Linearization -- Fixed-Point Theorems -- Degree Theory and Applications -- Minimization Methods -- Topological and Variational Methods.Nonlinear analysis has developed rapidly in the last three decades. Theories, techniques and results in many different branches of mathematics have been combined in solving nonlinear problems. This book collects and reorganizes up-to-date materials scattered thr…
Basic Material -- Approximation of Integrals -- Boundary Layer Behaviour -- Two-Point Boundary Value Problems -- Nonlinear Boundary Value Problems -- Elliptic Boundary Value Problems -- Boundary Layers in Time -- Evolution Equations with Boundary Layers -- The Continuation Method -- Averaging and Timescales -- Advanced Averaging -- Averaging for Evolution Equations -- Wave Equations on Unbounde…
Advances for New Model and Solution Approaches -- A Scatter Search Tutorial for Graph-Based Permutation Problems -- A Multistart Scatter Search Heuristic for Smooth NLP and MINLP Problems -- Scatter Search Methods for the Covering Tour Problem -- Solution of the SONET Ring Assignment Problem with Capacity Constraints -- Advances for Solving Classical Problems -- A Very Fast Tabu Search Algorith…
A Particle Strategy for Solving the Fokker-Planck Equation Modelling the Fiber Orientation Distribution in Steady Recirculating Flows Involving Short Fiber Suspensions -- Extended Meshfree Method for Elastic and Inelastic Media -- Meshfree Petrov-Galerkin Methods for the Incompressible Navier-Stokes Equations -- The ?-shape Based Natural Element Method in Solid and Fluid Mechanics -- A Particle…
4d Formalism -- On Establishing Balance and Conservation Laws in Elastodynamics -- From Mathematical Physics to Engineering Science -- Evolving Interfaces -- The Unifying Nature of the Configurational Force Balance -- Generalized Stefan Models -- Explicit Kinetic Relation from “First Principles” -- Growth & Biomechanics -- Surface and Bulk Growth Unified -- Mechanical and Thermodynamical Mo…
The Dilute Bose Gas in 3D -- The Dilute Bose Gas in 2D -- Generalized Poincaré Inequalities -- Bose-Einstein Condensation and Superfluidity for Homogeneous Gases -- Gross-Pitaevskii Equation for Trapped Bosons -- Bose-Einstein Condensation and Superfluidity for Dilute Trapped Gases -- One-Dimensional Behavior of Dilute Bose Gases in Traps -- Two-Dimensional Behavior in Disc-Shaped Traps -- The…
Squares -- Numbers, Numbers Everywhere -- Fibonacci Numbers -- Prime Numbers -- Choice and Chance -- Geometrical Constructions -- The Algebra of Group.Mathematics Is Not a Spectator Sport challenges the reader to become an active mathematician. Beginning at a gentle pace, the author encourages the reader to get involved, with discussions of an exciting variety of topics, each placed in its hist…
Introduction: The Birth and Growth of a Community -- History or Heritage? An Important Distinction in Mathematics and for Mathematics Education -- Ptolemy’s Mathematical Models and their Meaning -- Mathematics, Instruments and Navigation, 1600–1800 -- Was Newton’s Calculus a Dead End? The Continental Influence of Maclaurin’s Treatise of Fluxions -- The Mathematics and Science of Leonhar…
Mathematics, Art and Architecture -- Mathematics, Art and Architecture -- From Tiling the Plane to Paving Town Square -- Mathematics in Contemporary Arts — Finite and Infinity -- De Insana Geometria -- Ovals in Borromini’s Geometry -- Fractals: A Resonance between Art and Nature -- Mathland — From Topology to Virtual Architecture -- Visual Mathematics and Computer Graphics -- Introduction…
Mathematical Models -- Introduction to State Space Theory -- Stability Theory -- Perturbation Theory -- Uncertain Spaces -- Appendix: Linear Algebra -- Complex Analysis -- Convolutions and Transforms -- Linear Operators.This book presents the mathematical foundations of systems theory in a self-contained, comprehensive, detailed and mathematically rigorous way. This first volume is devoted to t…