Theory of Calculus in One Real Variable -- Metric Spaces -- Theory of Calculus in Several Real Variables -- Theory of Ordinary Differential Equations and Systems -- Lebesgue Measure and Abstract Measure Theory -- Measure Theory for Euclidean Space -- Differentiation of Lebesgue Integrals on the Line -- Fourier Transform in Euclidean Space -- Lp Spaces -- Topological Spaces -- Integration on Loc…
Fondamenti degli elementi finiti -- Problemi stazionari -- Il metodo di Galerkin-elementi finiti per problemi di tipo ellittico -- Problemi di diffusione, trasporto e reazione -- Il metodo delle differenze finite -- Problemi tempo-dipendenti -- Equazioni di tipo parabolico -- Equazioni di tipo iperbolico -- Equazioni di Navier-Stokes per fluidi a densità costante.Questo testo contiene una racc…
to Boundary-Value Problems -- Compact Self-Adjoint Operators -- Topics in Euclidean Fourier Analysis -- Topics in Functional Analysis -- Distributions -- Compact and Locally Compact Groups -- Aspects of Partial Differential Equations -- Analysis on Manifolds -- Foundations of Probability.Basic Real Analysis and Advanced Real Analysis (available separately or together as a Set) systematically de…
Mathematical Preliminaries -- Introductory Applications -- Further Applications -- The Method of Multiple Scales -- Some Worked Examples Arising from Physical Problems.Many areas of science and engineering produce difficult mathematical problems , i.e., problems that cannot be solved in any conventional sense. In many cases, against all the apparent odds, it is possible to construct systematic …
Equations with One Dependent Function -- Systems of Equations -- Method of the Degenerate Hodograph -- Method of Differential Constraints -- Invariant and Partially Invariant Solutions -- Symmetries of Equations with Nonlocal Operators -- Symbolic Computer Calculations.Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Each so…
Differential Mathematical Models -- Integrable Differential Equations -- Dynamic Model of Systems with Heat Generation -- Stiff Differential Equations -- Heat Transfer near the Stagnation Point at Cross Tube Flow -- The Falkner-Skan Equation of Boundary Layer -- Rayleigh’s Equation: Hydrodynamical Instability -- Kinematic Waves of Concentration in Ion-Exchange Filter -- Kinematic Shock Waves …
This volume is an expanded version of Chapters III, IV, V and VII of my 1963 book "Linear partial differential operators". In addition there is an entirely new chapter on convolution equations, one on scattering theory, and one on methods from the theory of analytic functions of several complex variables. The latter is somewhat limited in scope though since it seems superfluous to duplicate the…
Linear Partial Differential Equations -- Nonlinear Model Equations and Variational Principles -- First-Order, Quasi-Linear Equations and Method of Characteristics -- First-Order Nonlinear Equations and Their Applications -- Conservation Laws and Shock Waves -- Kinematic Waves and Real-World Nonlinear Problems -- Nonlinear Dispersive Waves and Whitham’s Equations -- Nonlinear Diffusion-Reactio…
Mathematical Methods -- Passive Scalar Diffusion as a Damped Wave -- Extremalizing Vector Fields as Guides Toward Understanding Properties of Turbulence -- Low-Wavenumber Forcing and Turbulent Energy Dissipation -- New Potential Symmetries for a Generalised Inhomogeneus Nonlinear Diffusion Equation -- DNS and New Scaling Laws of ZPG Turbulent Boundary Layer Flow -- Linear Instability of a Slowl…
I Preliminaries -- II Semimartingales and Stochastic Integrals -- III Semimartingales and Decomposable Processes -- IV General Stochastic Integration and Local Times -- V Stochastic Differential Equations -- VI Expansion of Filtrations -- References.It has been 15 years since the first edition of Stochastic Integration and Differential Equations, A New Approach appeared, and in those years many…