What is Vector analysis: Definition and 123 Discussions

Vector Analysis is a textbook by Edwin Bidwell Wilson, first published in 1901 and based on the lectures that Josiah Willard Gibbs had delivered on the subject at Yale University. The book did much to standardize the notation and vocabulary of three-dimensional linear algebra and vector calculus, as used by physicists and mathematicians. It was reprinted by Yale in 1913, 1916, 1922, 1925, 1929, 1931, and 1943. The work is now in the public domain. It was reprinted by Dover Publications in 1960.

View More On Wikipedia.org
Recent contents Top users
  1. Shackleford

    What to brush up on before taking Vector Analysis

    I forgot to add this in my other thread. I'm taking Diff. Eq. and Vector Analysis this fall. I've already started brushing up on DE-related stuff. What should I review for Vector Analysis? Thanks.
  2. Shackleford

    Diff. EQ. and Vector Analysis at the same time?

    Thinking about doing this. I've already taken Linear Algebra and Cal. III. Diff. EQ. and Vector Analysis will probably be the only two courses I take in the fall. I MIGHT take the stupid only Writing Intensive core I need, but I can do whatever class that is at almost any time. So, what do...
  3. J

    Vector analysis question on acceleration

    Homework Statement A moving particle reaches its max. speed at the instant t = 3. (Before and after 3, its speed is less.) It follows that the particle's acceleration is 0 at the instant t = 3... Show that this is FALSE Homework Equations v = dR/dt a = d^2 R / dt^2 The Attempt at a Solution...
  4. C

    Calculus 3 vector analysis question (Newton's 2nd problem)

    This problem was discussed in my calculus 3 class, and there is one step that I don't understand. Homework Statement An object of mass m travels along the parabola y = x^{2} with a constant speed of 10 units/sec. What is the force on the object due to its acceleration at (0,0) (write the...
  5. G

    Vector analysis: \nabla applied on integral?

    Is it possible to simply or rewrite \nabla_{\vec{r}}\iiint\frac{f(\vec{r}\,')\mathrm{d}\vec{r}\,'}{4\pi|\vec{r}-\vec{r}\,'|} \nabla_{\vec{r}}\times\iiint\frac{\vec{A}(\vec{r}\,')\mathrm{d}\vec{r}\,'}{4\pi|\vec{r}-\vec{r}\,'|} ? What's a good reference (internet, book) to learn this...
  6. M

    Vector Analysis: Seeking Guidance on Identity and Calculation

    hi there! I´m doing vector analysis the last two weeks and I feel unsure about this identity. Can anyone of you say if I´m on the right way, and if not where my mistakes lie :) A_i(\vec r)=\sum_{j=1}^3R_{ij}x_j, R constant 3x3 matrix I have to calculate rot\vec A, rotrot\vec A...
  7. B

    Vector Analysis ifferential Calculus

    Vector Analysis:Differential Calculus Homework Statement The height of a certain hill(in feet) is given by h(x,y)=10(2xy-3x^2-4y^2-18x+28y+12) where y is the distance (in miles) north, x the distance east of South Hadley a)Where is the top of the hill located b) How high is the hill...
  8. J

    Helpful vector analysis interactive visuals

    There is some very helpful Vector Analysis (and Multivariable Calculus as a whole) supplementary material at http://www.math.umn.edu/~nykamp/m2374/readings/#vectorcalc". These informal "readings" contain some very instructive interactive 3D graphics animations utilizing "LiveGraphics3D" Java...
  9. Angelos K

    Vector analysis for a variational problem

    I'm reading a proof that is via variation. \vec {\delta A} stands for a variation of the vectorpotential \vec{A} . If I understand the argument correctly [many steps are presented as one] it means: (\nabla \times \vec{A})* (\nabla \times \vec{\delta A}) = (\nabla \times \nabla \times \vec...
  10. C

    Electron vector analysis question

    3 electrons q1, q2, q3 setup in a right angled triangle q1 |\ | \ q3-q2 charges are q1 = +2.5 X 10^-17C q2 = +3.0 X 10^-17C q3 = +3.5 X 10^-17C distances between the charges q1-q3 = .03 m q1-q2 = .05 m setup FBD \ \ 2F1 \ / / 3F1 q1 2F1 = k*q1*q2 / .05^2 = 2.7...
  11. C

