Kategoriarkiv: Calculus

l´Hôpital’s rules

sin(x)/x = 1 when x approaches infinity. Direct substitution of x=0 gives the indeterminate form 0/0. The limit of an indeterminate form can be any number. For instance kx/x= 0 , |x|/x2= &inf; as x tends towards infinty. Many indeteminate … Läs mer

Publicerat i Calculus, matematik 3c, matematik 4 | Märkt , | 3 kommentarer

Rotationskroppar

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. … Läs mer

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

Lagrangian mechanics

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. The variables, or degrees of freedom, can be … Läs mer

Publicerat i Calculus, Fysik 2, Mathematical physics | Märkt , , | Lämna en kommentar

Spherical harmonics

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} … Läs mer

Publicerat i Calculus | Märkt , , | Lämna en kommentar

Thermodynamics 2 Entropy

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 … Läs mer

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

MacLaurin-polynomials

→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) = … Läs mer

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

Integration by parts

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 … Läs mer

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

Techniques of integration

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 … Läs mer

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

Complex integral solved with Cauchy’s integral formula

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

Partial differential equations

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 … Läs mer

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