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1. Eigenvalues of perturbed matrix. Rouché's theorem.

Homework Statement Let \lambda_0 \in \mathbb{C} be an eingenvalue of the n \times n matrix A with algebraic multiplicity m , that is, is an m-nth zero of \det{A-\lambda I} . Consider the perturbed matrix A+ \epsilon B , where |\epsilon | \ll 1 and B is any n \times n matrix...
2. Proof sin(10) is irrational.

Homework Statement Prove \sin{10} , in degrees, is irrational. Homework Equations None, got the problem as is. The Attempt at a Solution Im kinda lost.
3. Quasilinear PDEs in industry, finance or economics.

Homework Statement I've been reading some introductory PDE books and they always seem to motivate the search for solutions of the first order quasilinear PDE by the method of characteristics, by introducing a flow model; i was thinking, could someone give an example of a phenomenon modeled by...
4. Boundary of closed sets (Spivak's C. on M.)

Homework Statement I have been self studying Spivak's Calculus on Manifolds, and in chapter 1, section 2 (Subsets of Euclidean Space) there's a problem in which you have to find the interior, exterior and boundary points of the set U=\{x\in R^n : |x|\leq 1\}. While it is evident that...
5. Compactness of point and compact set product

I was reading Spivak's Calculus on Manifolds and in chapter 1, section 2, dealing with compactness of sets he mentions that it is "easy to see" that if B \subset R^m and x \in R^n then \{x\}\times B \subset R^{n+M} is compact. While it is certainly plausible, I can't quite get how to handle...
6. Self studying little Spivak's, stuck on Schwartz ineq. for integrals

Homework Statement In an effort to keep me from spending all summer lying on the couch, I recently started reading Michael Spivak's Calculus on Manifolds; while working on problem 1-6 I got stuck on a technical detail and I was wondering if anyone could provide a little insight. Problem 1-6...
7. Self studying little Spivak's, stuck on problem 1-6

In an effort to keep me from spending all summer lying on the couch, I recently started reading Michael Spivak's Calculus on Manifolds; while working on problem 1-6 I got stuck on a technical detail and I was wondering if anyone could provide a little insight. Problem 1-6 says: Let f and g...
8. LTI System Problem

How do you represent the Fourier transform of a periodic signal as the input in a LTI system? More precisely, a sequence of triangle pulses symmetric to the origin. I know what the Fourier transform is 2\pi (sum (Xn delta(omega - (n)omega0))) I was told to reduce the Xn to...
9. Wheatstone bridge, prove converse.

Homework Statement You are given a standard Wheatstone bridge, prove that the bridge is balanced if and only if R_x = R_3 \frac{R_2}{R_1} . Subindexes depend on the names assigned to each resistance. Proving that if the bridge is balanced THEN the resistors satisfy said relationship is easy...
10. Bernoulli's (differential) equation.

I have been doing some self study on differential equations using Tom Apostol's Calculus Vol. 1. and I got stuck on a problem (problem 12, section 8.5, vol. 1). Homework Statement Let K be a non zero constant. Suppose P and Q are continuous in an open interval I. Let a\in I and b a real...
11. To prove right inverse implies left inverse for square matrices.

Homework Statement Let A be a square matrix with right inverse B. To prove A has a left inverse C and that B = C. Homework Equations Matrix multiplication is asociative (AB)C=A(BC). A has a right inverse B such that AB = I The Attempt at a Solution I dont really know where to...
12. Crystall structures of Cu, Al, and Fe at different temperatures.

I was wondering if someone could tell me (in pedestrian terms) what are the crystal structures of aluminum, copper and iron as a function of the temperature. I just read the chapter on crystalline arrays of Callister's Materials Ecience & Eng. but the book just says that Cu and Al have a FCC...
13. Two body applications of Newtons law of cooling.

