Series and Products in the Development of Mathematics
Series and Products in the Development of Mathematics
£77.99
GBPThis is the first volume of a two-volume work that traces the development of series and products from 1380 to 2000 by presenting and explaining the interconnected concepts and results of hundreds of unsung as well as celebrated mathematicians. Some chapters deal with the work of primarily one mathematician on a pivotal topic, and other chapters chronicle the progress over time of a given topic. This updated second edition of Sources in the Development of Mathematics adds extensive context, detail, and primary source material, with many sections rewritten to more clearly reveal the significance of key developments and arguments. Volume 1, accessible to even advanced undergraduate students, discusses the development of the methods in series and products that do not employ complex analytic methods or sophisticated machinery. Volume 2 treats more recent work, including deBranges' solution of Bieberbach's conjecture, and requires more advanced mathematical knowledge.
- New edition provides clarifying details from the original papers, additional mathematical context, more results, and includes nearly 500 new bibliographic entries
- Traces the origins of many ideas in areas of interest to applied mathematicians, scientists, and engineers
- Includes in-depth presentations and explanations of original proofs of important mathematical results by several hundred mathematicians, including at least sixty papers of Euler
- Organized by topic, chapters delineate the advancement of the topic over time, with original arguments and details, providing mathematical insight into the topic
- More than 200 exercises; hundreds of detailed proofs and examples within the text
Reviews & endorsements
'Roy is well-known for useful scholarship. This book continues his record.' Robert E. O'Malley, University of Washington
'I often turn to Ranjan Roy for his wide-ranging works on series, both historical and contemporary. His writing is meticulous and a pleasure to read. These volumes can be used to engage undergraduates in the exploration of mathematics through its history and as a resource for anyone working in mathematics.' David M. Bressoud, Director, Conference Board of the Mathematical Sciences
'an impressive source book with original materials from the creators of calculus (with excursions into algebra and number theory) from all over the world.' Pelegrı Viader, MathSciNet
Product details
March 2021Paperback
9781108709453
776 pages
252 × 176 × 42 mm
1.43kg
Available
Table of Contents
- 1. Power series in fifteenth-century Kerala
- 2. Sums of powers of integers
- 3. Infinite product of Wallis
- 4. The binomial theorem
- 5. The rectification of curves
- 6. Inequalities
- 7. The calculus of Newton and Leibniz
- 8. De Analysi per Aequationes Infinitas
- 9. Finite differences: interpolation and quadrature
- 10. Series transformation by finite differences
- 11. The Taylor series
- 12. Integration of rational functions
- 13. Difference equations
- 14. Differential equations
- 15. Series and products for elementary functions
- 16. Zeta values
- 17. The gamma function
- 18. The asymptotic series for ln Γ(x)
- 19. Fourier series
- 20. The Euler–Maclaurin summation formula
- 21. Operator calculus and algebraic analysis
- 22. Trigonometric series after 1830
- 23. The hypergeometric series
- 24. Orthogonal polynomials
- Bibliography
- Index.
