Category Archives: Gymnasiematematik(high school math)

Solving polynomial equations, descartes theorem

Publicerat den februari 28, 2013 av mattelararen

A large part of the algebra courses at upper secondary-school level are devoted to solving equations or factorization of polynomials. This is often the same thing. Some terminology. All of these are the same: Solving a polynomial equation. Finding roots … Fortsätt läsa →

Publicerat i Algebra, Gymnasiematematik(high school math), matematik 2c | Märkt , , , , | Lämna en kommentar

The area of the circle

Publicerat den februari 27, 2013 av mattelararen

‘Minute Physics’ derives the area of the circle with a string of pearls and a ruler:

Publicerat i Geometri, Gymnasiematematik(high school math) | Märkt , | Lämna en kommentar

Modular arithmetic & the Chinese Rest Theorem

Publicerat den februari 21, 2013 av mattelararen

modular arithmetic (sometimes called clock arithmetic) is a system of arithmetic for integers, where numbers ”wrap around” upon reaching a certain value—the modulus. An example of this is the clock which starts repeating itself when it has reached 12. Therefore it … Fortsätt läsa →

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

Exceldiagrams

Publicerat den februari 19, 2013 av mattelararen

Excel is a versatile programme for e.g. statisitics. Learn more!

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

Conical sections

Publicerat den februari 11, 2013 av mattelararen

The force of gravity determines the trajectories of the celestial bodies. Mathematical analysis reveals that there are three types of trajectories possible for a body moving in a gravitational field determined by Newton’s law of gravity. If one of the … Fortsätt läsa →

Publicerat i Geometri, Gymnasiematematik(high school math), matematik 2c | Märkt , , , | Lämna en kommentar

MacLaurin-polynomials

Publicerat den december 12, 2012 av mattelararen

→Taylor-expansion is a method of approximating a function f(x) around a point a with a polynomial of the argument x in the vicinity of a. The polynomial itself consists of the derivatives of the function of various orders. Tn(x) = … Fortsätt läsa →

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

Integration by parts

Publicerat den december 4, 2012 av mattelararen

Integration by  parts can be regarded as the inverse to the product rule for differentiation. Suppose U(X) and V(x) are  two differentiable functions. According to the product rule dU(x)V(x)/dx = U(x) dV(x)/dx + V(x)dU(x)/dx = U(x) dV(x)/dx+ V(x)dU(x)/dx Integrating both … Fortsätt läsa →

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

Techniques of integration

Publicerat den november 29, 2012 av mattelararen

If the primitive function of an integrand can be found it is always best to take advantage of the fundamental theorem of calculus. In order to be able to determine integrals whose indefinte integrals(primitive functions)  cannot be found immediately some … Fortsätt läsa →

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

Diophantine equations

Publicerat den november 21, 2012 av mattelararen

A Diophantine equation is an equation in which only integers are allowed as coefficients. Also the solutions must be integers. This can be written as ax + by = c. This is a linear diophantine equation. For non-linar diophantine equations … Fortsätt läsa →

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

Invited speaker at Matematikbromötet 2012

Publicerat den november 19, 2012 av mattelararen
Publicerat i Gymnasiematematik(high school math), Uncategorized | Märkt , | Lämna en kommentar