Handbook of algorithms for physical design automation part 26 ppt
Handbook of mathematics for engineers and scienteists part 14 ppt
... midradius,
and δ = R – r is the width of the annulus.
The area of the part of the annulus contained in a sector of central angle ϕ,givenin
degrees (see Fig. 3.22b), is given by the formula
S =
πϕ
360
(R
2
– ... volume of a pyramid is given by the formula
V =
1
3
SH,(3.2.2.3)
where S is the area of the base and H is the altitude of the pyramid.
The apex of a pyramid is projec...
Handbook of mathematics for engineers and scienteists part 18 pptx
... equations of a curve.
Parametric equations of a curve on the plane have the form
x = ϕ(t), y = ψ(t), (4.2.1.4)
where x and y are treated as the coordinates of some point A for each value of the ... in the pencil are called equations of the pencil.
88 ANALYTIC GEOMETRY
4.2.2. Main Problems of Analytic Geometry for Curves
4.2.2-1. Construction of equation for given curve.
Su...
Handbook of mathematics for engineers and scienteists part 21 pptx
... The points of
intersection of a second-order curve with its principal axes are called its vertices.
The directions of principal axes coincide with the directions of the eigenvectors of the
symmetric ... directions of principal axes and of their conjugate chords are called the principal
directions of a second-order curve. The angle between the positive direction of the axis O...
Handbook of mathematics for engineers and scienteists part 22 ppt
... families
of coordinate surfaces such that exactly one surface of each family passes through each
point of space. The position of a point in such a system is determined by the values of the
parameters ... Products of Vectors
4.5.3-1. Scalar product of two vectors.
The scalar product of two vectors is defined as the product of their absolute values times
the cosine of the ang...
Handbook of mathematics for engineers and scienteists part 23 pptx
... with respect to the point O of a force F applied at a point M is the cross product
of the position vector
−−→
OM by the force F; i.e., M =
−−→
OM × F.
4.5.3-3. Conditions for vectors to be parallel ... equation of plane.
The general (complete) equation of a plane has the form
Ax + By + Cz + D = 0,orr ⋅ N + D = 0.(4.6.1.3)
It follows from (4.6.1.1) that D =–Ax
0
– By
0
– Cz
0
. If on...
Handbook of mathematics for engineers and scienteists part 26 ppsx
... the coefficients, has 1 of 17 canonical forms, each of which is associated with a
certain class of quadrics (see Table 4.3).
4.7.2-3. Invariants of quadrics.
The shape of a quadric can be determined ... 4.56a.
Y
Y
ZZ
()a ()b
X
X
O
O
Figure 4.56. Families of rulings for one-sheeted hyperboloid (a) and for hyperbolic paraboloid (b).
Properties of rulings of the one-sheeted hy...
Handbook of mathematics for engineers and scienteists part 39 ppt
... explicitly by means of a formula (or several formulas) depending on the
argument x; for instance, y = 2 sin x + 1.
Implicit definition of a function consists of using an equation of the form F (x, y)=0,
from ... sequence.
The limit (finite or infinite) of a subsequence of a given sequence x
n
is called a partial limit
of x
n
. In the set of all partial limits of any sequence...
Handbook of mathematics for engineers and scienteists part 43 ppt
... o(ρ)forsmallΔx and Δy is widely used for approximate
calculations, in particular, for fi nding errors in numerical calculations of values of a function.
Example 1. Suppose that the values of the ... Variables
For the sake of brevity, we consider the case of a function of two variables. However, all
statements can be easily extended to the case of n variables.
6.3.2-1. Total...
Handbook of mathematics for engineers and scienteists part 56 pptx
... constant,
|f
(n)
(x)| ≤ M for all n.
Uniqueness of the Taylor series expansion. For a function f (x) that can be represented
as the sum of a power series, the coefficients of this series are determined ... representations of the remainder in the Taylor formula are given in Paragraph 6.2.4-4.
8.4. FOURIER SERIES 357
8.3.3-4. Simplest summation formulas for power series.
Suppose th...
Handbook of mathematics for engineers and scienteists part 59 ppt
... tangency of the envelope
to a curve of the family is called a characteristic point of the curve of the family (Fig. 9.13).
Figure 9.13. The envelope of the family of curves.
9.1. THEORY OF CURVES ... evolvent.
The locus of centers of curvature of a curve is called its evolute.Ifacurveisdefined via a
natural parameter s, then the position vector of a point of the evolute...
Từ khóa:
- a comparison of algorithms for the multivariate l1median
- a comparison of algorithms for vertex normal computation
- a comparison of algorithms for fitting the parafac model
- a comparison of algorithms for subpixel peak detection
- code of practice for buildable design
- code of practice for drainage design
- code of practice for anchor design and installation
- code of practice for foundation design
- code of practice for the design construction operation management