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# CALTECH GE 108 - Lecture notes

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Ge 108 Topics (weeks in parentheses) Fall 2005 A. P. Ingersoll (1) Math: logarithms, exponentials, significance of e, Taylor series expansions of sines, cosines and exponentials, complex exponentials. Differential equations: ordinary, linear, 1st order, constant coefficients, exponential decay. Examples from radioactive dating, Newtonian cooling, atmospheric structure, Rayleigh distillation of oxygen isotopes, depletion of a natural resource like oil, flushing a contaminant from a reservoir. (2) Simple harmonic oscillator with damping: sinusoidal forcing, resonance, phase lag, solution by complex exponentials, initial conditions, transients, width of spectral lines. (3) Wave equation: normal modes, violin string, harmonics, sound waves in air, modes of an open organ pipe, separation of variables, superposition, the musical scale. Introduction to fluid dynamics. Convection, criterion for instability. (4) Fourier analysis: periodic functions, sines and cosines, complex exponentials, power spectra, application to normal modes of the Earth and Milankovitch cycles. Spherical harmonics: Application to gravity, magnetism, normal modes. (5) Statistics: mean, variance, parent population, probability distributions, Poisson statistics, counting statistics, error of a mean, precision, accuracy, correlation, autocorrelation. (6) Linear least squares: two variables, N variables, determinants, matrices. (7) Gravity: conservative forces, potentials, circular orbits, angular momentum, equilibrium tide, tidal dissipation, effect of rotation, oblateness, spherical harmonic expansion, tidal disruption of small bodies, the Roche limit. Vectors: vector fields, divergence, gradient, curl, Laplacian, coordinate systems, unit vectors, differential equation for the gravitational potential, gravity and topography. (8) Diffusion equation: heat flow, cooling of a lithospheric plate, diurnal thermal wave, diffusion in porous media. The relation between length and time scales. (9) Electrostatics: potential, differential form of Coulomb’s law, dielectrics, polarization. (10) Magnetostatics: magnetic field of a current, force on a current, relativistic interpretation of magnetic force, differential form of Ampere’s law, magnetic materials, paramagnetism, ferromagnetism, current loops, dipoles, magnetic field of the Earth. _______________________________________________________________________ Reading from Feynman, Turcotte and Schubert, Bevington, Lowrie, Cole and Wolfson.Weekly graded homework and a final exam. Class notes with every lecture. Since we do not have a single textbook, it is important that you attend lectures. The grade will be based on earnest effort as well as performance. The TA is Kris Barkume (158 South Mudd, ext. 5888, [email protected]). Those who feel they do not have to take this course may petition out of it. I will give you a 15-minute oral exam in my office to see if you should take it. My goal is to help you with the basic math and physics that you will encounter in the geological and environmental sciences. I do not want this course to be a useless hurdle that tests you on subjects you will never use. Time and place: Monday 11-12, Wednesday 11-12, Thursday 11-12 in 251

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