHB How is the Domain of a Trigonometric Expression Determined?

    I have the expression $$\sqrt{ a ^2 - x^2}$$ using trig substitution (with $x = asin\theta$), I get$$\sqrt{ a ^2 - a^2sin^2\theta}$$ which gets simplified to $ a \sqrt{ cos^2\theta}$ and then $ a cos \theta$ for $$- \frac{\pi}{2} \le 0 \le \frac{\pi}{2} $$ what I don't get is domain of...
  6. M

    MHB An Artinian integral domain is a field

    Hey! :o I want to show that an Artinian integral domain is a field. Let $R$ be an Artinian integral domain and $a\in R$ with $a\neq 0$. Can we take then the sequence $(a)\supseteq (a)^2\supseteq (a^3)\supseteq \dots $ ? (Wondering) Since $R$ is an Artinian integral domain we have that...
  7. Dor

    Solve Laplace equation on rectangle domain

    Homework Statement I'm having issues with a Laplace problem. actually, I have two different boundary problems which I don't know how to solve analytically. I couldn't find anything on this situations and if anybody could point me in the right direction it would be fantastic. It's just Laplace's...
  8. A

    Finding the Domain of a Trigonometric Function

    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...
  9. S

    MHB Math Notation: How to explicitly specify the domain of a function symbolically?

    How can I specify the domain of a function symbolically? Assume I have a very simple linear function. $f(x)=2x$ If I want to say that the domain of this function is all the real numbers, how would I write this with symbols? Do I need to use set-builder notation? What would the set-builder...
  10. S

    Is xy>0 Sufficient to Determine the Domain of f(x, y) = xy√(x²+y)?

    Homework Statement Find the domain of the function: f(x,y) = xy*√(x2+y) Homework Equations The domain is the set of all input values for which the function is defined. The Attempt at a Solution D = {(x,y): xy>0} I plugged the function into Wolfram and it gave the result: D = {(x,y): x2+y ≥...
  11. S

    MHB Modifying values to lie within existence domain

    Given three parameters: $$a= \frac{(k-3)^2 \sqrt{v}}{s}, \ \ b = \frac{v}{s}(w-10s), \ \ c = s \sqrt{v}.$$ which exact values I know (that is, I know $v,s,k$ and $w$ exactly). I need to guarantee that $a<0$ (this is always satisfied in my calculations!) and $$0<b<1.08148a^2$$ For instance, if...
  12. S

    Find the domain of the function

    Homework Statement Find domain of f(x, y) = ln ((x2+2x+y2) / (x2−2x+y2)) Homework EquationsThe Attempt at a Solution Because the function is a natural ln, the restriction on the function is that everything inside the brackets has to >0, otherwise the function is undefined. I worked on the...
  13. M

    Help -- Time Domain Power, Volt-Amperes in lagging circuit

    Please find attached a spreadsheet trying to plot an inductive/resistive circuit in the time domain and show instantaneous power and Volt Amperes. Logic tells me power can not go negative, but I am not sure my power plot is correct. Can someone please review the spreadsheet and chart to tell me...
  14. C

    Find and Sketch the Domain of a Function

    Homework Statement ƒ(x,y) = √y + √[25-x2-y2] Homework Equations Quadratic The Attempt at a Solution The expression for f(x,y) is defined as long as x2 + y2 ≥ 25 and y ≥ 0 because of the square roots we can't have negative numbers. {(x,y) ∈ ℝ2 : y ≥ 0 and x2 + y2 ≥ 25} I'm not sure how I'd...
  15. RJLiberator

    Integral Domain, r^2 = r proof that r = 0 or 1

    Homework Statement Let r be an element of an integral domain R such that r^2 = r. Show that either r = 0_R or 1_R Homework Equations integral domain means no zero divisors. The Attempt at a Solution This is fundamental as 0 and 1 solve r^2 = r and are the only solutions. However, I'm not...
  16. J

    Run-time error M6201: math -log: DOMAIN error

    Hi all, I am facing the problem while executing my fortran (77) program. please help me how to fix it. As I understood, the error means that the domain of log function has included zero values or negative values...But I could not understand...In my case... there are no zero or negative...
  17. N

    D'Alembert solution of wave equation on semi infinite domain

    Homework Statement Wave equation: ytt=yxx Initial conditions: Y(x,0) =f(x) = x (0 ≤ x < 1) 2.5(5-x) (1 ≤ x < 3) 0 (Otherwise) and yt(x,0) = 0 Boundary condition: y(0,t) =0 Semi infinite domain: 0 ≤ x < infinity Homework Equations d'Alembert solution...
  18. M

    MHB Finding the Domain of a Function

    How do you find the Domain of \sqrt{(x^2 + 4)/(x^2 - 4)} ?
  19. King_Silver

    Local max and min (including a domain)

