The greatest mathematicians, such as Archimedes, Newton, and Gauss, always united theory and applications in equal measure. Felix Klein There exists the remarkable possibility that one can master a subject mathemati cally, without really understanding its essence. Albert Einstein Don't give us numbers: give us insight! A contemporary natural scientist to a mathematician Numerous questions in physics, chemistry, biology, and economics lead to nonlinear problems; for example, deformation of rods, plates, and shells; behavior of plastic materials; surface waves of fluids; flows around objects in fluids or gases; shock waves in gases; movement of viscous fluids; equilibrium forms of rotating fluids in astrophysics; determination of the shape of the earth through gravitational measu- ments; behavior of magnetic fields of astrophysical objects; melting processes; chemical reactions; heat radiation; processes in nuclear reactors; nonlinear oscillation in physics, chemistry, and biology; 2 Introduction existence and stability of periodic and quasiperiodic orbits in celestial mechanics; stability of physical, chemical, biological, ecological, and economic processes; diffusion processes in physics, chemistry, and biology; processes with entropy production, and self-organization of systems in physics, chemistry, and biology; study of the electrical potential variation in the heart through measure ments on the body surface to prevent heart attacks; determining material constants or material laws (e. g.
Auflage
1st ed. 1986. Corr. 3rd printing 1998
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Research
Illustrationen
1
1 s/w Abbildung
XXIII, 909 p. 1 illus.
Maße
Höhe: 241 mm
Breite: 160 mm
Dicke: 55 mm
Gewicht
ISBN-13
978-0-387-90914-1 (9780387909141)
DOI
10.1007/978-1-4612-4838-5
Schweitzer Klassifikation
Fundamental Fixed-Point Principles.- 1 The Banach Fixed-Point Theorem and Iterative Methods.- 2 The Schauder Fixed-Point Theorem and Compactness.- Applications of the Fundamental Fixed-Point Principles.- 3 Ordinary Differential Equations in B-spaces.- 4 Differential Calculus and the Implicit Function Theorem.- 5 Newton's Method.- 6 Continuation with Respect to a Parameter.- 7 Positive Operators.- 8 Analytic Bifurcation Theory.- 9 Fixed Points of Multivalued Maps.- 10 Nonexpansive Operators and Iterative Methods.- 11 Condensing Maps and the Bourbaki-Kneser Fixed-Point Theorem.- The Mapping Degree and the Fixed-Point Index.- 12 The Leray-Schauder Fixed-Point Index.- 13 Applications of the Fixed-Point Index.- 14 The Fixed-Point Index of Differentiable and Analytic Maps.- 15 Topological Bifurcation Theory.- 16 Essential Mappings and the Borsuk Antipodal Theorem.- 17 Asymptotic Fixed-Point Theorems.- References.- Additional References to the Second Printing.- List of Symbols.- List of Theorems.- List of the Most Important Definitions.- Schematic Overviews.- General References to the Literature.- List of Important Principles.- of the Other Parts.
