物理及工程中的分數維微積分(第1捲):數學基礎及其理論 [Fractional Derivatives for Physicists and Engineers Volume 1:Background pdf epub mobi txt 電子書 下載 2024
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一個運動質點位置函數的一階導數錶示速度,二階導數錶示加速度,那麼分數階導數的物理意義又是什麼呢?分數階導數是因何而産生,它對現代分析學在物理學的應用産生什麼衝擊,在將來又有什麼發展?《物理及工程中的分數維微積分》二捲本將為你提供一個詳細詮釋。
《物理及工程中的分數維微積分(第1捲):數學基礎及其理論》介紹分數維微積分的數學基礎和相應的理論,為這個現代分析學中的重要分支提供瞭詳細而又清晰的分析與介紹。
內頁插圖
目錄
Part Ⅰ Background
1 Heredity and Nonlocality
1.1 Heredity
1.1.1 Concept of heredity
1.1.2 A short excursus in history
1.2 Volterra's heredity theory
1.2.1 Volterra's heredity laws
1.2.2 Hereditary string
1.2.3 Hereditarv oscillator
1.2.4 Energv drinciple
1.2.5 Hereditary electrodynamics
1.3 Hereditary kinetics
1.3.1 Mechanical origin of heredity
1.3.2 Hereditary Boltzmann equation
1.3.3 Fokker-Planckequation
1.3.4 Pauli and Van Hove equations
1.3.5 Hybrid kinetic equations
1.4 Hereditary hydrodynamics
1.4.1 Physicalmotivation
1.4.2 Polymeric liquids
1.4.3 Turbulent diffusion
1.4.4 Coarse-grained diffusion models
1.5 Hereditarv viscoelasticity
1.5.1 Boltzmann's viscoelasticity model
1.5.2 Elastic solid: a mesoscopic approach
1.5.3 One-dimensional harmonic lattice
1.5.4 Axiomatic approach to continuum mechanics
1.6 Hereditary thermodynanucs
1.6.1 Mechanical approach
1.6.2 Hereditary heat-transfer
1.6.3 Extendedirreversible thermodynamics
1.6.4 Axiomatic approach
1.6.5 Ecology and climatology
1.7 Nonlocal models
1.7.1 Many-electron atoms
1.7.2 Electron correlation in metals
1.7.3 Plasma
1.7.4 Vlasov's nonlocal statistical mechanics
1.7.5 Turbulence
1.7.6 Aggregation equations
1.7.7 Nonlocal models in nano-plasticity
1.7.8 Nonlocal wave equations
References
2 Selfsinularity
2.1 Power functions
2.1.1 Standard power function
2.1.2 Properties ofpower functions
2.1.3 Memory
2.1.4 Fractals
2.2 Hydrodynamics
2.2.1 Newtonian fluids
2.2.2 Turbulence
2.2.3 Microscopic fluctuations
2.2.4 Non-Newtonian fiuids
2.3 Polymers
2.3.1 The Nutting law
2.3.2 Relaxation ofpolymer chains
2.3.3 Interpenetrating polymer networks
2.4 Reaction-diffusion
2.4.1 Diffusion
2.4.2 Polymerization
2.4.3 Coagulation and fragmentation
2.5 Solids
2.5.1 Dielectrics
2.5.2 Semiconductors
2.5.3 Spinglasses
2.5.4 Jonscher's universal relaxation law
2.6 Optics
2.6.1 Luminescence decay
2.6.2 Anomalous exciton kinetics
2.6.3 Blinking fluorescence of quantum dots
2.7 Geophysics
2.7.1 Atmosphere and ocean turbulence
……
PartⅡ Theory
Index
物理及工程中的分數維微積分(第1捲):數學基礎及其理論 [Fractional Derivatives for Physicists and Engineers Volume 1:Background 下載 mobi epub pdf txt 電子書
物理及工程中的分數維微積分(第1捲):數學基礎及其理論 [Fractional Derivatives for Physicists and Engineers Volume 1:Background pdf epub mobi txt 電子書 下載