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Garcia-Pacheco

Abstract Calculus

A Categorical Approach

Medium: Buch
ISBN: 978-0-367-76220-9
Verlag: Taylor & Francis Ltd (Sales)
Erscheinungstermin: 09.09.2021
Lieferfrist: bis zu 10 Tage
Abstract Calculus: A Categorical Approach provides an abstract approach to calculus. It is intended for graduate students pursuing PhDs in pure mathematics but junior and senior researchers in basically any field of mathematics and theoretical physics will also be interested. Any calculus text for undergraduate students majoring in engineering, mathematics or physics deals with the classical concepts of limits, continuity, differentiability, optimization, integrability, summability, and approximation. This book covers the exact same topics, but from a categorical perspective, making the classification of topological modules as the main category involved.

Features

- Suitable for PhD candidates and researchers

- Requires prerequisites in set theory, general topology, and abstract algebra, but is otherwise self-contained

Dr. Francisco Javier García-Pacheco is a full professor and Director of the Departmental Section of Mathematics at the College of Engineering of the University of Cádiz, Spain.

Produkteigenschaften


  • Artikelnummer: 9780367762209
  • Medium: Buch
  • ISBN: 978-0-367-76220-9
  • Verlag: Taylor & Francis Ltd (Sales)
  • Erscheinungstermin: 09.09.2021
  • Sprache(n): Englisch
  • Auflage: 1. Auflage 2021
  • Serie: Chapman & Hall/CRC Monographs and Research Notes in Mathematics
  • Produktform: Gebunden
  • Gewicht: 730 g
  • Seiten: 396
  • Format (B x H x T): 156 x 234 x 22 mm
  • Ausgabetyp: Kein, Unbekannt

Autoren/Hrsg.

Autoren

Garcia-Pacheco, Francisco Javier

I. Functional Calculus. 1. Functions. 1.1. Set Theory. 1.2. Relations. 1.3. Operations. 2. Limits. 2.1. Limits of Filters and Functions. 2.2. Limits of Nets and Sequences. 3. Continuity. 3.1. Types of Continuity. 3.2. Topological Operations. II. Differential Calculus. 4. Differentiability. 4.1 Derivations. 4.2. Derivative. 4.3. Differential Manifolds. 5. Optimization. 5.1. Multiobjective Optimization. 5.2. Convex Optimization. 5.3. Normed Optimization. III. Integral Calculus. 6. Summability. 6.1. Sequences and Series. 6.2. Convergence and Summability Methods. 7. Integrability. 7.1. Measures. 7.2. Integration. IV. Appendix. A. Category Theory. Bibliography. Index.