What is parts: Definition and 838 Discussions

In science and engineering, the parts-per notation is a set of pseudo-units to describe small values of miscellaneous dimensionless quantities, e.g. mole fraction or mass fraction. Since these fractions are quantity-per-quantity measures, they are pure numbers with no associated units of measurement. Commonly used are parts-per-million (ppm, 10−6), parts-per-billion (ppb, 10−9), parts-per-trillion (ppt, 10−12) and parts-per-quadrillion (ppq, 10−15). This notation is not part of the International System of Units (SI) system and its meaning is ambiguous.

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  1. P

    2nd order PDE using integration by parts

    Homework Statement Find the general solution of the equation (\zeta - \eta)^2 \frac{\partial^2 u(\zeta,\eta)}{\partial\zeta \, \partial\eta}=0, where ##\zeta## and ##\eta## are independent variables. Homework Equations The Attempt at a Solution I set ##X = \partial u/\partial\eta## so that...
  2. S

    Audio/Video DIYaudio, Parts Express, Madisound, any audiophiles out there?

    What goes through an Engineer's mind upon designing a loudspeaker? Surely there must be some general guidelines, no? Perhaps. Although this is most likely dependent upon the circumstances (cost, enclosure, available power, etc). If these guidelines do exist, what are they. If you could order...
  3. M

    Gaussian integral using integration by parts

    Homework Statement Show in detail that: \sigma_{x}^{2} = \int_{-\infty}^{\infty} (x -\bar{x})^{2} \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} = \sigma^{2} where, G_{X,\sigma}(x) = \frac{1}{\sigma \sqrt{2 \pi}}e^{-\frac{(x-X)^{2}}{2\sigma^{2}}} Homework Equations \int u...
  4. MarkFL

    MHB Find x Coordinate of Point A for Maths Integration Area Problem

    Here is the question: I have posted a link there to this topic so the OP can see my work.
  5. F

    MHB Indefinite integral with two parts

    I'm trying to integrate \int e^{4\ln{x}}x^2 dx I can't see using u-substition, x^2 isn't the derivative of e^{4\ln{x}} nor vice-versa. I tried integrating by parts and that didn't work. I used u=e^{4\ln{x}} and dv=x^2 dx I know I can't rewrite e^{4\ln{x}} as e^4e^\ln{x}
  6. F

    MHB Integration by parts, why is this allowed?

    I'm following this example where it is asked to integrate \int \ln{x} dx using integration by parts. I don't understand how it's legal to set v=x since the only x in the equation is the argument of ln and that's already accounted for by u.
  7. Lebombo

    Algebraic Manipulation within Integration by Parts problem

    Homework Statement I'm doing an integration by parts problem. After setting up [∫udv = uv - ∫vdu], I come across this situation. How is this algebraic manipulation accomplished? From: \int\frac{x^{3}}{1+x^{2}}dx To: \int x - \frac{x}{1+x^{2}}dx
  8. M

    Find beats formula using imaginary parts

    Homework Statement Using the imaginary parts When using complex representation, it is customary to use the real parts. Instead use the imaginary part of e^{j\theta} to calculate an expression for the sum: \sin(\omega t) + \sin((\omega + \Delta \omega)t) Remember, it should come out to...
  9. DreamWeaver

    MHB About fractional parts and floor functions....

    Hi all! :D I wasn't really sure where to post this, but Analysis seemed a fair bet. While searching on-line recently, I came across the following expressions for the Fractional Part \{x\} and Floor Function \lfloor x \rfloor respectively: \{x\}=\frac{i\log\left(-e^{-2\pi i...
  10. F

    MHB Can a bipartite graph have two non-connected parts?

    For example vertice A connected to vertice B and vertice C connected to vertice D? Would this be considered two different graphs? Here is a graph, would it be bipartite?
  11. C

    Skipping parts of Landau\Lifshitz Mechanics?

