Vector calculus Definition and 422 Threads

  1. E

    Solving Parametric Equations for Tangent Line to Space Curve

    Hello everyone, I found a random question regarding finding the parametric equations for a tangent line to a space curve and I'm striving to solve it, but no results. I consulted the book but there isn't anything similar. Find the parametric equations for the tangent line to the space curve...
  2. D

    What are one-forms and why are they sometimes called covectors?

    I've recentlty been studying vector calculus at uni and now that we are almost up to the general Stokes's theorem and its many froms I am just beginning to understand it and actually enjoy it. One thing that is really annoying me though is that I have heard one-forms being referred to as...
  3. R

    Help with Vector Calculus Derivative

    Hey... i was hopeing somebody can help me with a homework question... its about vector calc... taking the deriviative. d/dx[r(t) dot r(t)] = r'(t) dot r(t) + r(t) dot r'(t) = 2r'(t) dot r(t) I know it sounds sillly, but i was just wondering how on Earth they got 2r'(t) dot r(t) ?
  4. E

    Solving Vector Calculus Problems in r1(t) and r2(t)

    Vector Calculus Greetings everyone, I have a problem: "Consider the curves r1(t)=(t, 1-t, 16+t^2) and r2(t)=(8-s,s-7, s^2) a) At what point do they meet? b) Find their angle of intersection The first part is easy, but I'm encountering some problems with b). To find the angle we need...
  5. L

    Proving Diagonal Trisection in a Parallelogram using Vector Calculus

    the problem goes: ABCD is a parallelogram in which points P and Q are the midpoints of sides BC and CD, respectively. Use vector calculus to prove that AP and AQ trisect the diagonal BD at the points E and F. ...A _________B .../...F.../ .../...E.../P D/________/C ...Q (Imagine...
  6. L

    Discovering Parallel, Intersecting, and Skew Lines: A Vector Calculus Problem

    Ok here is the problem: Given two lines in space, either they are parallel, or they intersect or they are skew. Determine whether the lines taken two at a time, are parallel, intersect or are skew. If they intersect find the point of intersection. line 1: x=1+2t, y=-1-t, z=3t...
  7. G

    How Do You Derive the Cartesian Equation from a Vector Function?

    i having so much trouble with this vector calculus question, someone please help. At time t, a moving particle has position r(t)=((e^t) + (e^-t))/2 i + ((e^t) - (e^-t))/2 j. a) find the cartesian equation of the path I know all you have to do is let the i component to equal x(t) and...
  8. N

    Why Vector Calculus would be a perquisite or a co-requisite?

    Could anyone tell me why Vector Calculus would be a prequisite or a co-requisite? Specifically, what topics are required to know vector calculus in PDE's? I suspected a course in ODE's would be enough. Thanks
  9. N

    Understanding Curvilinear Coordinates and Vector Calculations in Stokes' Theorem

    A vector field is defined by \vec{A}(\vec{r})} = \rho^2 \hat{\phi} + \rho \sin \phi \hat{z} Verify Stokes' theorem by explicit calcluation where S is the circle of radius a in the z = 0 plane. You may like to employ the ideas that \vec{dS} = \rho d\phi dz \hat{\rho} + dz d\rho \hat{\phi} +...
  10. B

    Ideal gases and Vector calculus

    In my physics book, the 4 properties of an ideal gase are 1. nonviscous 2. steady flow (laminar) 3. incompressible 4. irrotational My question is the properties of being irrotional the same as the vector functions that have a Curl=O iff irrotational My physics book states the...
  11. A

    Understanding Divergence: Can You Find the Divergence of a Scalar Function?

    I'm doing an assignment where the lecturer has said scalar function g(x,y,z) = x^3 + y + z^2 and vector field F = (2xz,sin y,e^y) and asked find a) grad g which is fairly easy, but then b) div g and my understanding was that you can only find the divergence of a vector...
  12. N

    Need Good book on Vector Calculus

    Hi All, I need some suggestion on a good book for vector calculus/advanced vector calculus. current book I am reading just give equations like del x ( A x B ) = A del.B - Bdel.A + (B.del)A - (A.del)B A x ( B x C ) = B(del.A) - C(A.B) del x (f A) = f del x A + del f x A etc...
  13. H

    How Do You Solve a Vector Calculus Integral Over a Sphere?

    Anyone take a look at this vector calculus question for me: ===== Q. If n is the uni normal to the surface S, evaluate Double Integral r.n dS over the surface of a sphere of radius 'a' centred at the origin. ===== So I did: r = (x,y,z) Sphere: x^2 + y^2 + z^2 = a^2 let f = x^2 +...
  14. H

    How Do I Verify Stokes' Theorem for a Hemispherical Surface?

    Hi, I have this vector calculus question to do, and I can't seem to get it right! Could someone take a look for me? ===== Q. The vector A(r) = (y,-x,z). Verify Stokes' Theorem for the hemispherical surface |r|=1, z>=0. A. I considered, the line integral about the circle in the xy plane...
  15. F

    Need help with some vector calculus problems

    f = 2xy in the x dir, (x^2 - z^2) in the y dir, -3xz^2 in the z dir. particle travles from (0,0,0) to (2,1,3) im supposed to find the line integral from (0,0,0) to (2,1,3). if i make z = 3/2 x and y = 1/2 x and substitute those into the integral of F dot dl i end up with an answer of...
  16. F

    Calculating the Line Integral of a Vector Field Using Vector Calculus

    f = 2xy in the x dir, (x^2 - z^2) in the y dir, -3xz^2 in the z dir. particle travles from (0,0,0) to (2,1,3) along the segments (0,0,0) ->(0,1,0)->(2,1,0)->(2,1,3) the integral is F dot product with dl. i can't figure this out. do i dot product each part individually and evaluate? i...
  17. J

    Vector Calculus: Solve Chain Weight Problem - 25 N, 37°

    I have a problem that I don't even know how to start. Can anyone assist me with the following problem? The tension T at the end of each chain has magnitude 25 N and makes an angle of 37 degrees with the horizontal. What is the weight of the chain? Thanks in advance.
  18. G

    Unifying concepts in vector calculus

    I'm a week or two away fromt the end of my vector calculus class and we are covering topics like surface integration, green's theorem and such. The problem I'm having so far is that everything just seems so disjointed and ad hoc, with all these theorems I feel I have to memorize instead of...
  19. G

    Therefore \oint_{S}\vec{r}\cdot\vec{n}dS=3V

    Hi All, I've been working through a series of vector calculus problems and I need some help to get started with this one. Anyone care to help? The problem is: Evaluate \oint_{s} r.n.dS where S is a closed surface. Cheers
  20. V

    Need Help Proving Vector Calculus Formula? Look No Further!

    Vector Calculus Proof Help Please :) Heya Ppl i have a problem i am trying to solve. Prove that (Delta) . ( (fi)F) = (fi)(Delta) . F + F . (Delta)(fi) were these contain GRAD DIV in my opinion but i seem to not be able to get the answer. F = Vector F where F = F1i + F2j + F3k is a...
  21. G

    What Are Good Online Resources for Learning Vector Calculus?

    Hi All, I've started to study vector calculus and am finding it a bit daunting. The notes the lecturer has supplied aren't too helpful. Does anyone know of some decent resources on the web that could help me out? Many Thanks, Pete
  22. D

    Understanding Vector Calculus: A Brief Summary

    Can anyone give me a very brief summary of what vector calculus means? I know this sounds like a "specify what you mean" type question, but I hope it isn't. Let me explain further. I know all the equations, how to find line integrals, what Green's theorem is, etc. but I don't exactly know what...
Back
Top