Author Archives: mattelararen

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About mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics

More vectorcalculus: Gauss theorem and Stokes theorem

Publicerat den maj 25, 2012 av mattelararen

Since the divergence of a vectorfield provides us with the number of field lines radiating outward from the source of the vectorfield it can be intuitively understood that the volume integral of the divergenbde of F equals the surface integral … Fortsätt läsa →

Publicerat i Uncategorized | Lämna en kommentar

Number theory-more on numbers

Publicerat den maj 23, 2012 av mattelararen

De första talen människan använde sig av var förmodligen positiva heltalen de sk. naturliga talen. De användes för att ange kvantiteter av olika ting: fem tomater, 10 persikor etc.. Då människan började med handel kunde man bli skuld satt och … Fortsätt läsa →

Publicerat i Gymnasiematematik(high school math), matematik 1c | Märkt , | 5 kommentarer

The decimalsystem and some terminology

Publicerat den maj 17, 2012 av mattelararen

At this point it  might be wise to take a closer look at the decimalsystem which is the way we use to represent quatities in mathematics. The decimalsystem is a positionsystem (based on powers of ten)  which means that the value of … Fortsätt läsa →

Publicerat i matematik 1c, Uncategorized | Lämna en kommentar

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

Vector algebra-adding and subtacting vectors

Publicerat den april 21, 2012 av mattelararen

The mass of your body is a measure of the amount of matter (atoms) that constitute your body. This number is a quantity that can be pinpointed on the x-axis (or any line of numbers). Such quantities are called scalars.  … Fortsätt läsa →

Publicerat i Advanced | 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

Definite integrals

Publicerat den april 2, 2012 av mattelararen

In a geometrical context the integral can be interpreted as the area between the graph of the integrand f(x) and the x-axis. The idea is to summarize infinitely many infinitely thin rectangles. (An alternative approach to areacomputation is the Lebesgue-integration where you … Fortsätt läsa →

Publicerat i Calculus, Gymnasiematematik(high school math), matematik 3c, matematik 4 | Märkt | 1 kommentar