    I've recently picked up Machanics by Landau and Lifshitz to brush up on Lagrangian\Hamiltonian mechanics, but this book contains a huge chunk of sections on molecular vibrations\scattering theory\collisions etc etc. My question would be: Will skipping these sections leave me at a disadvantage...
  12. S

    MHB Finding the real and imaginary parts of a function

    If f:C-->C is holomorphic and , find the real and imaginary parts ug and vg of g in terms of the real and imaginary parts uf and vf of f.
  13. C

    Do functions with complex parts differentiate/integrate like usual?

    To get straight to the point: If I have a function f( x)= 3x2+2ix Would f'(x)= 6x+2i? More generally, does complex differentiation follow the same rules as normal differentiation? (Ie; power rule, quotient rule, product rule, chain rule etc.) Thanks!
  14. V

    Integration by parts problem involving vector functions

    Hi, I am trying to chew through the proof of reciprocity in MRI. At some point I come across to the following expression: \Phi_{M}=\oint\vec{dl}\cdot\left[\frac{\mu_{0}}{4\pi}\int{d^{3}r'}\frac{\vec{\nabla'}\times\vec{M}(\vec{r'})}{\left|\vec{r}-\vec{r'}\right|}\right] Now it says that...
  15. H

    Difficult integration by parts

    Homework Statement Calculate the following integral with partial integration: \int\frac{1 - x}{(x^2 + 2x + 3)^2}dx The Attempt at a Solution I guess you need to write the integral in easier chunks but I still fail every time.
  16. siddharth23

    Tension in different parts of a rod pivoted at1 end & rotating in HP

    I read that if a bar is pivoted at one end and is rotating in a horizontal plane, the tension at a specific point decreases as you go away from the pivoted end. Only inference I could draw from this is that the centrifugal force, which is the cause of tension, increses as you go towards the...
  17. Y

    MHB Integration by Parts: Solving \(\int ln(3x+1)dx\) and \(\int (ln(x))^{2}dx\)

    Hello I am working on this integral. \[\int ln(3x+1)dx\] I choose u=ln(3x+1) and v'=1. It got me to: \[x\cdot ln(3x+1)-\int \frac{3x}{3x+1}dx\] What should I do from here ? Some substitution ? The x up there bothers me...no easier way ? Thank! I also need to solve: \[\int (ln(x))^{2}dx\]...
  18. Albert1

    MHB Divide ABCDE into two parts with equal area

    ABCDE is a pentagon,please construct a line (passing through point A),and divide ABCDE into two parts with equal area
  19. paulmdrdo1

    MHB How Can I Solve These Integration Problems Using Integration by Parts?

    how would i go about solving these problems? \begin{align*}\displaystyle \int\frac{xe^x}{(1+x)^2}dx\end{align*} \begin{align*}\int\frac{(1-x)dx}{\sqrt{1-x^2}}\end{align*} this is my solution to prob 2...
  20. paulmdrdo1

    MHB Solving Integration by Parts: x^3e^x^2

    any idea how to solve this? \begin{align*}\displaystyle \int x^3e^{x^{2}}\,dx\end{align*}
  21. J

    Resolve a force into three parts (3D)

    Hey! I have been trying to solve this problem without success. Any help will be appreciated Homework Statement Resolve the 170 N force into three parts: one of which is parallel to OQ, another parallel to OP, and the third parallel to the y axis. (See the graph) Are these the components of F...
  22. Albert1

    MHB Dividing a Quadrilateral into Equal Parts

    ABCD is a quadrilateral,and point P is a point on AD ,and between points A and D please construct a line (passing through point P),and divide ABCD into two parts with equal area
  23. A

    Electronics parts complete assortment

    Well I have no where else to look. I have tried various websites stores etc. I have looked into various sources sites extensively. And so far everything is just a source of aggravation. I can find all of the various parts but its over priced and takes to much searching to find parts. I just...
  24. C

    Integrating xe[itex]^{x}[/itex] without integration by parts

    Homework Statement Use the method of separation of variables or an integrating factor to find a particular solution of the differential equation that satisfies the given initial condition. y'=x-y+2 ; y(0)=4 2. The attempt at a solution I've used an integrating factor of e^{x} to...
  25. T