Homework Statement What's the formula that better describes the temperature as a function of time for an enclosed body of water with certain initial temperature T_a immersed in another body of water of initial temperature T_b? More clearly, I performed an experiment in which I put a...
14. Linear function F continuous somewhere, to prove continuous everywhere

Homework Statement Let f:A\subset{\mathbb{R}}^{n}\mapsto \mathbb{R} be a linear function continuous a \vec{0} . To prove that f is continuous everywhere. Homework Equations If f is continuous at zero, then \forall \epsilon>0 \exists\delta>0 such that if \|\vec{x}\|<\delta then...
15. Effects of high and low pressure on the human body.

Homework Statement I was asked by my lab teacher to investigate the effects on the human body of being exposed to very high and very low pressures, and while I have found some good sources of info it is not that easy to find good and quotable sources, I was wondering if anyone could offer some...
16. On the properties of non-commutative groups

Homework Statement Let [G,+,0] be a non-abelian group with a binary operation + and a zero element 0 . To prove that if both the zero element and the inverse element act on the same side, then they both act the other way around, that is: If \forall a \in G , a + 0 = a , and a + (-a)...
17. Questions regarding something in Feynman's lectures.

This isn't quite homework help, although it might seem a little like it. I was reading my copies of the Feynman's lectures the other day and in volume 1, chapter 2, section 2, "Physics before 1920" he mentioned something which confused me a little: when explaining electric charges and...
18. Mathematica Changing interval in Histogram, Mathematica

Hello again. Sorry for all the posts. I have a histogram of frequencies in Mathematica and the intervals on the x axis are predefined and kind of unrepresentative. I changed the bin number (with 'Histogram[mydata, binnumber]') but I can't seem to find anything on the internet about changing...
19. Mathematica Plotting in Mathematica

I have imported a list of data of this kind 4.447E-02 1.620E-02 1.281E-02 2.585E-02 3.676E-02 1.232E-01 7.635E-02 1.756E-02 1.142E-02 3.676E-02 and it goes on, 2000-ish numbers. I try to do a ParetoPlot and all I get is an empty plot. I have loaded the Statistic Plot Package. Is it...
20. Help plotting 3D data in 2D

Hello. I was asked to import a number of data to mathematica from an output file for wien2k (based in fortran). The thing is, I have to draw a graph that considers a matrix full of data in three dimensions, but the graph itself should only have two parameters. To sum up: how to represent 3D data...
21. Need help plotting data points in GNUplot

Homework Statement Hello everyone, I was wondering if someone could help me plot data points I got in a lab experiment. I've been trying to plot points of data with Gnuplot but the error bars don't show up no matter what I do, below is the data list I am using as input, the first column is...
22. Proof of Euler's fuction.

Hello. I have been reading a book with an introductory section on number theory and the part regarding Euler's function just said that \varphi (n) = n-1 when n is prime and that \varphi (n) = n(1-\frac{1}{p_{1}})(1-\frac{1}{p_{2}})...(1-\frac{1}{p_{n}}) when n is a composite number. The...
23. Help with proof of theorem related to Fermat's.

Hello everyone, I have been trying to teach myself number theory and I am stuck trying to prove a (I am sure) very easy to prove theorem related to that of Fermat's. The theorem I am to prove states: Let e be the lowest number (natural) such that a^e \equiv 1 (\bmod \ p) for p prime such...
24. (this is not homework) Eletronics and circuitry for dummies.

Hello everyone, this isn't homework so I figured I'd post it here. I want to learn basic electronics, I mean, being able to move cables and diodes around is not only interesting but useful, I've seen a few diagrams on how to build certain types of guitar/bass pedals and/or amps and such and...
25. Help proving matrix properties:

Homework Statement Let A, B be both matrices with the same dimensions. Is AB^2 = (A^2)(B^2) a valid claim? Homework Equations The Attempt at a Solution I attempted to show that (AB)^2 = (AB)(AB) = A(BA)B and that (A^2)(B^2) = (AA)(BB) = A(AB)B, so for A(BA)B to be equal to A(AB)B, AB...
26. Physicist, mathematician and engineer jokes.

Found this while lurking around, thought I'd share: http://www.cs.northwestern.edu/~riesbeck/mathphyseng.html Bai bai.