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.