Vector analysis Definition and 126 Threads

Could you suggest me any textbook on Co-ordinate Geometry and Vector Analysis?

Homework Statement I have these vectorfields defined on the specified set. All of them are conservative on their set. Also i have three unit circles C1, C2 and C3 centered respectively on (0,0) , (-2,0) and (-1,0) I need to find the line integrals over all of them on H (beregn = calculate...

Hi pf, Having some trouble with basis vectors for expanding a given vector in 3-D space. Any given vector in 3-D space can be given by a sum of component vectors in the form: V = e1V1 + e2V2 + e3V3 (where e1, e2 and e3 are the same as i, j and k unit vectors). Equation 1. I am happy with...

Homework Statement F[/B]=(y + yz- z, 5x+zx, 2y+xy ) use stokes on the line C that intersects: x^2 + y^2 + z^2 = 1 and y=1-x C is in the direction so that the positive direction in the point (1,0,0) is given by a vector (0,0,1) 2. The attempt at a solution I was thinking that I could decide...

Homework Statement The dimension h is to be determined to that a worker can comfortably slides boxes weighing up to 106 lb up and down a frictionless incline. If the worker can apply a 50 lb horizontal force to the box, what is the largest value h should have? Hint given: Before taking any...

Senior in Fall. Is a full course on vector analysis necessary: Stockes theorem, Green Theorem, differential forms, etc. I feel like Griffith's Electrodynamics gives a sufficient overview of Vector analysis in Chapter 1 covering all you need. I've only taken the required Calc 1 - 3 sequence +...

Homework Statement [/B] The block shown in Fig. P-223 is acted upon by its weight W = 200lb, a horizontal force Q = 600lb and the pressure P exerted by the inclined plane. The resultant R of these forces is up and parallel to the incline thereby sliding the block up it. Determine P and R. Hint...

A vector field is specified as F= $2(x+y)\sin(\pi z)a_x-(x^2+y)a_y+\left(\frac{10}{(x^2+y^2)}\right)a_z$. Specify the locus of all points at which: a. $F_x=0$; b. $F_y=0$; c. |F|=1 Please kindly help me to get started with this problem! thanks!

Given the vector field $F=0.4(y-2x)a_{x}-(\frac{200}{x^2+y^2+z^2})a_{z}$ : 1. evaluate $|F|$ at $P(-4,3,5)$; 2. Find unit vector specifying the direction of $|F|$ at P. 3. Describe the locus of all points for which $ F_{x}=1; |F_{x}|=2$ I managed to solve the 1 and 2 By substituting the...

Homework Statement Homework Equations Va = Vb + Va/b Va = Vb + (wab x ra/b) The Attempt at a Solution OK so here is part of my solution: My velocity for B is correct according to the book. But I'm confused about D. The only problem here is that the velocity of D only has an i...

Homework Statement problem form div curl grad and all that by h.m.schey An object moves in xy-plane in such a way that its position vector r is given as a some function of "t" by r= i acosωt+j bsinωt show the object moves on the elliptical path Homework Equations (x/a)^2+(y/b)^2=1The Attempt...

Homework Statement This picture is taken from Div, curl, grad and all that by schey, while finding the unit normal vector of the surface S (defined as w=f(x,y)) at a point P, to find the normal vector he considered a two tangent non-collinear vectors (u and v) at a point P, to find u...

I'm quite interested in the history behind vector analysis especially Curl and Divergence and gradient operators etc. When James Maxwell derived Maxwell's equations of electromagnetism where these sorts of operations well known and commonly used, or are they modern fabrications. Did Maxwell...

So I'm transferring from community college to university this fall and I will have all of my basic math completed (Calculus I-III, Linear Algebra), and I was wondering if Vector Analysis would be a good first 300 level class. I'm not sure I'm ready for 300 level math but I have done well in...

Homework Statement Assume F⃗ is a vector field and ∇× F⃗ = 0 What can one conclude about F? A. F=0 B. F=∇ƒ C. F=∇*g D. F=∇×g E. Something else Homework Equations None The Attempt at a Solution I haven't really made a proper attemt at solving the problem since I'm...

Homework Statement http://imgur.com/wNusHOw Homework Equations I have the solutions and how they did it. THey took the deriv for the velocity vector, and then using t=0 and t=14, they found e=3.5 and f=-0.125 The Attempt at a Solution I understand the math, but I don't understand...

