This second edition of Sources in the Development of Mathematics, now in two volumes, traces the development of series and products from 1380-2000 through the interconnected concepts and results of unsung and celebrated mathematicians. Extensive context, detail, and primary source material are added, with Volume 1 accessible to undergraduates.
This second edition of Sources in the Development of Mathematics, now in two volumes, traces the development of series and products from 1380-2000 through the interconnected concepts and results of unsung and celebrated mathematicians. Extensive context, detail, and primary source material are added, with Volume 1 accessible to undergraduates.
Ranjan Roy is the Ralph C. Huffer Professor of Mathematics and Astronomy at Beloit College, Wisconsin, and has published papers and reviews on Riemann surfaces, differential equations, fluid mechanics, Kleinian groups, and the development of mathematics. He has received the Allendoerfer Prize, the Wisconsin MAA teaching award, and the MAA Haimo Award for Distinguished Mathematics Teaching, and was twice named Teacher of the Year at Beloit College. He co-authored Special Functions (2001) with George Andrews and Richard Askey and co-authored chapters in the NIST Handbook of Mathematical Functions (2010); he also authored Elliptic and Modular Functions from Gauss to Dedekind to Hecke (2017) and the first edition of this book, Sources in the Development of Mathematics (2011).
Inhaltsangabe
Volume 1: 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 ¿(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 Volume 2: 25. q-series 26. Partitions 27. q-Series and q-orthogonal polynomials 28. Dirichlet L-series 29. Primes in arithmetic progressions 30. Distribution of primes: early results 31. Invariant theory: Cayley and Sylvester 32. Summability 33. Elliptic functions: eighteenth century 34. Elliptic functions: nineteenth century 35. Irrational and transcendental numbers 36. Value distribution theory 37. Univalent functions 38. Finite fields Bibliography Index.
Volume 1: 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 ¿(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 Volume 2: 25. q-series 26. Partitions 27. q-Series and q-orthogonal polynomials 28. Dirichlet L-series 29. Primes in arithmetic progressions 30. Distribution of primes: early results 31. Invariant theory: Cayley and Sylvester 32. Summability 33. Elliptic functions: eighteenth century 34. Elliptic functions: nineteenth century 35. Irrational and transcendental numbers 36. Value distribution theory 37. Univalent functions 38. Finite fields Bibliography Index.
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