    Question on integration by parts

    I want to start out by saying that this is not a homework problem, this is something I'm trying to figure out for thesis work. If that should go in the homework problem section, I will gladly post there. A certain mass model I'm working with (Bissant & Gerhard) has a particularly gross form...
  26. J

    Integration by Parts Homework Help

    Homework Statement Hi, I attached the question.Just integral trouble. Homework Equations The Attempt at a Solution
  27. F

    Integration by Parts using Ln(x)

    Homework Statement \int_4^5 \frac{dx}{(3x)(ln(x))(ln^3(ln(x)))} \, Homework Equations I'll probably need to use u-substitution as well as integration by parts for this problem. The Attempt at a Solution \int_4^5 \frac{dx}{(3x)(ln(x))(ln^3(ln(x)))} \, 1. Factor out 1/3 for...
  28. L

    Parameters of helix approximated by parts of torus

    Hello, I am approximating a helix by parts of torus, to build an optical fiber wrapped around a cylinder simulation. Due to the software limitations, there is no easier way. So I take a part of the torus, rotate it so the one end points slightly up, connect similar part of the torus to the...
  29. M

    Custom RC Plane Parts Manufacturer?

    Hello. I am a 3rd year Aerospace Engineering major and I am set out to build my own RC plane from the ground up. My biggest concern now is to find a manufacturer that will custom built the plane parts from a CAD model. Does anyone know of companies that are willing to do that? I've tried...
  30. Fernando Revilla

    MHB Integration by parts curious question (chem's question at Yahoo Answers)

    Here is the question: Here is a link to the question: Integration by parts question? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  31. A

    Integration by Parts with Complex Exponentials

    I'm looking at this problem here. (Exam practice, move to homework if you want...) First part is easy, but it's the second part that I can't quite figure out. I'm trying to get from ∫xe2x cos(2x)dx to this answer: ¼e2x(x cos(2x) + x sin(2x) - ½sin(2x))+C
  32. T

    Problem with the expansion of integration by parts

    I've come across this funny problem while messing around with integration by parts. Probably made a mistake somewhere. In the integration of parts expression, it's possible to expand it further. Plugging the second expression into the first, we get I don't think...
  33. Femme_physics

    Machine parts, conic clutch two teachers, two different results

    Machine parts, conic clutch...two teachers, two different results! :( So a friend of mine who studies for the same test scanned me his teacher's solution to a problem they solved in class. We solved the same problem with a different teacher. I could really use your help to figure out who out of...
  34. trollcast

    Integration By Parts: Solving Find \int (2x^4\ln3x)\ dx

    Homework Statement Find \int (2x^4\ln3x)\ dx Homework Equations The Attempt at a Solution I let u = ln3x and dv/dx = x4 and I've managed to solve it and get an answer of: x^5(\frac{2}{5}\ln(3x) - \frac{1}{45} + c) Which is really close to the answer from wolfram alpha but the...
  35. A

    Project, parts id and physics explain

    im going to need help filling holes and someone to explain to me what I am trying to say/do ill start with what i want to do, and hopfully someone will be able to tell me what i need part-wise (i have some idea but not much) 1) I am looking at needing some sort of spring assembly in order...
  36. F

    Integrating Gaussian integral by parts

    Homework Statement We define I_{n} = \int_{-∞}^{∞}x^{2n}e^{-bx^{2}}dx, where n is a positive integer. Use integration by parts to derive:I_{n}=\frac{2n-1}{2b}I_{n-1} Homework Equations Parts formula. The Attempt at a Solution So I'm just stuck here, I'm baffled and confused. Firstly if I...
  37. A

    Project help, parts ID and layouts

    trying to make a device but don't know what i need, only what i need it to do... my aim is to use a lever (ratcheting) to store energy in a coil, then route that energy to a pair of vertical cylinders making them spin counter and clockwise or left spins left and right right any help...
  38. V

    Integral of 1/sqrt(x)exp(-ix) dx using integration by parts

    Hi, Homework Statement I have already evaluated the integral 1/sqrt(x)exp(-ix) using The Residue Theorem and now I was looking for another method. So I thought of applying integration by parts and I got this attached formula. Now I am wondering how to evaluate this series. My first...
  39. cocopops12

    Do all complex functions have orthogonal real and imaginary parts?

    z = h(x) + ig(x) True or False: By the definition of the complex plane, h(x) and ig(x) will always be orthogonal. If this was true, wouldn't that mean that we can find a 'very general' Fourier series representation of any function f(x) as an infinite series of An*h(x) + infinite series of...
  40. B

    Telescoping Series involving 3 parts.

