Kategoriarkiv: Calculus

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 … Fortsätt läsa

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) = … Fortsätt läsa

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 … Fortsätt läsa

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 … Fortsätt läsa

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 … Fortsätt läsa

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

Differential equations of the second order

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

Separable variables

Differential equations of the form dy/dx = – P(x)/Q(y) then it is possible to separate the variables Q(y)dy = – P(x) dx → Q(y) dy + P(x) dx = 0 Ex y´+ sinx y = 0 y´ = -sinx y dy/y … Fortsätt läsa

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

Differential equations

An equation containing the derivative of a function is called a differential equation. Depending on the order of the derivatives it is of the first, second or higher order. The simplest differential equation is an ordinary linear homogenous differential equation of the first order: y’ + … Fortsätt läsa

Publicerat i Calculus, Gymnasiematematik(high school math), Uncategorized | Märkt , , | 1 kommentar

Cauchy’s integralformula

Theorem Suppose U is an open subset of the complex plane C, f : U → C is a holomorphic function and the closed disk D = { z : | z − z0| ≤ r} is completely contained in U. Let … Fortsätt läsa

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