COURSE IN ANALYSIS, A - VOLUME I: INTRODUCTORY CALCULUS, ANALYSIS OF FUNCTIONS OF ONE REAL VARIABLE

Jacob, Niels; Evans, Kristian P

ISBN 10: 9814689084 / ISBN 13: 9789814689083

Verlag: World Scientific Publishing Company, 2015

Beschreibung

Bestandsnummer des Verkäufers ABLIING23Apr0412070100134

Bibliografische Details

• Titel: COURSE IN ANALYSIS, A - VOLUME I: INTRODUCTORY CALCULUS, ANALYSIS OF FUNCTIONS OF ONE REAL VARIABLE
• Verlag: World Scientific Publishing Company
• Erscheinungsjahr: 2015
• Sprache: Englisch
• ISBN-10: 9814689084
• ISBN-13: 9789814689083
• Einband: Hardcover
• Zustand: New

Über diesen Titel

Inhaltsangabe

 

Part 1 begins with an overview of properties of the real numbers and starts to introduce the notions of set theory. The absolute value and in particular inequalities are considered in great detail before functions and their basic properties are handled. From this the authors move to differential and integral calculus. Many examples are discussed. Proofs not depending on a deeper understanding of the completeness of the real numbers are provided. As a typical calculus module, this part is thought as an interface from school to university analysis.

Part 2 returns to the structure of the real numbers, most of all to the problem of their completeness which is discussed in great depth. Once the completeness of the real line is settled the authors revisit the main results of Part 1 and provide complete proofs. Moreover they develop differential and integral calculus on a rigorous basis much further by discussing uniform convergence and the interchanging of limits, infinite series (including Taylor series) and infinite products, improper integrals and the gamma function. In addition they discussed in more detail as usual monotone and convex functions.

Finally, the authors supply a number of Appendices, among them Appendices on basic mathematical logic, more on set theory, the Peano axioms and mathematical induction, and on further discussions of the completeness of the real numbers.

Remarkably, Volume I contains ca. 360 problems with complete, detailed solutions.

Über die Autorin bzw. den Autor

Charlotte y Peter Fiell son dos autoridades en historia, teoría y crítica del diseño y han escrito más de sesenta libros sobre la materia, muchos de los cuales se han convertido en éxitos de ventas. También han impartido conferencias y cursos como profesores invitados, han comisariado exposiciones y asesorado a fabricantes, museos, salas de subastas y grandes coleccionistas privados de todo el mundo. Los Fiell han escrito numerosos libros para TASCHEN, entre los que se incluyen 1000 Chairs, Diseño del siglo XX, El diseño industrial de la A a la Z, Scandinavian Design y Diseño del siglo XXI.