Recent content by samgrace

Hello, I am want to prove that: $$ \sum_{1}^{\infty} \frac{1}{n^{2} + 1} < \frac{1}{2} + \frac{1}{4}\pi $$ Cauchy's Convergence Integral If a function decreases as n tends to get large, say f(x), we can obtain decreasing functions of x, such that: $$ f(\nu - 1) \geqslant f(x) \geqslant...

Ah, right, yes. In that case I'll only do a few more and then start doing calculus for physics. Thanks for putting the wind in my sails.

Thanks, sorry for the delayed response I learn a variety of things throughout the week. I started reading an analysis book and managed to prove the simple power law for both differentiating and integrating. The integral derivation used the sum of squares relationship to simplify which was...

Hello, Please take a look at this handbook of derivatives and integrals: http://myhandbook.info/form_diff.html http://integral-table.com/downloads/single-page-integral-table.pdf I would appreciate it if someone could point me in the direction of exemplary books that derive these...

Oh! Thanks, that's clarified the technique, I can do the rest of worksheet now.

Hello, here is my problem.http://imgur.com/VAu2sXl'][/PLAIN] http://imgur.com/VAu2sXl My confusion lies in, why those particular partial derivatives are chosen to be acted upon the auxiliary function and then how they are put together to get the Euler-Lagrange equation? My guess is that it's...

No need for an answer I have now solved it

Need all of the elements in rows 1 and 3 to be multiplied by two and this cannot be acheived if some are ones. Also need all the elements in rows 2 and 4 to remain the same and this cannot be acheied if some are twos. Tried an algebraic finding of the weighing coefficients but to no avail.

Homework Statement \begin{bmatrix} 3x_{1}& 7x_{2}& 4x_{3} \\ 3x_{1}& 4x_{2}& 5x_{3} \\ x_{1}& 10x_{2}& 8x_{3} \\ 8x_{1}& 8x_{2}& 6x_{3} \\ \end{bmatrix} = \begin{bmatrix} 26 \\ 16 \\ 33 \\ 46 \\ \end{bmatrix} the measurements represented by equations 1 and 3 above can be trusted more than those...

Hello, I am a physics student studying set theory in his spare time, set theory is completely useless in the physics sense? What about the cartesian product of two sets and their respective ordered pairs that are mapped into Real/2-dimensional Euclidian space? Particularly if the two elements of...

The history slash evolvement of mathematics is what I am looking for, however now that you've said that, it seems that I should get a book on the material I want to learn, and then back track to other books that cover the material that I don't understand in that book.

Hello, I am a physics student and have catagorised most of physics, e.g classical mechanics, relativistic mechanics, quantum mechanics and quantum field theory, and have also identified all the mathematics involved in each of these catagories. For example classical mechanics involves Calculus...

Homework Statement Integreate: ##T = ∫ \frac{dy}{V_ab (y)} = \frac{2}{v}∫[1 + \frac{\alpha^2 y}{L} + 2\alpha \sqrt\frac{y}{L} cos(\phi(y))]^\frac{-1}{2} dy## where ## \phi (y) = \frac{\pi}{6} + sin^-1(\frac{\alpha\sqrt{y}}{2\sqrt{L}}) ## The limits are between 0 and L Homework EquationsThe...

Hello, I have been attempting to reduce Maxwell's equations to the forms shown in the image, by substituting the plane wave solutions for E and B of the wave equations back into Maxwell's equations, but I cannot find a way. Anybody know how to do this?

Homework Statement A harmonic oscillator of mass m and angular frequency ω experiences the potential: V(x) = 1/2mω^{2}x^{2} between -infinity < x < +infinity and solving the Schrödinger equation for this potential yields the energy levels E_n = (n + 1/2)...