    Vector analysis homework question

    3 electrons q1, q2, q3 setup in a right angled triangle q1 |\ | \ q3-q2 charges are q1 = +2.5 X 10^-17C q2 = +3.0 X 10^-17C q3 = +3.5 X 10^-17C distances between the charges q1-q3 = .03 m q1-q2 = .05 m setup FBD \ \ 2F1 \ / / 3F1 q1 2F1 = k*q1*q2 /...
  12. E

    Vector Analysis Identity derivation

    Homework Statement derive the identity: del((F)^2) = 2 F . del(F) + 2Fx (del x F) the dot is a dot product Homework Equations The Attempt at a Solution first i set F = <a,b,c>, making F^2 = a^2 + b^2 + c^2 I took the partial derivatives with respect to x, y, and z (to get the necessary parts...
  13. E

    Vector Analysis for Minimum Temperature on a Curve: Solve with Grad(p) Method

    Homework Statement By vector methods, find the point on the curve x = t, y = t^2, z = 2 at which the temperature p(x,y,z) = x^2 - 6x + y^2 takes its minimum value Homework Equations The Attempt at a Solution As far as I got was finding grad(p). From there I'm not sure where to go...
  14. E

    Expressing an Arbitrary Vector in Terms of Noncoplanar Vectors

    Homework Statement Show that an arbitrary vector V can be expressed in terms of any three noncoplanar vectors, A, B, C, according to: V = [V,B,C]A/[A,B,C] + [V,C,A]B/[A,B,C] + [V,A,B]C/[A,B,C] Homework Equations A Hint is given: We know that V can be expressed as aA + bB +cC; to...
  15. O

    Exploring Vector Analysis with Del Operator

    hello every one, i am working on vector analysis and i have come across this definition of del operator.i don't understand where does it come from but it works great to determine rotation curl gradient or other stuff of a vector field.can anyone tell me how we are getting this magical operator...
  16. I

    Vector Analysis: Bridging Math and Physics with Rigor and Visuals

    something for a mathematician that likes physics or a physicist that likes math. rigorous but with pictures and examples and the such?
  17. R

    Master Vector Analysis with Expert Help: Proven Solutions to Common Problems

    Need help on vector analysis :( Guys, I need ur help please... Can u help me to answer these problems? I'm very confused... 1. Show that the vector Ai + Bj + Ck is normal to the plane which equation is Ax + By + Cz = D, where A, B, C, D are constants 2. n = 0.5i + 0.5j + 0.7071k is...
  18. N

    How to Use Vector Analysis Identity to Solve a Closed Loop Integral?

    Homework Statement we are to show a=(1/2) closed loop integral over [r x dl] Homework Equations The Attempt at a Solution I suppose this can be done formally from the alternative form of Stokes' theorem that can be obtained by replacing the vector field in curl theorem by VxC...
  19. C

    Never *really* learned vector analysis, should I self learn?

    Hello, I am a physics major and just transferred to UC Davis from a community college. My multivariable calculus course did not for some reason include vector analysis even though it tranferred as such. In other words, the requirement is met, but I don't have the knowledge. I did audit a...
  20. Z

    Vector Analysis using Graphical and Analytical

    1.a A hot air balloon drifts 12km in a direction 70 degrees South of East. An abrupt charge in air movement then comes the balloon 8.0km in a direction 40 degrees South of West. Estimate the record displacement from the starting position after the two drifts. (magnitude & displacement)...
  21. Astronuc

    Improper use of [nabla operator] in vector analysis

    I just happened across this paper which caught my attention. http://hdl.handle.net/2027.42/7869 Perhaps this has been discussed here before, but it's new to me and I have learned from several of these books. What is the correct use or intepration of \nabla and it's use in the 'div'...
  22. B

    Vector analysis notation question

    what exactly does (\mathbf{A} \cdot \nabla) \mathbf{B} mean? is this the same as the divergence of A multiplied by B? if this was the case, why wouldn't it be written in a clearer notation? edit: I'm having trouble with the latex. further edit: note to self--use...
  23. G

    Learn How to Derive Gauss and Stokes Theorems for Vector Analysis"

    Hi All, I got a couple questions that I need some help getting started on. Any tips would be appreciated. 1. Derive Gauss and Stokes theorems for the field B = Ap(r), where A is a constant vecotr and p (rho)is a scalar field. r is the unit vector. 2. Compute the flux of the field...
Back
Top