Category Archives: Calculus

Separable variables

Publicerat den oktober 21, 2012 av mattelararen

Differential equations of the form dy/dx = – P(x)/Q(y) then it is possible to separate the variables Q(y)dy = – P(x) dx → Q(y) dy + P(x) dx = 0 Ex y´+ sinx y = 0 y´ = -sinx y dy/y … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 4, Uncategorized | Märkt , | Lämna en kommentar

Differential equations

Publicerat den oktober 13, 2012 av mattelararen

An equation containing the derivative of a function is called a differential equation. Depending on the order of the derivatives it is of the first, second or higher order. The simplest differential equation is an ordinary linear homogenous differential equation of the first order: y’ + … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), Uncategorized | Märkt , , | 1 kommentar

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

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

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

Divergence and curl of vectorfields

Publicerat den maj 11, 2012 av mattelararen

According to the Helmholtz-theorem a vectorfield is completely defined by the divergence and  curl of the vectorfield. the divergence is a measure of the strength of the source of the vectorfield whereas the degree of rotation of the field is given … Fortsätt läsa →

Publicerat i Calculus, Uncategorized, Vectors | 1 kommentar

Vectorproducts

Publicerat den maj 4, 2012 av mattelararen

Vectors can be multiplied in two ways: 1. The scalar product gives product of a vector and the projection of  the other vector upon the first one. This is calculated according to a b = ab cos(v) The result is a … Fortsätt läsa →

Publicerat i Calculus, Uncategorized | Märkt , | 2 kommentarer

Numerical methods for calculation of integrals

Publicerat den april 27, 2012 av mattelararen

For many functions it is impossible to find a primtive function and therefore it is impossible to use the fundamental theorem of calculus to solve the integral. Luckily there are ways to cope with such circumstances with the aid of … Fortsätt läsa →

Publicerat i Calculus, matematik 5 | Märkt | Lämna en kommentar

Symmetries, translations and dilatations

Publicerat den april 16, 2012 av mattelararen

A good definition of symmetry was given by the mathematician Hermann Weyl:  An object is symmetrical  if, after you performed an operation on it, it still looks the same as it did before. A function can be moved in the … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), Uncategorized | Lämna en kommentar

Properties of integrals

Publicerat den april 11, 2012 av mattelararen

 the integral of a linear combination is the linear combination of the integrals, If a > b then define 3. Additivity of integration on intervals. If c is any element of [a, b], then 4. Upper and lower bounds. An … Fortsätt läsa →

Publicerat i Calculus, matematik 3c, matematik 4 | Märkt | Lämna en kommentar