EAS 2655: Quantitative Methods

Objectives: To study basic maths and physics applied to the earth sciences.

In the schoolroom her quick mind had taken readily that strong starch of unexplained rules and disconnected facts which saves ignorance from any painful sense of limpness. - George Eliot, 1876: Daniel Deronda, Bk. 1, Ch. 4.

In contrast, EAS 2655 seeks to interest you in basic reasoning.

Text: Reference textbooks and class notes.

Professor: George Chimonas
ES&T 1102
Phone 4-3985
george.chimonas@eas.gatech.edu

Office hours: MWF 3:00-4:00, or any time you find me free in my office, or by appointment.

Grading: Three midterm exams, counting for 10 points each, a final examination, counting for 20 points, and five homeworks, counting for 10 points each.

86 - 100 = A
76 - 85 = B
66 - 75 = C
56 - 65 = D

Syllabus

• Weeks 1-2. Large numbers: power notation with integers; generalization of the power notation. The hydrostatic equation. Solving a differential equation with Excel. The standard bases 2, 10, and e. Logarithms. Integrals and derivatives of powers. Equations for natural growth and decay. Fitting data using logarithmic plots.
  
  
• Weeks 3-4. Random walks: the Gaussian and an Excel model. Molecules; gas pressure and energy. Estimating and quantifying errors. Fitting data with straight lines. The rms error.
  
  
• Weeks 5-6. Conservative and non-conservative systems in mechanics. Kinetic energy, potential energy, total energy and conservation of energy. Perfect differentials. Particles falling under gravity. Stability and instability; the potential energy function. Hookeâs law and simple harmonic oscillation about a stable equilibrium position. Friction: Stokes drag; Rayleigh friction; turbulent friction. Terminal velocity. Diffusion in the atmosphere.
  
  
• Week 7. Energy and Work. Heat as a form of energy. Specific heat. