|
Showing 1 - 6 of
6 matches in All Departments
Aspects of Integration: Novel Approaches to the Riemann and
Lebesgue Integrals is comprised of two parts. The first part is
devoted to the Riemann integral, and provides not only a novel
approach, but also includes several neat examples that are rarely
found in other treatments of Riemann integration. Historical
remarks trace the development of integration from the method of
exhaustion of Eudoxus and Archimedes, used to evaluate areas
related to circles and parabolas, to Riemann’s careful definition
of the definite integral, which is a powerful expansion of the
method of exhaustion and makes it clear what a definite integral
really is. The second part follows the approach of Riesz and Nagy
in which the Lebesgue integral is developed without the need for
any measure theory. Our approach is novel in part because it uses
integrals of continuous functions rather than integrals of step
functions as its starting point. This is natural because Riemann
integrals of continuous functions occur much more frequently than
do integrals of step functions as a precursor to Lebesgue
integration. In addition, the approach used here is natural because
step functions play no role in the novel development of the Riemann
integral in the first part of the book. Our presentation of the
Riesz-Nagy approach is significantly more accessible, especially in
its discussion of the two key lemmas upon which the approach
critically depends, and is more concise than other treatments.
Features Presents novel approaches designed to be more accessible
than classical presentations. A welcome alternative approach to the
Riemann integral in undergraduate analysis courses. Makes the
Lebesgue integral accessible to upper division undergraduate
students. How completion of the Riemann integral leads to the
Lebesgue integral. Contains a number of historical insights. Gives
added perspective to researchers and postgraduates interested in
the Riemann and Lebesgue integrals.
Sturm-Liouville problems arise naturally in solving technical
problems in engineering, physics, and more recently in biology and
the social sciences. These problems lead to eigenvalue problems for
ordinary and partial differential equations. Sturm-Liouville
Problems: Theory and Numerical Implementation addresses, in a
unified way, the key issues that must be faced in science and
engineering applications when separation of variables, variational
methods, or other considerations lead to Sturm-Liouville eigenvalue
problems and boundary value problems.
In the mid-19th century, Asian-Americans flocked to America and
provided cheap immigrant labour. Their numbers grew so high and
fast that several restrictive immigration laws were enacted, and
were not eased until the mid-20th century. Since that time,
Asian-Americans have consistently been cited as one of the fastest
growing segments of the population and seem on the cusp of
increased political activity and influence. Despite the rise in
Asian-American citizens since the 1960s, however, there has not
been a corresponding growth of political participation. Voter
turnout is low, and the number of Asian-American representatives
has lagged. However, Asian-Americans have often been notable
political donors and campaign financiers, indicating a
behind-the-scenes political influence. As the Asian population
increases in the nation, so do the chances of their wielding wider
impact on election results and the issues of importance nationally.
In order to understand the development of the Asian-American
political block, this book discusses the history of Asian
immigration and political participation. Using reports based on
census data, the patterns of Asian-American behaviour are assessed.
No segment of American society can be ignored, and this book is
necessary for coming to understand the implications of and history
behind the political influence of a significant slice of the
American pie.
|
You may like...
Loot
Nadine Gordimer
Paperback
(2)
R383
R318
Discovery Miles 3 180
|