Category Archives: matematik 5

svensk gymnasiekurs

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

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

Multiplication and additionprinciple

Publicerat den mars 14, 2013 av mattelararen

If you are in a situation where you have two make two consecutive choices and the first one can be selected from n alternatives and the second can be selected from m alternatives the total number of possible combinations is … Fortsätt läsa →

Publicerat i Gymnasiematematik(high school math), matematik 1c, matematik 4, matematik 5, Probability | Märkt , | Lämna en kommentar

Venn-diagrams

Publicerat den november 25, 2012 av mattelararen

A good way of illustrating probabilities is to use so-called Venn-diagrams. In effect this means representing the probability of an event with circles. Mutually excluding events can be represented by two separate non-overlapping ciecles. P(A) + P(B) = P(A U … Fortsätt läsa →

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

Differential equations of the second order

Publicerat den oktober 23, 2012 av mattelararen

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 … Fortsätt läsa →

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

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

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

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