Quantum Calculus

Name: Quantum Calculus
Price: 43.45 USD
Availability: InStock
ISBN: 9780387953410

ISBN-10: 0387953418

ISBN-13: 9780387953410

Edition: 2002

Authors: Pokman Cheung, Victor G. Kac

List price: $69.99

This item qualifies for FREE shipping.

30 day, 100% satisfaction guarantee!

Buy new: $67.44

Marketplace

3 new & used from $43.45

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

Description:

Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by Professor Kac over the last few years at MIT.

Book details

List price: $69.99
Copyright year: 2002
Publisher: Springer New York
Publication date: 11/16/2001
Binding: Paperback
Pages: 112
Size: 6.10" wide x 9.25" long x 0.25" tall
Weight: 0.484
Language: English



Introduction



q-Derivative and h-Derivative



Generalized Taylor's Formula for Polynomials



q-Analogue of (x - a)[superscript n], n an Integer, and q-Derivatives of Binomials



q-Taylor's Formula for Polynomials



Gauss's Binomial Formula and a Noncommutative Binomial Formula



Properties of q-Binomial Coefficients



q-Binomial Coefficients and Linear Algebra over Finite Fields



q-Taylor's Formula for Formal Power Series and Heine's Binomial Formula



Two Euler's Identities and Two q-Exponential Functions



q-Trigonometric Functions



Jacobi's Triple Product Identity



Classical Partition Function and Euler's Product Formula



q-Hypergeometric Functions and Heine's Formula



More on Heine's Formula and the General Binomial



Ramanujan Product Formula



Explicit Formulas for Sums of Two and of Four Squares



Explicit Formulas for Sums of Two and of Four Triangular Numbers



q-Antiderivative



Jackson Integral



Fundamental Theorem of q-Calculus and Integration by Parts



q-Gamma and q-Beta Functions



h-Derivative and h-Integral



Bernoulli Polynomials and Bernoulli Numbers



Sums of Powers



Euler-Maclaurin Formula



Symmetric Quantum Calculus


App.: A List of q-Antiderivatives


Literature


Index