Volume 1: Distributional and Fractal Calculus, Integral Transforms, and Wavelets. - Part I: Distributions and Their Basic Applications.- Basic Definitions and Operations.- Basic Applications: Rigorous and Pragmatic.- Part II: Integral Transforms and Divergent Series.- Fourier Transform.- Asymptotics of Fourier Transforms.- Stationary Phase and Related Method.- Singular Integrals and Fractal Calculus.- Uncertainty Principle and Wavelet Transforms.- Summation of Divergent Series and Integrals.- Answers and Solutions.- References.- Index.- Volume 2: Linear and Nonlinear Dynamics in Continuous Media .- Part III: Potentials, Diffusions, and Waves.- Potential Theory and Fundamental Solutions of Elliptic Equations.- Diffusions and Parabolic Evolution Equations.- Waves and Hyperbolic Equations.- Part IV: Nonlinear Partial Differential Equations.- First-Order Nonlinear PDEs and Conservation Laws.- Generalized Solutions of First-Order Nonlinear PDEs.- Nonlinear Waves and Growing Interfaces: 1-D Burgers-KPZ Models.- Other Standard Nonlinear Models of Higher Order.- Answers and Solutions.- References.- Index.- Volume 3: Random and Anomalous Fractional Dynamics in Continuous Media .- Part V: Random Dynamics.- Basic Distributional Tools for Probability Theory.- Random Distributions: Generalized Stochastic Processes.- Dynamical and Statistical Characteristics of Random Fields and Waves.- Forced Burgers Turbulence and Passive Tracer Transport in Burgers Flows.- Probability Distributions of Passive Tracers in Randomly Moving Media.- Part VI: Anomalous Fractional Dynamics.- Levy Processes and their Generalized Derivatives.- Linear Anomalous Fractional Dynamics in Continuous Media.- Nonlinear and Multiscale Anomalous Fractional Dynamics in Continuous Media.- Appendix: Basic Facts about Distributions.- References.- Index. Skryť popis