Author Archives: mattelararen

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About mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics

Hyperbolic functions

Publicerat den juni 8, 2013 av mattelararen

The hyperbolic functions have similar names to the trigonometric functions, but they are defined in terms of the exponential function. In this unit I define the three main hyperbolic functions, and sketch their graphs. I also discuss some identities relating … Fortsätt läsa →

Publicerat i Geometri, Uncategorized | Märkt | Lämna en kommentar

Matrices

Publicerat den maj 19, 2013 av mattelararen

A matrix is a square or retangular array of numbers or function of numbers that obeys certain laws. The numbers are distinguished by two subscripts ij. The first indicating the row and the second indicating the column (vertical). in which … Fortsätt läsa →

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

Spherical harmonics

Publicerat den maj 12, 2013 av mattelararen

The spherical harmonics are functions describing the angular dependence of many physical problems e.g solutions to the Schrödinger equation for the hydrogen atom. If the latitiude is denoted by v and x= cosv then  the equation is (d/dx){(1 – x2)dPndx} … Fortsätt läsa →

Publicerat i Calculus | Märkt , , | Lämna en kommentar

The Meton Cycle

Publicerat den april 18, 2013 av mattelararen

The ancient greek astronomer Meton observed that the lunar phases are repeated on the same weekday once every 19th year. therefore this period is referred to as the Meton Cycle.  Theses days were carved in a stone at Forum Romanum in ancinet … Fortsätt läsa →

Publicerat i Astronomy | Lämna en kommentar

The KAngaroocompetition 2013

Publicerat den april 3, 2013 av mattelararen

On March 21th I participated in the Kängurutävlingen arranged by the Royal Swedish academy of Science. My result was 45p. See examples from last years competition here

Publicerat i Uncategorized | Lämna en kommentar

Eulers polyederformula

Publicerat den mars 27, 2013 av mattelararen

Definition: A graph is called planar if can be drawn in one plane without any arcs crossing each other. Definintion: The graph G = (V,E) is called bipartite if the nodes can be divided into two disjunct parts V = … Fortsätt läsa →

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

More Graphtheory

Publicerat den mars 19, 2013 av mattelararen

More graph-terminology: The distance between two nodes is the shortest distance between the two nodes. A graph that starts and ends in the same node is called a cycle or a closed circuit. A simple path trespasses every node only … Fortsätt läsa →

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

Graph theory

Publicerat den mars 18, 2013 av mattelararen

Complicated relations between different objects/phenomena can be visualized with graphs. a graph G is defined as an ordered pair of sets G = (V,E). where E is an ordered pair {a, b}, a,b ∈V. e.g. constitutes a pair of element … Fortsätt läsa →

Publicerat i Uncategorized | Lämna en kommentar

Combinations

Publicerat den mars 15, 2013 av mattelararen

It is called acombination of r elements if the order of the elements in a selection of r elements out of n elements is irrelevant and redundance is not allowed. Another way of ststing this is to say that all … Fortsätt läsa →

Publicerat i Gymnasiematematik(high school math), matematik 1c, matematik 5, Probability, Uncategorized | Märkt | Lämna en kommentar

Permutations

Publicerat den mars 14, 2013 av mattelararen

A permutation is an ordered arrangement of objects. Ex. If you have n objects to choose from you have n options for the first object, (n-1) options for teh second, (n-2) for the third and so on. Therefore the number … Fortsätt läsa →

Publicerat i matematik 1c, Uncategorized | Lämna en kommentar