IItsHi.I have a problem that i am trying to solve.The complete question is shown in the image: In this question i solved the (a) and (b) part.But i did'nt understand the (c) part.Can you please explain?Thank you.(Note:The answers is given beneath the question)

Homework Statement Let L: R2 → Rn be a linear mapping. We call L a similarity if L stretches all vectors by the same factor. That is, for some δL, independent of v, |L(v)| = δL * |v| To check that |L(v)| = δL * |v| for all vectors v in principle involves an infinite number of...

$\newcommand{\unit}[1]{\hat{\mathbf{#1}}}$ Let $\varphi = F_1h_1$ and $\mathbf{v} = \frac{\unit{u}_1}{h_1}$. Why is $\varphi\nabla\times\mathbf{v} = 0$ but $\nabla\varphi\times\mathbf{v}$ not?

Hi. I have heard that the marsden and Tromba book is not very rigorous. Is this true? I seek a vector book that is something proof intensive. I took vector analysis b4 with a book called vector calculus by Susan colley, I am looking for something more rigorous than this. Anyone read vector...

Homework Statement n/a Homework Equations ∇ x F = 0 ∂Q/∂x = ∂P/∂y The Attempt at a Solution n/a Given that no sketch of the vector field is given; Is determining the curl of a vector field the most fail proof of determining whether it is conservative? I'm just...

edit: vector* analysis; sorry for the typo Homework Statement Given that A = ||ru||2, B = ru\bulletrv, C = ||rv||2 surface area of S is Area(S) = \int^{d}_{c}\int^{b}_{a} = sqrt (AC - B2) dudv The Dirichlet energy can be thought of as a function as follows E(S) =...

In case of a circularly polarized wave, is the poynting vector also circularly polarized? If not what happens in this case?

I have been struggling with this homework question for a week and it still makes no sense to me. I am asked to "choose a nontrivial second order tensor in R^2 and determine whether or not it can be identified with a first order tensor in R^4 in a natural way, and if it can be, is every...

Homework Statement Let x,y is in Vn, such that x is not equal to zero. Show that you can find vectors y┴ and y// is in Vn such that y=y┴ + y// and y// is parallel to x and y┴ is perpendicular to x. Homework Equations x//y => x=ky x.y=0 if x┴y The Attempt at a Solution I calculated...

Can you suggest me a book in vector analysis which covers spherical and cylindrical coordinates. My professor discusses the calculation of volume, surface area and curve length, by integrating differential surface and volume elements in terms of cartesian, spherical and cylindrical coordinates...

I am working on a dual undergrad degree program, with my primary degree being Electrical Engineering. This fall will start the last semester to get my B.S. in Math completed. For the engineering side I am taking Electromagnetics and Signals and Systems Analysis this semester. I need only to...

Dear all, I have two vector fields \vec{B} and \vec{A} related by: \vec{B}=\nabla \times \vec{A} How can I simplify the following term: \frac{\partial }{\partial \vec{A}} B^{2} where \frac{\partial }{\partial \vec{A}}=(\frac{\partial }{\partial A_{x}} \frac{\partial }{\partial...

Homework Statement Prove: the sum of the squares of the sides of any quadrilateral, minus the sum of the squares of the two diagonals, equals four times the square of the distance between the midpoints of the diagonals. Homework Equations A(dot)B = |A||B|cos(theta) I honestly don't...

Homework Statement 4. Let r=r(t) be a vector whose length is always 1 (it may vary in direction). Prove that either r is a constant vector or dr/dt is perpendicular to r. hit: differentiate r.r Homework Equations basic derivatives with respect to t for velocity and acceleration...

Homework Statement I don't know if its possible to do this, but I ran into this problem when trying to right a program which creates orbits for individual points. Anyways... Given 2 position vectors (tails anchored to the origin), say A and B and the angle between them \theta, A is unknown...

Okay. How the heck do I integrate this sum? I have to be doing something wrongly. http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-02193820.jpg?t=1283474406 http://i111.photobucket.com/albums/n149/camarolt4z28/2010-09-02192641.jpg?t=1283474140

Homework Statement The temperature at a point (x,y,z) in space is given by T(x,y,z) = x^2+y^2-z. a mosquito located at (1,1,2) desires to fly in such a direction that it will get warm as soon as possible. in what direction should it fly? Homework Equations Grad T = Txi+Tyj+Tkz The...

