Vector analysis Definition and 124 Threads

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.

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  1. J

    Vector Analysis using Basis Vectors

    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...
  2. A

    Stokes theorom question with a line

    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...
  3. A

    Finding largest value of H of a ramp, from a FBD

    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...
  4. Lagraaaange

    Full course of Vector Analysis vs Griffith Text self study?

    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 +...
  5. jove8414

    Vector Addition: Find the Resultant Vector

    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...
  6. D

    MHB Where Are the Points Satisfying All Conditions in This Vector Field?

    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!
  7. D

    MHB What is the locus of points where $F_x = 1$ and $|F_x| = 2$?

    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...
  8. Y

    Kinematics using vector analysis

    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...
  9. M

    Vector analysis: show the object moves on the elliptical path

    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...
  10. M

    Vector Analysis Homework: Finding the Unit Normal Vector at P

    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...
  11. C

    Uncovering the Origins of Vector Analysis in Maxwell's Equations

    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...
  12. sheldonrocks97

    Vector Analysis: Ready for 300 Level Math?

    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...
  13. K

    Understanding Vector Fields and Their Properties: Analyzing a Homework Statement

    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...
  14. P

    How do I solve for the position vector using 2-D vector analysis?

    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...
  15. rizwanibn

    Electromagnetics: Vector analysis

    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)
  16. M

    Vector Analysis - Similarities on Orthonormal Basis

    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...
  17. D

    MHB Vector Analysis: $\varphi$, $\mathbf{v}$, and Their Cross Products

    $\newcommand{\unit}[1]{\hat{\mathbf{#1}}}$ 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?
  18. M

    Vector Calculus by Marsden and Tromba vs. Vector Analysis by Brand

    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...
  19. B

    Vector Analysis - Determining whether a vector field is conservative

    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...
  20. R

    Surface area proof (vector analysis)

    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) =...
  21. X

    Circularly Polarized Wave: Poynting Vector Analysis

    In case of a circularly polarized wave, is the poynting vector also circularly polarized? If not what happens in this case?
  22. 1

    Vector analysis, comparing tensors to vectors

    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...
  23. D

    Vector Analysis: Show x,y in Vn can be Separated into y┴ & y//

    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...
  24. I

    Which vector analysis textbook covers spherical and cylindrical coordinates?

    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...
  25. S

    Can't decide between PDEs or Vector Analysis

    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...
  26. H

    Simplifying Vector Analysis Derivatives with \nabla \times \vec{A}: Expert Tips

    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...
  27. J

    Vector Analysis (Calculus IV) question

    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...
  28. L

    Is dr/dt Always Perpendicular to r for a Unit Vector r(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...
  29. T

    Can Vector Projection Solve Angular Displacement in Orbit Calculations?

    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...
  30. Shackleford

    Vector Analysis Review for Mechanics course

    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
  31. A

    Optimal Direction for Mosquito Flight to Warmth

    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...
  32. P

    Vector Analysis of Point Charges: Solving for Net Force

    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...
  33. R

    Vector Analysis 2: Sum Formulas for Cosine & Sine

    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...
  34. R

    Verifying U.del(R)=U: Vector Analysis

    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...
  35. B

    Vector analysis in cylindrical coordinate system

    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=...
  36. Shackleford

    Vector Analysis Help: #4 & #10

    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...
  37. J

    Vector Analysis Identity simplification/manipulation

    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...
  38. Shackleford

    How can I simplify vector analysis and understand the notation better?

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

    Solve Schaum's Vector Analysis Prob 4.65: Find Constants a,b,c

    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...
  40. I

    How Do Vector Components Relate in Orthogonal Projections and Cross Products?

    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)
  41. I

    Is the Determinant of Vectors A, B, and C Non-Zero for Linear Independence?

    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.
  42. P

    Help with Vector Analysis in spherical velocity-space coordinates

    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...
  43. S

    Problem involving del operator in vector analysis

    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...
  44. E

    Interatomic forces in an ensemble via vector analysis

    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...
  45. Shackleford

    What to brush up on? Modern Physics I and Vector Analysis

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

    Vector analysis in mathematica

    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...
  47. N

    How Does the Cross Product Transform Under Inversion in Vector Analysis?

    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...
  48. M

    Coulomb's Law - Vector Analysis

    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...
  49. M

    Vector Analysis: Sketching Hyperbola x^2-y^2=1 with Vector-Valued Function

    1. Sketch the plane curve represented by the vector-valued function r(t)=cosh ti +sinh tj on the interval 0</(trying to say less then or equal to)t</(also less then or equal to)5. Show that the rectangular equation corresponding to r(t) is the hyperbola x^2-y^2=1. Verify your sketch using a...
  50. Rasalhague

    Vector Analysis: Introduction to Tensor Notation and Index Conventions

    In Introduction to Vector Analysis, § 1.16 Tensor notation, Davis and Snider introduce index notation and the Einstein summation convention, Kronecker's delta and the Levi-Civita symbol. They present the following equation, on which they base some proofs of vector algebra identities...
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