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This textbook offers a concise but self-contained introduction to the art of numerical modelling in sciences. It discusses all the steps, from the mathematical foundations of the model to the solution procedures that are commonly used by advanced practitioners.
List of contents
- Part I - Mathematical concepts
- 1: Introduction to real valued calculus
- 2: Introduction to multivariate calculus
- 3: Elements of complex calculus
- 4: Elements of linear algebra
- 5: Treating functions as vectors
- 6: Ordinary Differential Equations (ODEs)
- 7: Partial Differential Equations (PDEs)
- Part II - Numerical Modeling, Ordinary Differential Equations (ODEs)
- 8: First order ODE (time integration): The nuclear decay equation as a starting point
- 9: What controls convergence? What relates convergence and stability?
- 10: Box Models: from single to multiple coupled ODEs
- 11: Higher order ODEs
- 12: Higher order discretization methods
- Part III - Numerical Modeling, Partial Differential Equations (PDEs)
- 13: Important mathematical notions when working with PDEs
- 14: Von Neumann stability analysis: concepts
- 15: 1-D advection equation
- 16: Diffusion equation
- 17: 1-D advection-diffusion equation
- 18: 1-D wave equation
- 19: The shallow water equation
- Part IV - Overview of other numerical methods
- 20: Top-down approaches
- 21: Bottom-up approaches
About the author
Chistian Huber grew up in Geneva, Switzerland, where he studied earth sciences and physics. He then moved to the University of California Berkeley where he gained his PhD in earth and planetary sciences, before joining the faculty at the Georgia Institute of Technology and then moving to Brown University in 2016. His main interests are in magmatic processes and planetary geodynamics.
