Download A Course in Mathematics for Students of Physics: Volume 1 by Bamberg P. G., Sternberg Sh. PDF

By Bamberg P. G., Sternberg Sh.

After the fundamental theories of differential and fundamental calculus are defined, they're utilized to fascinating difficulties in optics, electronics (networks), electrostatics, wave dynamics and eventually, to classical thermodynamics.

Show description

Read Online or Download A Course in Mathematics for Students of Physics: Volume 1 PDF

Similar mathematics_1 books

Quasiconformal Space Mappings

This quantity is a suite of surveys on functionality idea in euclidean n-dimensional areas situated round the subject of quasiconformal house mappings. those surveys disguise or are regarding a number of subject matters together with inequalities for conformal invariants and extremal size, distortion theorems, L(p)-theory of quasiconformal maps, nonlinear strength conception, variational calculus, price distribution idea of quasiregular maps, topological houses of discrete open mappings, the motion of quasiconformal maps in distinctive periods of domain names, and worldwide injectivity theorems.

Multiple Gaussian Hypergeometric Series

A a number of Gaussian hypergeometric sequence is a hypergeometric sequence in two
or extra variables which reduces to the ordinary Gaussian hypergeometric
series, every time just one variable is non-zero. fascinating difficulties in the
theory of a number of Gaussian hypergeometric sequence consist in constructing
all targeted sequence and in developing their areas of convergence. either of
these difficulties are relatively straight forward for unmarried sequence, they usually have
been thoroughly solved in relation to double sequence. This publication is the 1st to
aim at featuring a scientific (and thorough) dialogue of the complexity
of those difficulties while the measurement exceeds ; certainly, it supplies the
complete resolution of every of the issues in case of the triple Gaussian
hypergeometric sequence.

Learning and Teaching Mathematics in The Global Village: Math Education in the Digital Age

This booklet presents a basic reassessment of arithmetic schooling within the electronic period. It constitutes a brand new frame of mind of ways details and data are processed via introducing new interconnective and interactive pedagogical techniques. Math schooling is catching up on expertise, as classes and fabrics use electronic resources and assets an increasing number of.

Extra info for A Course in Mathematics for Students of Physics: Volume 1

Example text

1; and also the q-binomial coefficient is defined by n k := q [n]q ! [n − k]q ! It is well-known that the polynomials in (1) and (2) are positive and linear, and so their approximation properties can easily be obtain from the classical Korovkin theorem (see [15]). However, in recent years, a nonlinear modification of the classical Bernstein polynomial has been introduced by Bede and Gal [5] (see, also, [4]). Although, of course, the Korovkin theorem fails for this nonlinear operator, they showed in [5] that the new operator has a similar approximation behavior to the classical Bernstein polynomial.

However, so far, there is no such an improvement on the q-Bernstein polynomial given by (2). The aim of the present paper is to fill in this gap in the literature. This paper is organized as follows. In the second section, we construct a nonlinear q-Bernstein operator of max-product kind, and in the third section, we obtain an error estimation for these operators. In the last section, we give an statistical approximation theorem and discuss some concluding remarks. 2 Construction of the Operators In this section, we construct a nonlinear approximation operator by modifying the q-Bernstein polynomial given by (2).

75) Explanation: for x, y ∈ [−1, 0] we get that 1 − x, 1 − y ≥ 1 , and 0 ≤ h 1 − α1h 1 , h 2 − α2h 2 < 1. Hence (1 − x)h 1 −α1h1 , (1 − y)h 2 −α2h2 ≥ 1, and then (1 − x)h 1 −α1h1 (1 − y)h 2 −α2h2 ≥ 1, so that Hence again 1 − (1 − x)h 1 −α1h1 (1 − y)h 2 −α2h2 ≤ 0. (76) 2 L Q ∗∗ n,m (x, y) ≥ 0, for (x, y) ∈ [−1, 0] . (77) References 1. : Monotone approximation by pseudopolynomials. In: Approximation Theory. Academic Press, New York (1991) 2. : Bivariate monotone approximation. Proc. Amer. Math. Soc.

Download PDF sample

A Course in Mathematics for Students of Physics: Volume 1 by Bamberg P. G., Sternberg Sh.

by Brian

Rated 4.44 of 5 – based on 28 votes