Buch, Englisch, 278 Seiten, Format (B × H): 162 mm x 242 mm, Gewicht: 1310 g
Applications to Partial Differential Equations
Buch, Englisch, 278 Seiten, Format (B × H): 162 mm x 242 mm, Gewicht: 1310 g
Reihe: Applied and Numerical Harmonic Analysis
ISBN: 978-0-8176-4354-6
Verlag: Birkhauser Boston
Differential geometry techniques have very useful and important applications in partial differential equations and quantum mechanics. This work presents a purely geometric treatment of problems in physics involving quantum harmonic oscillators, quartic oscillators, minimal surfaces, and Schrödinger's, Einstein's and Newton's equations.
Geometric Mechanics on Riemannian Manifolds is a fine text for a course or seminar directed at graduate and advanced undergraduate students interested in elliptic and hyperbolic differential equations, differential geometry, calculus of variations, quantum mechanics, and physics. The text is enriched with good examples and exercises at the end of every chapter. It is also an ideal resource for pure and applied mathematicians and theoretical physicists working in these areas.
Zielgruppe
Graduate
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Mathematische Analysis Variationsrechnung
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
- Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
Weitere Infos & Material
Introductory Chapter.- Laplace Operators on Riemannian Manifolds.- Lagrangian Formalism on Riemannian Manifolds.- Harmonic Maps from a Lagrangian Viewpoint.- Conservation Theorems.- Hamiltonian Formalism.- Hamilton-Jacobi Theory.- Minimal Hypersurfaces.- Radially Symmetric Spaces.- Fundamental Solutions for Heat Operators with Potentials.- Fundamental Solutions for Elliptic Operators.- Mechanical Curves.
