Recent content by smize

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    Proof of the Lindemann-Weierstrass Theorem

    I am wanting to find a good proof of the Lindemann-Weierstrass Theorem. Most importantly I need the part that states that eα is transcendental where α ≠ 0 is algebraic. What are good online resources or books for the proof? Thank-you.
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    Some remarks on complex numbers

    The complex numbers are a very important aspect of mathematics. They are utilized often in Analysis (obviously), Mathematical Physics, Algebra, and Number Theory (I am not certain about Geometry/Topology). There was a problem that was solved in the 19th century: Can one construct a square...
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    Determining a formula for a (sub)sequence

    The sequence is the set of n's where | ∑_{k=0}^{n} a_{k}z^{k} | is a local maximum in the sequence of the magnitudes of partial sums (the partial sums are complex valued).
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    Determining a formula for a (sub)sequence

    I currently have the first 125,256 terms of a sequence of natural numbers. I need to find a formula for any non-finite sub-sequence. Are there any good methods for obtaining such a formula? I can already say that it isn't a linear distribution, and I highly doubt it being polynomial (although...
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    Principal root of a complex number

    Thank-you. So it is how I though. As for the latter question, we can ignore that since I understand it now. Thank-you.
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    Solve a differential equation for the initial conditions,

    Edit: What (s)he was trying to state is that y = 0 is an equilibrium solution of the differential equation. What would this imply about the equation?
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    Principal root of a complex number

    Evaluate the integral of ∫\Gamma f(z) dz, where f(z) is the principal value of z1/2, and \Gamma consists of the sides of the quadrilateral with vertices at the pints 1, 4i, -9, and -16i, traversed once clockwise. I understand how to compute this for the most part. I'm just not 100% confident...
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    Principal root of a complex number

    Homework Statement I am doing a problem of a contour integral where the f(z) is z1/2. I can do most of it, but it asks specifically for the principal root. I have been having troubles finding definitively what the principal root is. Anyplace it appears online it is vague, my book doesn't...
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    Verify that the Stokes' theorem is true for the given vector field

    This is a problem from an old final exam in my Calc 3 class. My book is very bad at having examples for these types of problems, and my instructor only went over one or two. Help would be much appreciated. Homework Statement Verify that the Stokes' theorem is true for the vector field...
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    Need help understanding Lagrange multipliers at a more fundamental level.

    Nevermind. I understand now. I spent 2 seconds on the wikipedia page for it, and I finally had that "Oh my God. I get it." moment.
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    Need help understanding Lagrange multipliers at a more fundamental level.

    So, is the max and min found a max and min based on the constraint, and not a regular max/min of f(x,y) or f(x,y,z) ?
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    Need help understanding Lagrange multipliers at a more fundamental level.

    I understand that for Lagrange multipliers, ∇f = λ∇g And that you can use this to solve for extreme values. I have a set of questions because I don't understand these on a basic level. 1. How do you determine whether it is a max, min, or saddle point, especially when you only get one...
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    Use Lagrange multipliers to find the max & min

    Ah! Yes, I know this function. I just didn't know it's name. Thank-you for reminding me of it!
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    Use Lagrange multipliers to find the max & min

    I am sorry, but can you elaborate more on what a Hessian is? Currently we have only covered Lagrange multipliers.
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    Use Lagrange multipliers to find the max & min

    Homework Statement Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraint. f(x,y) = exy; g(x,y) = x3 + y3 = 16 Homework Equations ∇f(x,y) = λ∇g(x,y) fx = λgx fy = λgy The Attempt at a Solution ∇f(x,y) = < yexy, xexy > ∇g(x,y) = <...
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