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Foreword; Preface; Who Should Read this Book; How Should this Book be Read; Acknowledgements; Contents; Part I Introduction to Scientific Python; 1 Bird's Eye View; 1.1 Bird's Eye View; 1.2 History; 1.3 Programming or Scripting; 1.4 Python Interfaces; 1.4.1 IPython: Interactive Python; 1.5 Few Words on Syntax; 1.6 Extending Python; 1.6.1 Importing Libraries; 1.7 NumPy: Numerical Python; 1.8 Visualization; 2 Visualization; 2.1 The MatPlotLib Visualization Library; 2.1.1 Plotting a 2D Field; 2.1.2 Plotting a Map; 2.1.3 NetCDF and ETOPO; 2.1.4 Plotting a Seismic Waveform.
2.2 Plotting in 3D with MatPlotLib2.2.1 VTK File Format; 2.3 Example: Length of the Day; 2.4 IPython and Jupyter Notebooks; 2.5 Paraview and VisIt; 2.6 Python as a wrapper: SEATREE and Underworld; 3 Fast Python: NumPy and Cython; 3.1 How Fast is Your Computing Machine?; 3.2 Numerical Python; 3.2.1 NumPy Types; 3.2.2 ndarrays; 3.3 Indexing and Slicing; 3.3.1 N-Dimensional Indexing; 3.3.2 Boolean Indexing; 3.3.3 Transposing and Axis Rotation; 3.4 Strides; 3.5 Vector Products; 3.6 Linear Algebra; 3.7 Cython; 3.7.1 Cython in iPython; 3.8 Going Parallel: mpi4py and PETSc4py.
3.9 Other Computational ModulesPart II Second Part: Mechanics; 4 Mechanics I: Kinematics; 4.1 Computation of Velocity and Acceleration; 4.2 Integrate Acceleration; 4.3 Projectile Trajectory; 4.4 Circular Motion; 5 Mechanics II: Newtonian Dynamics; 5.1 Analytical Solutions for 1D Dynamics; 5.1.1 1-D Dynamics; 5.1.2 2D Dynamics; 5.1.3 Potential, Dissipated, Kinetic, Mechanical Energies for the Droplet; 5.2 Monte Carlo Simulation of the Pyroclastic flow ... ; 5.3 Precession of a Gyroscope; 6 Physics of Stokes Flow; 6.1 Momentum and Continuity Equations; 6.1.1 Navier Stokes Equation.
6.2 Stokes Flow: Simple but Not Obvious6.2.1 Stokes' Paradox; 6.2.2 Flow Reversibility; 6.2.3 Origin of the Paradoxes; 6.3 Fundamental Solutions of Stokes Flow; 6.3.1 Rotlet; 6.3.2 Stokeslet; Part III Lattice Methods; 7 Lagrangian Transport; 7.1 Strain and Strain Rate; 7.2 Rigid Rotation; 7.2.1 Cell-Particles Projections; 7.2.2 Motion of the Particles; 7.3 Thinning Flow; 7.4 Lagrangian Advection of a Continuous Field; 7.5 Upwind Scheme Versus Lagrangian Transport; 8 Operator Formulation; 8.1 Strain Rates; 8.2 Cell-Centered Strain Rates from Linear Operators; 8.2.1 Sparse Derivative Operator.
8.3 Reversible and Irreversible9 Laplacian Operator and Diffusion; 9.1 Diffusion Processes in Geodynamics; 9.2 Explicit Diffusion Implementation; 9.3 Explicit Formulation Using Operators; 9.4 Implicit Formulation; 9.5 Two-Dimensional Diffusion Equation; 9.6 Biharmonic Equation; 10 Beyond Linearity; 10.1 Operator Form of the Stokes Equation; 10.2 Implementation of the Homogeneous Stokes Equation; 10.3 The Finite Volume Method; 10.4 Implementation of the Nonhomogenous Stokes Equation; 10.5 Long-Range Interaction; 10.6 Advection-Diffusion Equation; Part IV Advanced Techniques; 11 Trees, Particles, and Boundaries.
2.2 Plotting in 3D with MatPlotLib2.2.1 VTK File Format; 2.3 Example: Length of the Day; 2.4 IPython and Jupyter Notebooks; 2.5 Paraview and VisIt; 2.6 Python as a wrapper: SEATREE and Underworld; 3 Fast Python: NumPy and Cython; 3.1 How Fast is Your Computing Machine?; 3.2 Numerical Python; 3.2.1 NumPy Types; 3.2.2 ndarrays; 3.3 Indexing and Slicing; 3.3.1 N-Dimensional Indexing; 3.3.2 Boolean Indexing; 3.3.3 Transposing and Axis Rotation; 3.4 Strides; 3.5 Vector Products; 3.6 Linear Algebra; 3.7 Cython; 3.7.1 Cython in iPython; 3.8 Going Parallel: mpi4py and PETSc4py.
3.9 Other Computational ModulesPart II Second Part: Mechanics; 4 Mechanics I: Kinematics; 4.1 Computation of Velocity and Acceleration; 4.2 Integrate Acceleration; 4.3 Projectile Trajectory; 4.4 Circular Motion; 5 Mechanics II: Newtonian Dynamics; 5.1 Analytical Solutions for 1D Dynamics; 5.1.1 1-D Dynamics; 5.1.2 2D Dynamics; 5.1.3 Potential, Dissipated, Kinetic, Mechanical Energies for the Droplet; 5.2 Monte Carlo Simulation of the Pyroclastic flow ... ; 5.3 Precession of a Gyroscope; 6 Physics of Stokes Flow; 6.1 Momentum and Continuity Equations; 6.1.1 Navier Stokes Equation.
6.2 Stokes Flow: Simple but Not Obvious6.2.1 Stokes' Paradox; 6.2.2 Flow Reversibility; 6.2.3 Origin of the Paradoxes; 6.3 Fundamental Solutions of Stokes Flow; 6.3.1 Rotlet; 6.3.2 Stokeslet; Part III Lattice Methods; 7 Lagrangian Transport; 7.1 Strain and Strain Rate; 7.2 Rigid Rotation; 7.2.1 Cell-Particles Projections; 7.2.2 Motion of the Particles; 7.3 Thinning Flow; 7.4 Lagrangian Advection of a Continuous Field; 7.5 Upwind Scheme Versus Lagrangian Transport; 8 Operator Formulation; 8.1 Strain Rates; 8.2 Cell-Centered Strain Rates from Linear Operators; 8.2.1 Sparse Derivative Operator.
8.3 Reversible and Irreversible9 Laplacian Operator and Diffusion; 9.1 Diffusion Processes in Geodynamics; 9.2 Explicit Diffusion Implementation; 9.3 Explicit Formulation Using Operators; 9.4 Implicit Formulation; 9.5 Two-Dimensional Diffusion Equation; 9.6 Biharmonic Equation; 10 Beyond Linearity; 10.1 Operator Form of the Stokes Equation; 10.2 Implementation of the Homogeneous Stokes Equation; 10.3 The Finite Volume Method; 10.4 Implementation of the Nonhomogenous Stokes Equation; 10.5 Long-Range Interaction; 10.6 Advection-Diffusion Equation; Part IV Advanced Techniques; 11 Trees, Particles, and Boundaries.