1. ### Calculus Multivariable Calc for IPhO

Hi guys, i´m pretty well in calculus 1 and i´m studying for the International Physics Olympiad. So I´d like to know some multivariable calculus books that cover vector calc too, are balanced (proofs are welcome) and emphasizes physical intuitions. Thank you already!
2. ### Vector Analysis Problem Involving Divergence

Homework Statement [/B] Let f and g be scalar functions of position. Show that: \nabla f \cdot \nabla(\nabla ^2 g)-\nabla g \cdot \nabla(\nabla ^2f) Can be written as the divergence of some vector function given in terms of f and g. Homework Equations [/B] All the identities given at...
3. ### Finding the curl of velocity in spherical coordinates

Homework Statement The angular velocity vector of a rigid object rotating about the z-axis is given by ω = ω z-hat. At any point in the rotating object, the linear velocity vector is given by v = ω X r, where r is the position vector to that point. a.) Assuming that ω is constant, evaluate v...
4. ### I Laplacian in integration by parts in Jackson

I am reviewing Jackson's "Classical Electromagnetism" and it seems that I need to review vector calculus too. In section 1.11 the equation ##W=-\frac{\epsilon_0}{2}\int \Phi\mathbf \nabla^2\Phi d^3x## through an integration by parts leads to equation 1.54 ##W=\frac{\epsilon_0}{2}\int |\mathbf...
5. ### I Proofs of Stokes Theorem without Differential Forms

Hello, does anyone have reference to(or care to write out) fully rigorous proof of Stokes theorem which does not reference Differential Forms? I'm reviewing some physics stuff and I want to relearn it. I honestly will never use the higher dimensional version but I still want to see a full proof...
6. ### I Kronecker Delta and Gradient Operator

I am looking at an explanation of the gradient operator acting on a scalar function ## \phi ##. This is what is written: In the steps 1.112 and 1.113 it is written that ## \frac {\partial x'_k} {\partial x'_i} ## is equivalent to the Kronecker delta. It makes sense to me that if i=k, then...
7. ### Vector Calculus - Tensor Identity Problem

Homework Statement Homework Equations The Attempt at a Solution I am really lost here because our professor gave us no example problems leading up to the final exam and now we are expected to understand everything about vector calculus. This is my attempt at the cross product and...
8. ### Evaluating Cartesian integral in polar coordinates

Homework Statement Transform given integral in Cartesian coordinates to one in polar coordinates and evaluate polar integral. ##\int_{0}^3 \int_{0}^x \frac {dydx}{\sqrt(x^2+y^2)}## Homework Equations The Attempt at a Solution I drew out the region in the ##xy## plane and I know that ##0...
9. ### Find center of mass of planar quadrilateral

Homework Statement Consider the planar quadrilateral with vertices (0, 0), (2, 0), (1, 1) and (0, 1). Suppose that it has constant density. What is its center of mass? Homework Equations The Attempt at a Solution Since it has constant density, could I assume that the center of mass would be...
10. ### Finding transformation T such that T(D*)=D

Homework Statement If ##D^*## is the parallelogram whose vertices are ##(0,0)##,##(-1,3)##, ##(1,2)##, and ##(0,5)## and D is the parallelogram whose vertices are ##(0,0)##, ##(3,2)##,##(1,-1)## and ##(4,1)##, find a transformation ##T## such that ##T(D^*)=D##. Homework Equations The Attempt...

30. ### I Magnetic vector potential of infinite straight wire

The magnetic field generated by an infinitely long straight wire represented by the straight line ##\gamma## having direction ##\mathbf{k}## and passing through the point ##\boldsymbol{x}_0##, carrying a current having intensity ##I##, if am not wrong is, for any point ##\boldsymbol{x}\notin...