Introduction -- 1. Quantities and Measures -- 2. Variables and Functions -- 3. Trigonometry, Geometry of Plane and Space -- 4. Cartography -- 5. Derivation -- Integration and Differential Equations.This undergraduate textbook presents a unique comprehensive overview on Mathematics in Earth Sciences and Geography. It deals with fundamental theoretical and applied mathematics, needed by bachelor …
Background -- The Equations of Motion for Extensible Strings -- Elementary Problems for Elastic Strings -- Planar Steady-State Problems for Elastic Rods -- to Bifurcation Theory and its Applications to Elasticity -- Global Bifurcation Problems for Strings and Rods -- Variational Methods -- Theory of Rods Deforming in Space -- Spatial Problems for Rods -- Axisymmetric Equilibria of Shells -- Ten…
Constraint Retraction for Dynamic Constraint Satisfaction Problems over Disjoint Real Intervals -- Computational Methods for Large Distributed Parameter Estimation Problems in 3D -- Robust Parameter Estimation for Identifying Satellite Injection Orbits -- On the Numerical Simulation of the Free Fall Problem -- Searching the Web: a Semantics-Based Approach -- Adaptive Computation with Perfectly …
Seismic Interpretation -- to Seismic Texture -- Atlas of 3D Seismic Attributes -- The Use of Structure Tensors in the Analysis of Seismic Data -- Automated Structural Interpretation Through Classification of Seismic Horizons -- Automatic Fault Extraction Using Artificial Ants -- Geological Model Building -- Geological Modelling and Reservoir Simulation -- Geological Model Building: A Hierarchic…
Stochastic Methods in Statistical Physics -- Coarse-Graining Techniques for (Random) Kac Models -- Euclidean Gibbs Measures of Quantum Crystals: Existence, Uniqueness and a Priori Estimates -- Some Jump Processes in Quantum Field Theory -- Gibbs Measures on Brownian Paths: Theory and Applications -- Spectral Theory for Nonstationary Random Potentials -- A Survey of Rigorous Results on Random Sc…
Physics -- Chain Conformations and Phase Behavior in Confined Polymer Blends -- Thermal Quark Anti-quark Free Energies, Energies and Screening in Hot SU(3) Gauge Theory -- Simulations of Particle Suspensions at the Institut für Computerphysik -- Numerical Modelling of Convection and Dynamo Processes in Fully Convective Stars -- Large Scale Simulation of a Cooled, Pulsed Jet in Symbiotic Stars …
Basic Tensor Algebra -- Tensor Spaces -- to Tensors -- Homogeneous Tensors -- Change-of-basis in Tensor Spaces -- Homogeneous Tensor Algebra: Tensor Homomorphisms -- Special Tensors -- Symmetric Homogeneous Tensors: Tensor Algebras -- Anti-symmetric Homogeneous Tensors, Tensor and Inner Product Algebras -- Pseudotensors; Modular, Relative or Weighted Tensors -- Exterior Algebras -- Exterior Alg…
1+1 Dimensional Integrable Systems -- 2+1 Dimensional Integrable Systems -- N + 1 Dimensional Integrable Systems -- Surfaces of Constant Curvature, Bäcklund Congruences and Darboux Transformation -- Darboux Transformation and Harmonic Map -- Generalized Self-Dual Yang-Mills Equations and Yang-Mills-Higgs Equations -- Two Dimensional Toda Equations and Laplace Sequences of Surfaces in Projectiv…
General Definitions, Conservation Laws -- Lagrangian Coordinates -- Constitutive Laws -- The Principle of Material Frame-Indifference -- Replacing Entropy with Temperature -- Isotropy -- Equations in Lagrangian Coordinates -- Linearized Models -- Quasi-static Thermoelasticity -- Fluids -- Linearized Models for Fluids, Acoustics -- Perfect Gases -- Incompressible Fluids -- Turbulent Flow of Inco…
Prerequisites -- Invariant Measures -- The Birkhoff Ergodic Theorem -- The Central Limit Theorem -- More on Ergodicity -- Homeomorphisms of the Circle -- Mod 2 Uniform Distribution -- Entropy -- The Lyapunov Exponent: One-Dimensional Case -- The Lyapunov Exponent: Multidimensional Case -- Stable and Unstable Manifolds -- Recurrence and Entropy -- Recurrence and Dimension -- Data Compression.Erg…