Course Notes

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For several classes I have written notes on a variety of topics. Some of these have proven useful to other people. These notes are informal and may contain errors. The date of last revision is noted in the description. MATLAB Primer. Last edited in 2004. This primer has been used as an early introduction to programming in the MATLAB environment. The reading assumes the reader does not know linear algebra and therefore contains none of the matrix-vector operations that make MATLAB quite useful. Numerical solutions to differential equations. Last edited 2003. An early introduction to using MATLAB to solve differential equations numerically. The focus is on Euler's method and other simple methods such as midpoint. Introduces Runge-Kutta and shows how to use ode45, the built in MATLAB function. The reading assumes student does not know linear algebra and therefore does not solve systems of equations. Diffusion. Last edited 2007. An introduction to diffusion processes, solutions via simple finite difference methods (in MATLAB), RC circuit analogies to 1D conduction, non-dimensionalization, and an introduction to separation of variables. Fourier series in MATLAB. Last edited 2002. A basic introduction to Fourier series and how power spectra are computed. Shows the reader how to interpret the data returned by MATLAB's FFT (fast Fourier Transform) command. MATLAB's data acquisition toolbox. Last edited 2002. An introduction to using MATLAB's data acquisition toolbox. Below are a few of my "solutions" to papers/projects which I assigned as part of a course. While my solutions are far from groundbreaking research, they included a few interesting results. Ideal gas piston. Last edited 2004. An interesting problem in thermodynamics is the dynamics of a piston in the middle of a gas filled tube. Such a device was once used to infer the ratio of specific heats by measuring the system resonance. The piston has the interesting property that if the dynamics are fast, the gas will be compressed adiabatically and the piston will oscillate forever, if there were no mechanical friction. If the piston dynamics are slow, then the gas will be compressed isothermally which will also oscillate forever. Between these two limits, the process is irreversible and oscillations will be thermodynamically damped. This paper was used very early in an introductory thermodynamics course. Tank draining by a siphon. Last edited 2006. A simple problem in fluid dynamics is the draining of a tank by a siphon. The paper provides an introduction to making equations dimensionless. This paper shows a nice transistion from Toricelli's law to an exponential as the length of the tube is increased. The non-dimensionalization collapses all the data well regardless of tube length. The model works quite well when compared to experimental data (though I did not include the experiments in this paper).