Focus of the class:

    This class focuses on introducing numerical methods for (Earth) sciences. Students will learn to use Matlab (the supporting language for the class). We will introduce different numerical methods to find roots and integrate functions, as well as solve Ordinary Differential Equations (ODE’s) and Partial Differential Equations (PDE’s). The problems we will solve for will be drawn from Earth Sciences, including for example (not exhaustive):

1. • Box models: the Carbon cycle, the Calcium budget in seawater.
   

2. • Non-linear ODE, Kepler’s orbit, trajectory of a charged particle in an electromagnetic field.
   

3. • Diffusion equations: heat transfer, mass transfer, porous media flow.
   

4. • Advection-diffusion equations: Cosmogenic nuclide production in soils experiencing erosion-sedimentation
   

5. • Wave equation: propagation of seismic waves in an heterogeneous medium (see movie above)
   

6. • Poisson’s equation: electrical field around charged bodies (see above, right).
   

7. • Non-linear iterative methods: the Stefan problem, diffusion and phase change.
   

8. • Chaotic systems, the Lorenz model for ocean dynamics.
   

Organization of the class:

    The class is held Monday-Wednesday-Friday from 9 to 10 am in room L1116 in the ES&T building. 5 homework sets cover the material seen in class and comprise 25% of the total grade, the rest being 2 exams - 40% - and a final project 30% and its presentation 5%.

Syllabus:

    The syllabus can be downloaded here ESMSyllabus.doc