Vector analysis Definition and 124 Threads

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...

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...

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.

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...

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...

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...

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...

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...

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...

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...

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...

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 /...

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...

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...

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...

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...

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

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...

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...

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...

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)...

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'...

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...

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...