Author Archives: mattelararen

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About mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics

Cauchy’s integralformula

Publicerat den september 17, 2012 av mattelararen

Theorem Suppose U is an open subset of the complex plane C, f : U → C is a holomorphic function and the closed disk D = { z : | z − z0| ≤ r} is completely contained in U. Let … Fortsätt läsa →

Publicerat i Calculus, Imaginary numbers | Märkt | Lämna en kommentar

Cauchy’s integral theorem

Publicerat den september 12, 2012 av mattelararen

Cauchy‘s integral theorem states that an analytic function f(z) the line integral around a closed path C is zero. ∫f(z)dz = 0  . This means that the curve integrals over 2 curves with the same endpoints for an analytic function … Fortsätt läsa →

Publicerat i Imaginary numbers | Lämna en kommentar

The Cauchy-Riemann equations

Publicerat den september 11, 2012 av mattelararen

In order for a complex function of a  single complex variable to be differentiable it must be differentiable both parallell to the imaginary axis δy →0 and parallell to the real axis δx →0. This condition leads to the CAuchy –Riemann equations- The … Fortsätt läsa →

Publicerat i Advanced, Calculus, Imaginary numbers | Lämna en kommentar

de Moivre’s formula and complex-conjugation.

Publicerat den september 10, 2012 av mattelararen

(e^ix )^n = cos(nx) + i sin(nx) is called de Moivre’s formula. The formula is named after the 17 th. century French huguenot mathematician Abraham de Moivre. Also the variable in of a function can be a complex number. f(z) … Fortsätt läsa →

Publicerat i Gymnasiematematik(high school math), Imaginary numbers, matematik 4, matematik 5 | Märkt , , , | Lämna en kommentar

Alternative representations of complex numbers

Publicerat den september 9, 2012 av mattelararen

As mentioned in the latest post any complex number may be represented by an arrow in the complex plane. This number is unambiguously described by two numbers: its real part x and its imaginary part y. z= x+iy. This is … Fortsätt läsa →

Publicerat i Imaginary numbers, matematik 4, matematik 5 | Märkt , , , | Lämna en kommentar

Imaginary numbers

Publicerat den september 6, 2012 av mattelararen

A solution to the simple second-degree equation x2 + 1 =0 can not be found along the line of real-numbers. Therefore it was necessary to invent a fictive number i such that i2=-1. i.e. the imaginary numbers making it possible … Fortsätt läsa →

Publicerat i matematik 1c, matematik 4, matematik 5 | Märkt , , , | 2 kommentarer

The first man on the Moon

Publicerat den september 5, 2012 av mattelararen

Last week the first human ever to set a foot on the Moon, Neil Armstrong (born 1930) expired. His family wrote wrote this as a final tribute: ”For those who may ask what they can do to honor Neil, we have … Fortsätt läsa →

Publicerat i Astronomy | Lämna en kommentar

Bessel functions

Publicerat den augusti 30, 2012 av mattelararen

Friedrich Wilhelm Bessel (1784-1846)  was an outstanding mathematician and astronomer in the 19 th. century. Professor at the Albertina university in the no longer existing town of Königsberg. He was the first astronomer to use the parallax of a star … Fortsätt läsa →

Publicerat i Calculus | Märkt , | 2 kommentarer

Line integrals

Publicerat den augusti 28, 2012 av mattelararen

The line integral along the curve C can be written as where C is parametrisized as r(t) with the parmeter t. ∫¦r'(t)¦ dt equals the arc length i.e. the length of the curve. Consider eg the circle.  x2+ y2 = r2. … Fortsätt läsa →

Publicerat i Gymnasiefysik(high school physics), matematik 5 | Lämna en kommentar

Exercises on the masterclass

Publicerat den augusti 22, 2012 av mattelararen
Publicerat i Uncategorized | 2 kommentarer