to Shape Optimization Theory and Some Classical Problems -- Optimization Problems over Classes of Convex Domains -- Optimal Control Problems: A General Scheme -- Shape Optimization Problems with Dirichlet Condition on the Free Boundary -- Existence of Classical Solutions -- Optimization Problems for Functions of Eigenvalues -- Shape Optimization Problems with Neumann Condition on the Free Bound…
Preliminaries -- Steinhaus Type Theorems -- Boundedness and Continuity of Solutions -- Differentiability and Analyticity -- Regularity Theorems on Manifolds -- Regularity Results with Fewer Variables -- Applications.This book is about regularity properties of functional equations. In the second part of his fifth problem, Hilbert asked, concerning functional equations, "In how far are the assert…
Preliminary general material -- Steady-State Problems -- Pseudomonotone or weakly continuous mappings -- Accretive mappings -- Potential problems: smooth case -- Nonsmooth problems; variational inequalities -- Systems of equations: particular examples -- Evolution Problems -- Special auxiliary tools -- Evolution by pseudomonotone or weakly continuous mappings -- Evolution governed by accretive …
Introduzione -- Calcolo numerico e calcolo simbolico -- Modelli discreti -- Somme e serie -- Modelli continui -- Derivate e integrali -- Modelli discreti a più dimensioni -- Modelli continui a più dimensioni -- Modelli dinamici.Questo libro è nato dall'esperienza del corso di Matematica Generale all'Università Bocconi. Nel presentare gli oggetti matematici insegna allo studente l'utilizzo d…
Fibonacci Numbers -- Homogeneous Linear Recurrence Relations -- Finite Difference Equations -- Generating Functions -- Nonnegative Difference Equations -- Leslie’s Population Matrix Model -- Matrix Difference Equations -- Modular Recurrences -- Computational Complexity -- Some Nonlinear Recurrences.Difference equations are models of the world around us. From clocks to computers to chromosomes…
Dynamics of First-Order Difference Equations -- Linear Difference Equations of Higher Order -- Systems of Linear Difference Equations -- Stability Theory -- Higher-Order Scalar Difference Equations -- The Z-Transform Method and Volterra Difference Equations -- Oscillation Theory -- Asymptotic Behavior of Difference Equations -- Applications to Continued Fractions and Orthogonal Polynomials -- C…