General quantum numerical analysis
This book is focused on the qualitative theory of general quantum calculus, the modern name for the investigation of calculus without limits. It centers on designing, analysing and applying computational techniques for general quantum differential equations.
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| Format: | UnknownFormat |
| Sprache: | eng |
| Veröffentlicht: |
Boca Raton, London, New York
CRC Press
2024
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| Ausgabe: | First edition |
| Schriftenreihe: | Advances in applied mathematics
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| Online Zugang: | Inhaltsverzeichnis |
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Tag hinzufügen | Zusammenfassung: | This book is focused on the qualitative theory of general quantum calculus, the modern name for the investigation of calculus without limits. It centers on designing, analysing and applying computational techniques for general quantum differential equations. Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Contents -- Preface -- 1. General Quantum Differentiation -- 1.1. The β-Operator -- 1.2. Definition for β-Derivative -- 1.3. Properties of the β-Derivative -- 1.4. Rules for β-Differentiation -- 1.5. Properties of β-Differentiable Functions -- 1.6. Chain Rules -- 1.7. A Mean Value Theorem -- 1.8. Higher Order β-Derivatives -- 1.9. The β-Rolle Theorem -- 1.10. Advanced Practical Problems -- 1.11. Notes and References -- 2. General Quantum Integration -- 2.1. β-Antiderivatives -- 2.2. Definition for β-Integral -- 2.3. Properties of β-Integrals -- 2.4. Inequalities and β-Integrals -- 2.5. General Quantum Monomials -- 2.6. The Taylor Formula -- 2.7. Improper Integrals of the First Kind -- 2.8. Improper Integrals of the Second Kind -- 2.9. Advanced Practical Problems -- 2.10. Notes and References -- 3. β-Elementary Functions -- 3.1. β-Regressive Functions -- 3.2. β-Exponential Functions -- 3.3. β-Trigonometric Functions -- 3.4. β-Hyperbolic Functions -- 3.5. Advanced Practical Problems -- 3.6. Notes and References -- 4. General Quantum Polynomial Interpolation -- 4.1. General Quantum Lagrange Interpolation -- 4.2. β-Lagrange Interpolation -- 4.3. Hermite Interpolation -- 4.4. β-Hermite Interpolation -- 4.5. β-Differentiation -- 4.6. Advanced Practical Problems -- 4.7. Notes and References -- 5. Numerical β-Integration -- 5.1. Newton-Cotes Formula -- 5.2. β-Newton-Cotes Formula -- 5.3. Error Estimates -- 5.4. β-Error Estimates -- 5.5. Composite Quadrature Rules -- 5.6. β-Composite Quadrature Rules -- 5.7. The Euler-Maclauren Expansion -- 5.8. The β-Euler-Maclauren Expansion -- 5.9. Construction of Gauss Quadrature Rules -- 5.10. Error Estimation for Gauss Quadrature Rules -- 5.11. β-Gauss Quadrature Rules -- 5.12. Error Estimation for β-Gauss Quadrature Rules. |
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| Beschreibung: | Literaturangaben |
| Beschreibung: | x, 360 Seiten Illustrationen |
| ISBN: | 9781032741505 978-1-032-74150-5 9781032750507 978-1-032-75050-7 |