I think this is very common route for students to first learn calculations and later learn theory. I guess calculations are more important at first but if you want to go deeper in physics you will need some theoretical background to better understand what is going on. Try Spivak's "Calculus" for...
You can integrate k-form on k dimensional manifold. You can have k-form on n dimensional manifold, where n>k. This can be integrated on k-dimensional submanifold of original manifold. For example you can integrate 2-form on a surface in three dimensional space.
Remember that n^0 is identity matrix. For positive , n^k=n. Therefore we have \exp (2\pi i n)= \sum _{k=0}^{\infty}\frac{1}{k!}(2 \pi i n)^k=id + \sum _{k=1}^{\infty}\frac{1}{k!}(2 \pi i n)^k=id + \sum _{k=1}^{\infty}\frac{1}{k!}(2 \pi i)^kn
=id +\left( \sum _{k=1}^{\infty}\frac{1}{k!}(2 \pi...
Do you impose any restirictions on the polynomial you are looking for? The way you stated your problem P(x)=x-a where a is your number will do. Or even P(x)=0. I guess that's not what you were looking for though, so you need to make your question more precise.
Remember that every polynomial...
Well you can use divergence theorem to calculate flux through your paraboloid WITH plane attached. Then if you can calculate flux through the plane you can substract it from what you got; what is left is obviously flux through paraboloid.
I loved the comment about falling asleep but still being good for you. Oh god, how true is that.
Regarding reading the book you really need to try out for yourself. I know I couldn't do that myself. I read textbooks on maths or physics in places like buses etc. pretty often. However, when...
Regarding complement of a set:
You can only take complement of a set B relative to its superset (A is superset of B if B is a subset of A). Complement of B relative to A is set of all elements of A that are not in B.
For example: Let A be set of all natural numbers: 1,2,3,... and B be set of...
Squaring Lagrangian is not really what I've done. Here's how I exactly got to my equations.
I assumed that parametrization is chosen such that L=\frac{\mathrm{d}s}{\mathrm{d}t}=1. We then have \frac{\mathrm{d}L}{\mathrm{d}t}=0 and \frac{\partial L}{\partial \theta}=\frac{\sin 2\theta...
I don't know this book you have either, but what comes to my mind is that it might be about stuff like surfaces and curves in higher dimensional Euclidean spaces. One can see curved surface as being drowned in three dimensional Euclidean space. That is old fashioned approach to differential...
Let's say that numenator is polynomial of degree m (with coefficient A before m-th degree term) and denominator is polynomial of degree n (with coefficient B), that is:
Q(x)=\frac{Ax^m+...}{Bx^n+...}
When you go to inifnity those higher order terms dominate. That is no matter what are the...
Hello
I'm struggling with well-known problem of finding shortest path between two points on a sphere using calculus of variations. I managed to find correct differential equations of great circles, but I'm not confident about validity of methods I used. Below I describe my approach.
In...
Lorentz invariance means roughly that if given law holds in one inertial frame it should hold unchanged in any other inertial frame and transformation law of physical quantities is given by Lorentz transformation.
For example if 4-momentum is conserved in some physical system according to some...
This problem led me to following conjecture: There is nothing wrong with my calculations, theorem in K&N is true, but the fact they omitted is that for derivations in differential forms spaces k is always even for Leibnitz derivations (example: Lie derivative) and odd for skew derivations...