Generalized Quantum Calculus with Applications is devoted to the qualitative theory of general quantum calculus and its applications to general quantum differential equations and inequalities. The book is aimed at upper-level undergraduate students and beginning graduate students in a range of interdisciplinary courses including physical sciences and engineering, from quantum mechanics to differential equations, with pedagogically organized chapters that each concludes with a section of practical problems. Generalized quantum calculus includes a generalization of the q-quantum calculus and the time scale calculus. There are many open problems and difficulties in q-quantum calculus and time-scale calculus, and this book explores how to use the generalized quantum operators to solve difficulties arising in q-quantum calculus and time-scale calculus, including but not limited to generalized quantum integration, generalized quantum chain rules, and generalized quantum Taylor formula.
Since generalized quantum calculus includes the q-quantum and time-scale calculus, this book can be utilized by a wide audience of researchers and students. This text is one of few foundational books on generalized quantum calculus and can be used for future discoveries in the area of integral transforms, variational calculus, integral equations, and inequalities in the language of generalized quantum calculus. This book also offers detailed proofs, exercises, and examples to aid instructors, researchers, and users in their studies.
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1. Generalized Quantum Differentiation
2. Generalized Quantum Integration
3. β-Elementary Functions
4. The β-Laplace Transform
5. First Order Linear β-Differential Equations
6. Second Order Linear β-Differential Equations
7. β-Differential Systems
8. Linear β- Integral Inequalities
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Valuable, focused first edition that explores quantum calculus through illustrative examples
Explores cutting-edge research trends in quantum calculus
Provides practical information and techniques for building fundamental knowledge and applying contemporary quantum calculus in upper-undergraduate and graduate-level studies
Serves as a front-line book for budding researchers and experts of mathematics, along with students from several interdisciplinary fields
Offers additional resources such as detailed proofs, exercises, and examples to aid instructors and students in their work
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Produktdetaljer
ISBN
9780443328046
Publisert
2025-03-01
Utgiver
Vendor
Academic Press Inc
Høyde
235 mm
Bredde
191 mm
Aldersnivå
U, 05
Språk
Product language
Engelsk
Format
Product format
Heftet
Antall sider
320
Forfatter