    I have this function: f(x) = √3x + 2Cos(x) I have to find the local maxima and minima,where -π ∠ or equal to x ∠ or equal to 2π. 1: Differentiate the function given. f'(x) = 3/(2√x) -2Sin(x) 2: Find where f'(x) is undefined or = 0 to get critical points. 3: Find f''(x) [The second...
  20. DuckAmuck

    Domain Wall Questions: Exploring L=kρσ Interaction

    So I have learned that an interaction term in a Lagrangian like: L= kρσ can result in "domain wall" problems between the fields ρ and σ. I imagine this means that it can result in particles spontaneously changing mass, spin, or some other property, violating conservation laws. Is that why this...
  21. T

    Optimizing Across Noisy Domain

    Are there any established methods for optimizing across a 2D surface with noise? I am trying to find the maximum across a 2D surface, but the surface is extremely noisy. Ideally, I would numerically optimize a function without resorting to computing the entire surface, filtering the surface...
  22. davidbenari

    How does ifft(fft(x)) form the correct bijection with domain?

    I think my question is more appropriate here than in the computation section. My question is: (In the context of inverse fast-fourier transforms and fast-fourier transforms) Knowing ifft(fft(x)=x might be trivial as it is almost a definition; associating it with a domain ##t## is perfectly...
  23. gfd43tg

    Sketching Transfer function in time domain

    Homework Statement $$ y(s) = \frac {s}{(s+1)(2s+1)} u(s) $$ Where ##u(s)## is the step function ##\frac {1}{s}## Find the output at t=0 and t= infinity Homework EquationsThe Attempt at a Solution My question is kind of basic, so I know the final and initial value theorem $$ \lim_{s \to 0}...
  24. Y

    Integration in Frequency Domain

    How to integrate $$\int_{-0.5}^{0.5} {\bigg({\frac{1}{4-2e^{-j2{\pi}f}}}\bigg)}^2 df$$
  25. S

    MHB Given a range value, find the correspoding domain value

    Here is the problem: If -1 is a range value for the function f(x) = -6x + 11, find the domain value. thank you for your help
  26. C

    Finding solution of equation in complex domain?

    (1+a)n = (1-a)n I tried following: (1+a)n = (1-a)n [(1+a)/(1-a)]n=1 but what can i do next?
  27. yango_17

    Domain and range of a function of several variables

    Homework Statement Find the domain and range of the following function: f(x, y) = ln(x+y) Homework EquationsThe Attempt at a Solution I know that the natural log ln(x) is only defined when x>0, so does that mean that ln(x+y) is only defined when x+y>0? Also, would the range just be all positive...
  28. MathematicalPhysicist

    A path which its domain is a general compact set.

    How is a general path called instead of being a continuous function from an interval to some topological space, where we replace the domain from an interval to a compact set, is there a name for such a function? Perhaps I should add that the compact set is also convex.
  29. iwantcalculus

    Finding domain of function (need an explanation for 2 Qs)

    i need help with finding the domain for a function where there is a square root , here is the picture of such questions : http://imgur.com/YcqadOe please see the picture, there are two questions in it, 35 and 37 let's start with question 35, this is how i try to solve it : x^2 - 5x > 0 x...
  30. Aner

    How do I solve this multiple integral in the given domain?

    Homework Statement Hi, I have a problem with the following exercise. Let C={(x,y,z)∈ℝ3 : x2+y2+z2≤1, z≥√(3x2+8y2)} be a subset of ℝ3. Calculate ∫∫∫C z dxdydz.Homework Equations Spherical coordinates, given by x=ρsinΦcosθ, y=ρsinΦsinθ, z=ρcosΦ, and cylindrical coordinates which are x=ρcosα...
  31. K

    What is a frequency domain and s domain?

    What is a frequency domain and how can we understand the same in practical world? How is it related to complex plain sight domain?
  32. B

    MHB Finding Domain of f(x)=\frac{1}{x^{2}-x-6}

    I'm supposed to find the domain of this function, I know I'm supposed to set the denominator equal to 0 but I don't know what to do after that, please help! f(x)=\frac{1}{x^{2}-x-6} I can't figure out how to make this look like a real fraction but it's supposed to be 1 over x squared minus x...
  33. P

    Is the Domain of an Antiderivative Always a Subset?

    Isn't the domain of the derivative of a function a subset of the domain of the function itself? Does this mean that the domain of an integrand is always a subset of the corresponding indefinite integral?
  34. K

    MHB Is {0} Considered the Smallest Integral Domain?