Homework Statement i think i may have solved this but I am worried I am wrong because it seemed too simple. I wouldn't bother posting too check except that its for an assignment... the question is in the attachment- can someone please check this! Homework Equations The Attempt at a...

Homework Statement Find the sum formulas for cosine and sine using vector methods. Homework Equations Suggestion: use the following vectors A= cos xi + sin xj B= cos yi + sin yj C= cos yi - sin yj The Attempt at a Solution I actually solved the question by doing the dot...

Homework Statement Verification of the product U . del (R) = U Vectors are written in bold Homework Equations R = ix + jy + kz The Attempt at a Solution I cannot understand what is going on. If del R is the gradient vector of R, then the problem will be scalar product, whose...

if a point in cylindrical cordinates is A=(r1,\theta1,z1) and another point is B=(r2,\theta2,z2) (if ar,a\theta,az are unit vectors) then the position vector of A is = r1<ar>+\theta1<a\theta>+z1<az> and the position vector of B is = r2<ar>+\theta2<a\theta>+z2<az> so vector BA=...

I'm honestly totally clueless on 4 and 10. For #4a, I plugged in dN/ds and used the product but didn't see a solution. I did something similar for 4b. I also don't see how the two hints help. For 10, I multiplied f and the two vectors, tried to find the divergence, used the product rule twice, I...

Homework Statement Let \mathbf{G}(x,y,z) be an irrotational vector field and g(x,y,z) a C^1 function. Use vector identities to simplify: \nabla\cdot(g\nabla \times (g\mathbf{G})) Homework Equations The '14 basic vector identities' The Attempt at a Solution I tried using the...

I'm stuck on both problems. Here's my work thus far. I have no idea he got rtt in (b).

Homework Statement Schaum's vector analysis prob 4.65 Find the values of constants a,b,c so that directional derivative of phi=axy^2+byz+cz^2x^3 at (1,2,-1) has a maximum of magnitude 64 in a direction parallel to the z axis. Homework Equations The Attempt at a Solution...

104. If a, b, c and a’, b’, c’ are such that a’• a = b’• b = c’• c = 1 a’• b = a’• c = b’• a = b’• c = c’• a = c’ • b =0 Prove that it necessarily follows that a^'= (b x c)/(a• bxc) , b^'= cxa/(a•bxc) , c^'= axb/(a•bxc)

Show that a necessary and suffiecient condition that the vectors A= A1i + A2j +A3k, B=B1i + B2j + B3k, C= C1i + C2j + C3k be linearly independent is that the determinant |(A1&A2&A3@B1&B2&B3@C1&C2&C3)| be different from zero.

I'm looking at integrating a solid angle multiplied by the vector representing that solid angle over an entire sphere (4pi). I've split the terms into sin(\theta)cos(\phi)i, sin(\theta)sin(\phi)j, cos(\theta)k, but I am still integrating phi over [0,2pi] and theta over [0,pi]. This doesn't seem...

Homework Statement prove grad(f/g)=((g grad f)-(f grad g))/g^2,if g not equal to 0. Homework Equations no idea. The Attempt at a Solution rhs will be grad f -(f grad g)/g^2. can't make out what 2 do after that.referred other books but no help.it's a very obscure identity.found...

Hi all, My question is about obtaining the force between two particular atoms in an ensemble. Please excuse my ignorance on this topic. I can calculate all the forces in the system by the Hellmann–Feynman theorem using any quantum mechanical code. This is the print out from such a code...

I'm taking these next semester. I'm taking Differential Equations right now, so I'll have that under my belt.

Hi all, I'm trying to do some vector analysis in Mathematica 6. I have the vector analysis package loaded via: << VectorAnalysis` I'm working in the default cartesian coordinate system, but just to be on the safe side I have set: SetCoordinates[Cartesian] The grad operator seems to work ok...

Homework Statement How does the cross product (i.e. A X B) of two vectors transform under inversion? [The cross product of two vectors is properly called a pseudovector because of this "anomalous behavior]. Is the cross product of two pseudo vectors, a vector, and a pseudovector? Name two...

Homework Statement I've taken the liberty to translate the problem, along with its corresponding diagram, into an image: http://img15.imageshack.us/img15/9695/questionm.jpg angle q1 = 53* angle q2 = 37* angle q3 = 90* Homework Equations F21 = kq1q2/(r21)^2 F31 = kq1q3/(r31)^2...