Kategoriarkiv: Calculus

Partial differential equations

A Partial differential equation is a differential equation that contains unknown multivariable functions and their partial derivatives. They are used to formulate problems involving functions of several variables. They can either be solved by hand or used to create a relevant computer … Läs mer

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

Differential equations of the second order

Second order differential equations of the homogen type y” (x)+ a y'(x) + by(x) = 0 are possible to solve with the aid of the characteristic equation r2 + a r +b =0 If this have the roots r1 and … Läs mer

Publicerat i Calculus, matematik 4, matematik 5 | Märkt | 2 kommentarer

Separable variables

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 … Läs mer

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

Differential equations

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’ + … Läs mer

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

Cauchy’s integralformula

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 … Läs mer

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

The Cauchy-Riemann equations

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 … Läs mer

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

Bessel functions

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 … Läs mer

Publicerat i Calculus | Märkt , | 2 kommentarer

Divergence and curl of vectorfields

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 … Läs mer

Publicerat i Calculus, Uncategorized, Vectors | 1 kommentar

Vectorproducts

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 … Läs mer

Publicerat i Calculus, Uncategorized | Märkt , | 2 kommentarer

Numerical methods for calculation of integrals

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 … Läs mer

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