Elementary Differential Calculus on Discrete and Hybrid Structures 1st Edition by Howard A Blair, David W Jakel, Robert J Irwin, Angel Rivera ISBN 9783540727347

Elementary Differential Calculus on Discrete and Hybrid Structures 1st Edition by Howard A Blair, David W Jakel, Robert J Irwin, Angel Rivera – Ebook PDF Instant Download/Delivery. 9783540727347
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ISBN 10: 
ISBN 13: 9783540727347
Author: Howard A Blair, David W Jakel, Robert J Irwin, Angel Rivera

We set up differential calculi in the Cartesian-closed category CONV of convergence spaces. The central idea is to uniformly define the 3-place relation __ is a differential of __ at __ for each pair of convergence spaces X,Y in the category, where the first and second arguments are elements of Hom(X,Y) and the third argument is an element of X, in such a way as to (1) obtain the chain rule, (2) have the relation be in agreement with standard definitions from real and complex analysis, and (3) depend only on the convergence structures native to the spaces X and Y. All topological spaces and all reflexive directed graphs (i.e. discrete structures) are included in CONV. Accordingly, ramified hybridizations of discrete and continuous spaces occur in CONV. Moreover, the convergence structure within each space local to each point, individually, can be discrete, continuous, or hybrid.

Elementary Differential Calculus on Discrete and Hybrid Structures 1st Table of contents:

• Foundations of Differential Calculus
• Differential Calculus on Discrete Structures
• Differential Calculus on Hybrid Systems
• Numerical Methods for Discrete and Hybrid Systems
• Applications of Discrete and Hybrid Calculus
• Challenges and Advanced Topics
• Conclusion and Future Work

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