Discrete Calculus Methods for Counting /

• Main Authors: Mariconda, Carlo (Author), Tonolo, Alberto (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2016.
• Series: UNITEXT, 103
• Subjects: Mathematics.; Approximation theory.; Combinatorics.; Approximations and Expansions.

This book provides an introduction to combinatorics, finite calculus, formal series, recurrences, and approximations of sums. Readers will find not only coverage of the basic elements of the subjects but also deep insights into a range of less common topics rarely considered within a single book, su...

Table of Contents:

• 1 Let’s Learn to Count
• 2 Counting Sequences and Collections
• 3 Occupancy Constraints
• 4 Inclusion/Exclusion
• 5 Stirling Numbers and Eulerian Numbers
• 6 Manipulation of Sums
• 7 Formal Power Series
• 8 Generating Formal Series and Applications
• 9 Recurrence Relations
• 10 Linear Recurrence Relations
• 11 Symbolic Calculus
• 12 The Euler-Maclaurin Formulas of Order 1 and 2
• 13 The Euler-Maclaurin Formula of Arbitrary Order
• 14 Cauchy and Riemann Sums, Factorials, Ramanujan Numbers and their Approximations
• 15 Tables and Formulas
• 16 Appendix A.