Category Archives: Calculus

Rotationskroppar

Publicerat den september 26, 2013 av mattelararen

Ett elegant sätt att beräkna volymen av kroppar som genereras av en känd funktion s.k. rotationskroppar, är med hjälp av tvärsnittsformeln. Tanken är att en kurva med känd funktion y=f(x) roteras runt en av koordinataxlarna och därvid genereras en rotationskropp. … Fortsätt läsa →

Publicerat i Calculus, Gymnasiefysik(high school physics), matematik 4 | Märkt , | Lämna en kommentar

Lagrangian mechanics

Publicerat den augusti 5, 2013 av mattelararen

In functional analysis the variable itself is a function. This is used e.g. in the Lagrangian formulation of mechanics where one derives the Lagrangian i.e. L = kinetic energy – potential energy. This transforms classical Newtonian mechanics into differentialcalculus. The … Fortsätt läsa →

Publicerat i Advanced, Calculus, Fysik 2, Mathematical physics | 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

Thermodynamics 2 Entropy

Publicerat den januari 10, 2013 av mattelararen

A collection of rembrandts self-portraits serve as an illustration of the passage of time When left to itself snow spontaneously would never build a snowman. It will only form different kinds of heaps . This can be undestood as the … Fortsätt läsa →

Publicerat i Calculus, Gymnasiefysik(high school physics), Thermodynamics | 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

Complex integral solved with Cauchy’s integral formula

Publicerat den november 6, 2012 av mattelararen

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Publicerat i Calculus, Imaginary numbers, Uncategorized | Märkt , | Lämna en kommentar

Partial differential equations

Publicerat den oktober 25, 2012 av mattelararen

A Partial differential equation is a differential equation that contains unknown multivariable functions and their partial derivatives. They are used to formulate problems involving functions of several variables. They can either be solved by hand or used to create a relevant computer … Fortsätt läsa →

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