Translation of "Taylor expansion" in German

The performance of the comparison operation is based in this case on the Taylor series expansion.

Usually applied formula contains only elements of first order Taylor expansion.

Looking at the Taylor expansion around formula_20, we see that the first term that does not vanish is the quadratic one, so that we can requireformula_25,orformula_26,orformula_27.

Hence, the same expressions as in the Taylor expansion of equations (8) and (9) occur once more.

The final term in equation (10) represents an offset value that results from the Taylor series expansion.

Equation (10), which is linearized by the Taylor series expansion, can also be written, rearranged, as EPMATHMARKEREP where W i,k again represent weighting factors and C k is an offset value corresponding to the hypothesis H k .

In the case of a Kalman filter, distinction is made between a kinematic model variant which is based on a Taylor expansion of the current tilt angle, and a dynamic model variant which more precisely replicates the behaviour of the system specifically in the time periods in which no measurement values are provided.

Then I expanded the result in powers of this distortion (Taylor expansion) and I realized, as far as I could perform the expansion, that the boundary was the same for all n-2 different densities.

In an alternative simplification of equation (8), a Taylor series expansion of equation (8) about an offset sensor value Y j0 can be performed, which can be expressed by the equation

Equation (6) shows the Taylor series expansion for the sine function, and equation (7) shows the Taylor series expansion for the cosine function.

In every case in the range of small changes from a reference pose, the transformation can be approximated by a linear Taylor series expansion.

From a mathematical view it is a Taylor expansion of the radical with termination after the first expansion.

However if higher order partial derivatives with respect to parameters exist and uncertainties of input parameters are large, then one can expect, that neglected remainder of Taylor expansion will have significant value.

Course contents: The students know real and complex numbers, sequences and series, differential and integral calculus for real functions of a real variable Taylor expansion.

Differential and integral calculus for functions with multiple variables: Recapitulation of vector calculus, scalar fields, vector fields, partial differentiation, gradient, total differential, directional derivative, expanded chain rule, Taylor expansion, relative extreme values of functions with multiple variables, curves in Rn, line integral, path independency and antiderivative, double and surface integrals, trifold and volume integrals, fundamentals of vector analysis (gradient, divergence, rotation).

In order to allow the minimization of the non-linear functional, D is linearized using the Taylor series expansion and regularized with R. This leads either to a regularized gradient descent method or to a regularized Newtonian method.

For example, the values obtained metrologically or by means of field calculation can be represented by approximation functions The reference values can be approximated, for instance, by a polynomial approximation and/or by a Taylor series expansion.