    What is the smallest (most trivial) integral domain? {0,1} is an integral domain but is {0} an integral domain with unity = 0 and zero = 0? If {0} is not an integral domain then why not?
  35. M

    How do I calculate an area of joint uniform distribution with domain

    This technically isn't a coursework or homework problem: I have a uniform Joint density function for the lifetimes of two components, let's call them T1 and T2. They have a uniform joint density function, both are positive it follows, and the region is 0<t1<t2<L and L is some positive constant...
  36. Math Amateur

    MHB How Do GCDs Coincide in Principal Ideals According to Rotman's Proposition 3.41?

    I am reading Joseph J.Rotman's book, A First Course in Abstract Algebra. I am currently focused on Section 3. Polynomials I need help with the a statement of Rotman's concerning the definition of a gcd in a general domain ... the definition The relevant section of Rotman's text reads as...
  37. E

    Phase shift in frequency domain

    Hello, I'using Matlab to simulate phase shift in frequency domain (FD). I have got real and imaginary parts of the signal after FFT. I'd like to use phase shift in FD. This works: Y=fft(y); YY=Y.exp(-i*2*pi*nk/N*samples_delay); result=ifft(YY); But in my DSP I can't use the formula above and...
  38. Jaco Viljoen

    What is the Domain of l/g Without first calculating (l/g)(x)

    Homework Statement Write down Dl/g without first calculating (l/g)(x) Homework Equations g(x)=-(1/2)x-3 l(x)=√(2-x)-3 The Attempt at a Solution g(x)=-(1/2)x-3 Dg = {x∈ℝ} l(x)=√(2-x)-3 Dl = {x∈ℝ:x≤2} Dg/l = {x∈ℝ:x≤2}
  39. F

    Marginal stabilty in s domain

    I'm trying to get a better understanding of marginal stability and the s domain in general. According to my textbook, a system that is marginally stable has poles that are conjugates of each other on the jω axis, and their magnitude are the resonant frequency for which if a sinusoid of that...
  40. R

    How frequency domain topic should be taught in the academic course?

    This is a soft question but I think it's a real fact.The Frequency domain has made revolution in the field of Mathematics,Physics,Digital Signal and image Processing etc. Some of concepts which are very difficult to analyse in spatial or time domain can be very easily understood in the frequency...
  41. J

    How to measure displacement and Force simulatuously in Ansys Structural domain

    Hi i am performing a multiphysics simulation in which i am importing results of Electric-Thermal domain into Transient Structural domain in Ansys Workbench 14.5. As the simulation time is 5 hrs and given that i have to perform 20 case studies , so i want to know is their a way around in Ansys...
  42. CAH

    Domain and range of composite functions?

    hey! How do you work out the domain and range of fg(x), do you work out what range of g(x) will fit the domain of f(x)? I have no clue. Thanks
  43. T

    Domain and range of multivariable functions

    Homework Statement Specify the domain and range of f(x, y) = arccos(y − x2). Indicate whether the domain is (i) open or closed, and (ii) bounded or unbounded. Give a clear reason in each case.Homework EquationsThe Attempt at a Solution y-x2 >= -1 y >= x2 -1 y-x2 <= 1 y <= x2 +1 I sketched it...
  44. K

    MHB Showing a simple function is continuous on a restricted domain

    **Motivation:** I am studying for an exam over Chapters $1-3$ of *Real Analysis* by Royden and Fitzpatrick, 4th edition. I am stuck on understanding some of Proposition $11$, which I have reproduced below: **Proposition 11:** Let $f$ be a simple function defined on $E.$ Then for each...
  45. RJLiberator

    Domain and how it relates to a Level Curve

    Homework Statement Find the domain of the function f(x,y) = 1/sqrt(x^2-y). Sketch the level curves f=1, f=1/2, f=1/3. Homework EquationsThe Attempt at a Solution Domain is rather simple to find: x^2>y AND x^2-y cannot equal 0. Level curves are also simple to find. They are simply parabolas...
  46. Tsubaki

    Convert the domain of the Tan function to interval notation?

    Homework Statement Hey guys. So basically I'm doing some Calc I homework and I'm working on the domain of this function: g(x) = √tan(2x+π) Homework Equations Now to determine the domain, I know that the function under the root cannot be negative. The Attempt at a Solution So after...
  47. Mahathepp

    What is the domain of ascsin(x+y)

    Hey Try to figure out the way to find domain of the function ascsin (x+y) without using the formula can someone give the clue how I should start ? Always confuse about inverse of trigonometry function. Thanks in advance.
  48. F

    MHB How to find domain of function in implicit form

    What is the domain of y^2-2y=x^2-x-1? I don't know how to find it for implicit functions.
  49. S

    Selection of domain and codomain for wave function

    A wave function is a function in a Hilbert space of functions. When representing a physical sytem, what are the conventions for defining the domain and codomain of the wave function? For example, is the domain always the scalar variable representing time? Is the codomain a set of finite...
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