    Homework Statement Determine whether the series is convergent or divergent by expressing s sub n as a telescoping series. If convergent find the sum. \sum_{n=2}^\infty \frac{1}{n^3-1} The Attempt at a Solution First thing I did was partial fraction decomposition. Resulting in: Ʃ (n=2 to ∞)...
  41. 7

    Some weird integration by parts to derive momentum operator

    In a Griffith's book (page 15-16) an author derives a momentum operator. In the derivation he states that he used a integration by parts two times. He starts with this equation which i do understand how to get to. $$ \begin{split} \frac{d \langle x \rangle}{dt} = -\frac{i\hbar}{2m}...
  42. A

    Integrate by Parts: arctan(√x)dx Explained

    Homework Statement ∫arctan(√x)dx. Using the substitution √x=t: ∫arctan(√x)dx = ∫arctan(t)dt2 This is what I've got written in a solution manual. I don't see why the dt would be squared. Could anyone care explaining me? thanks
  43. L

    Integration by parts involving square root

    Homework Statement |x3sqrt(4-x2)dx Homework Equations uv - | vdu The Attempt at a Solution u = x2 v = -1/3(4-x2)3/2 du = -2xdx dv = x(4-x2)1/2 uv - | vdu x2(1/3)(4-x2)3/2 - | 1/3(4-x2)3/2(2xdx) x2(1/3)(4-x2)3/2 +(1/3)|(4-x2)3/2(2xdx) u = 4 - x2 du = -2xdx...
  44. W

    Integrate by Parts: x^5 * sqrt(x^3 + 5)

    Homework Statement Integrate by parts.Homework Equations (integral) (x^5 * sqrt(x^3 + 5) dx)The Attempt at a Solution i've tried using simple substitution, not by parts. integral (x^3 * x^2 * sqrt(x^3 + 5) dx u=x^3 + 5 du=3x^2 1/3(integral) (u-5) * u^1/2 du 1/3(u^3/2 - 5u^1/2)...
  45. W

    The Integration by Parts Method: How to Integrate x * 5^x

    Homework Statement integrate by parts. Integral: x * 5^xHomework Equations The Attempt at a Solution i got to (1/ln5) * 5^x ;; and I'm not sure how to integrate further.
  46. N

    Integration by parts of derivative of expectation value problem

    Homework Statement I don't know how the writer of the book took integral of the first statement and got the second statement? Can anybody clarify on this? Homework Equations Given in the photoThe Attempt at a Solution When I took the integral I just ended up with the exact same statement but...
  47. T

    Flight, without moving parts

    As a tenth grader with electronics on the mind, ionocraft is probably one of the most interesting topics I have run across(besides the Casimir effect; that, I believe, is quantum physics). But, what I am truly interested in is whether or not it is possible, with the use of technologies such as...
  48. B

    Medical Auto immune only attacks parts of the body?

    This has puzzled me for a while now: A friend of mine has been told he has an auto-immune disease that has attacked his right eye - something called ocre or maybe just ocr ? If my understanding was correct that an auto imune disease can attack certain types of tissues why wouldn't he...
  49. MarkFL

    MHB Integration by Parts: Calculus Integral Help?

    Here is the question: Here is a link to the question: Calculus integral help? - Yahoo! Answers I have posted a link there to this topic so the OP can find my response.
  50. Femme_physics

    Machine Parts - Screws fastening a board calculation

    Homework Statement Board AB is fixed to the wall through 6 screws as described in the drawing. Beams CD and DE are connected to the board by joints at points C, D, E. At point D acts a vertical force of 7500 [N]. Calculate: A) The reaction forces at joints C, E. B) Describe the external...
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