The goal here is make explicit some of the major assumptions used in the class in the hope that the students will also find it useful in understanding the class (e.g. why we will not be talking about the coriolis force when it’s a major topic in their physical oceanography class).

Assumption | Comment |
---|---|

All the fields of interest (e.g. pressure, velocity, density, and temperature) are continuous and differentiable | Lead a discussion of how the real world (e.g. reverse faults) and continuum mechanics ideas fits into this assumption. |

Use a flat earth model described with a right handed Cartesian coordinate system | At the spatial scales that the class will consider the curvature of earth will be considered negligible and gravity will have a constant value in the z direction ; however, it will be pointed out that in other scales and situations(e.g. modeling heat and mass flow modeling of the interior of the earth; modeling extraction of water from a well) why a curvilinear coordinate system may be more appropriate. |

Inertial frame of reference | At the spatial and temporal scales of interest to this class the effects of the earth’s rotation will not be considered. Will illustrate this with a discussion of the effect of the earth’s rotation on short scale beach waves vs. large scale tidal currents |

Only Real numbers are needed to describe geologic features and mathematical models | Give a basic background on complex numbers (e.g. cover section 2.1-2.5 of Boas) to deal with the exceptional times we will have to deal with complex numbers. |

Examples will only consider materials with homogeneous and isotropic properties | Lead a discussion on the limitations imposed by these restrictions and why they are some times necessary |

Deterministic Newtonian world | Note at the scale we will be working with we will neglect relativistic effects. We will also explore the world of random variables and the meaning of ‘real’ random events in nature (e.g. the probability for a given uranium atom to decay ) as. the more Bayesian idea that probability is a measure of uncertainty regarding ones knowledge of the physical world. |

Emphasize only reasonable (i.e. real valued, full rank with distinct eigenvalues) matrixes | When needed discuss: matrix multiplication and manipulations, matrix inverses, definition of rank, determinates, Gaussian elimination, and determination of eigenvalues-eigenvectors. |