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Browse College Analysis

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Uniform Convergence of a Sequence [8/16/1995]
I assert that uniform convergence of a sequence of functions on a given interval to a function, f, is a "stronger" statement than pointwise convergence of the sequence. Is my thinking correct?

Using Newton's Method to Solve an Implicit Equation [10/14/2007]
How can I solve the equation (sin(X))/X = 0.7031? My book gives the answer but does not explain how to find it.

Visualizing Functions of Complex Variables [05/09/2012]
A student wonders how to picture the functions that appear in her complex analysis course. Doctor Tom offers several ways to disassemble, measure, and otherwise "see" functions of complex variables.

Volume of a Hypersphere [06/03/1999]
Could you give me the formula for the volume of a hypersphere?

Weierstrass Curve [09/13/2002]
About 100 years ago the mathematician Weierstrass gave an example of a curve consisting of angles, or corners, and nothing else. Where can I find this equation?

X^Y = Y^X [11/13/2002]
Find (with proof) all pairs of integers {x,y} that satisfy x^y=y^x.

Zeros of the Zeta Function [08/09/1999]
I have read that the only real zeros to the zeta function are -2, -4, -6, etc., but since zeta(x)=1+1/2^x+1/3^x+1/4^x+..., how can any of these zeros work?

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