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AuthorKac, Victor. author
TitleQuantum Calculus [electronic resource] / by Victor Kac, Pokman Cheung
ImprintNew York, NY : Springer New York, 2002
Connect tohttp://dx.doi.org/10.1007/978-1-4613-0071-7
Descript IX, 112 p. online resource

SUMMARY

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. Victor Kac is Professor of Mathematics at MIT. He is an author of 4 books and over a hundred research papers. He was awarded the Wigner Medal for his work on Kac-Moody algebras that has numerous applications to mathematics and theoretical physics. He is a honorary member of the Moscow Mathematical Society. Pokman Cheung graduated from MIT in 2001 after three years of undergraduate studies. He is presently a graduate student at Stanford University


CONTENT

1 q-Derivative and h-Derivative -- 2 Generalized Taylorโ{128}{153}s Formula for Polynomials -- 3 q-Analogue of (x &t- a)n, n an Integer, and q-Derivatives of Binomials -- 4 q-Taylorโ{128}{153}s Formula for Polynomials -- 5 Gaussโ{128}{153}s Binomial Formula and a Noncommutative Bino-mial Formula -- 6 Properties of q-Binomial Coefficients -- 7 q-Binomial Coefficients and Linear Algebra over Finite Fields -- 8 q-Taylorโ{128}{153}s Formula for Formal Power Series and Heineโ{128}{153}s Binomial Formula -- 9 Two Eulerโ{128}{153}s Identities and Two q-Exponential Functions -- 10 q-Trigonometrie Functions -- 11 Jacobiโ{128}{153}s Triple Product Identity -- 12 Classical Partition Function and Eulerโ{128}{153}s Product Formula -- 13 q-Hypergeometric Functions and Heineโ{128}{153}s Formula -- 14 More on Heineโ{128}{153}s Formula and the General Binomial -- 15 Ramanujan Product Formula -- 16 Explicit Formulas for Sums of Two and of Four Squares -- 17 Explicit Formulas for Sums of Two and of Four Triangul?r Numbers -- 18 q-Antiderivative -- 19 Jackson Integral -- 20 Fundamental Theorem of q-Calculus and Integration by Parts -- 21 q-Gamma and q-Beta Functions -- 22 h-Derivative and h-Integral -- 23 Bernoulli Polynomials and Bernoulli Numbers -- 24 Sums of Powers -- 25 Euler-Maclaurin Formula -- 26 Symmetrie Quantum Calculus -- Literature


Mathematics Mathematical analysis Analysis (Mathematics) Combinatorics Quantum physics Quantum computers Spintronics Mathematics Analysis Quantum Physics Quantum Information Technology Spintronics Combinatorics



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