Integral, Measure and Derivative


Book Description

This treatment examines the general theory of the integral, Lebesque integral in n-space, the Riemann-Stieltjes integral, and more. "The exposition is fresh and sophisticated, and will engage the interest of accomplished mathematicians." — Sci-Tech Book News. 1966 edition.




Becoming Europe


Book Description

“We’re becoming like Europe.” This expression captures many Americans’ sense that something has changed in American economic life since the Great Recession’s onset in 2008: that an economy once characterized by commitments to economic liberty, rule of law, limited government, and personal responsibility has drifted in a distinctly “European” direction. Americans see, across the Atlantic, European economies faltering under enormous debt; overburdened welfare states; governments controlling close to fifty percent of the economy; high taxation; heavily regulated labor markets; aging populations; and large numbers of public-sector workers. They also see a European political class seemingly unable—and, in some cases, unwilling—to implement economic reform, and seemingly more concerned with preserving its own privileges. Looking at their own society, Americans are increasingly asking themselves: “Is this our future?” In Becoming Europe, Samuel Gregg examines economic culture—the values and institutions that inform our economic priorities—to explain how European economic life has drifted in the direction of what Alexis de Tocqueville called “soft despotism,” and the ways in which similar trends are manifesting themselves in the United States. America, Gregg argues, is not yet Europe; the good news is that economic decline need not be its future. The path to recovery lies in the distinctiveness of American economic culture. Yet there are ominous signs that some of the cultural foundations of America’s historically unparalleled economic success are being corroded in ways that are not easily reversible—and the European experience should serve as the proverbial canary in the coal mine.







Resolution of Curve and Surface Singularities in Characteristic Zero


Book Description

The Curves The Point of View of Max Noether Probably the oldest references to the problem of resolution of singularities are found in Max Noether's works on plane curves [cf. [148], [149]]. And probably the origin of the problem was to have a formula to compute the genus of a plane curve. The genus is the most useful birational invariant of a curve in classical projective geometry. It was long known that, for a plane curve of degree n having l m ordinary singular points with respective multiplicities ri, i E {1, . . . , m}, the genus p of the curve is given by the formula = (n - l)(n - 2) _ ~ "r. (r. _ 1) P 2 2 L. . ,. •• . Of course, the problem now arises: how to compute the genus of a plane curve having some non-ordinary singularities. This leads to the natural question: can we birationally transform any (singular) plane curve into another one having only ordinary singularities? The answer is positive. Let us give a flavor (without proofs) 2 on how Noether did it • To solve the problem, it is enough to consider a special kind of Cremona trans formations, namely quadratic transformations of the projective plane. Let ~ be a linear system of conics with three non-collinear base points r = {Ao, AI, A }, 2 and take a projective frame of the type {Ao, AI, A ; U}.







Calculus: Early Transcendentals Single Variable 10e Binder Ready Version + WileyPLUS Registration Card


Book Description

This package includes a three-hole punched, loose-leaf edition of ISBN 9781118129258 and a registration code for the WileyPLUS course associated with the text. Before you purchase, check with your instructor or review your course syllabus to ensure that your instructor requires WileyPLUS. For customer technical support, please visit http://www.wileyplus.com/support. WileyPLUS registration cards are only included with new products. Used and rental products may not include WileyPLUS registration cards. Anton, Bivens & Davis latest issue of Calculus Early Transcendentals Single Variable continues to builds upon previous editions to fulfill the needs of a changing market by providing flexible solutions to teaching and learning needs of all kinds. This 10th edition continues to focus on and incorporate new ideas that have withstood the objective scrutiny of many skilled and thoughtful instructors and their students. This 10th edition retains Anton's trademark clarity of exposition, sound mathematics, excellent exercises and examples, and appropriate level.