Author Archives: mattelararen

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About mattelararen

Licentiate of Philosophy in atomic Physics Master of Science in Physics

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

Indefinite integrals

Publicerat den mars 28, 2012 av mattelararen

If you need to calculate the distance travelled when you know the velocity as a function of time , since s'(t) = v(t) you need to be able to perform antiderivation i.e. finding a function whose derivative equals your function. … Fortsätt läsa →

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

Differentiating the natural logarithm, products and quotients

Publicerat den mars 26, 2012 av mattelararen

In order to be able to deduce the derivative of the natural logarithm we resort to using implicit differentiation. Let x= ey(x) Differentiating both sides gives dx/dx = d ey(x)/dx 1=ey(x) dy(x)/dx Solving for dy(x)/dx one obtains dy(x)/dx = 1/ey(x) … Fortsätt läsa →

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

Pi-day

Publicerat den mars 16, 2012 av mattelararen

March the 14th. has officially been named the international π-day to honour this magical number which equals the ratio of the circmference to the diameter for all circles. http://www.wikihow.com/Celebrate-Pi-Day In 1882 the german mathematician Ferdinand Lindemann showed that pi is … Fortsätt läsa →

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

Differentiation of the trigonometric functions

Publicerat den mars 9, 2012 av mattelararen

To be able to differentiate the trigonometric functions one needs some standard limits: With the aid of these and the definition of the derivative it is possible to show that f(x)= sin (x) implies  f ‘(x) = cos(x) and f(x) … Fortsätt läsa →

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

Radians and an attempt at squaring the circle

Publicerat den mars 4, 2012 av mattelararen

That one rotation equals 360 degrees is just a convention, There is nothing partcular about 360 except that it can be divided by many numbers. Another, and a more fruitful, approach to measuring angles is to use the length of … Fortsätt läsa →

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

Trigonometric formulae

Publicerat den februari 28, 2012 av mattelararen

    The trigonometric functions are defined with the aid of the unit circle as follows: The perhaps most important trigonometric formulas from which almost all other trigonometric formulas can be derived are the angle transformation formulas: These formulae can … Fortsätt läsa →

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

Law of Sine Sinussatsen

Publicerat den februari 19, 2012 av mattelararen

One useful trigonometric formula can be obtained by expressing the area of an arbitrary triangle with sinus.   If one then proceeds to divide through by abc/2 one gets the Sinustheorem. sinA/a = sinB/b= sinC/c which is a relation between the sinus of the angle A … Fortsätt läsa →

Publicerat i matematik 3c | Märkt , | Lämna en kommentar