1  Notation and Scope of Mathematics

• coordinate systems, sign conventions
• scalar functions, vector functions
• ordinary versus partial derivatives
• dimensional analysis

2  Continuum Versus Discrete-Particle/Cellular Concepts

• physical point, Knudsen scale
• cellular automata

3  Physical and Thermodynamic Properties of Fluids and Granular Materials

• state variables, statics, rheology
• phase transitions, equations of state

4  Conservation of Mass, Energy and Momentum

• control volumes
• divergence, local and particle derivatives
• source and sink terms

5  Constitutive (Transport) Laws and Formulae

• gradient
• linear laws and formulae
• nonlinear formulae

6  One-Dimensional Flows and Transport

7  Complex Systems – The Philosophy of Reductionist Versus Synthesist Viewpoints

• few-component versus many-component systems, linear versus nonlinear behavior
• the upscaling problem, emergent behavior, homogenization
• evaluating factor significance, toy models versus "real" models
• the full significance of conservation

8  Advection-Diffusion-Reaction Systems

9  Scaling – Interactions Among Length and Time Scales

• characteristic quantities, dimensionless numbers
• scale models

10  Elementary Numerical Analysis

11  Applications to Selected Earth/Environmental Systems

A PDF of the outline on this page can be obtained from the link below.

Course Outline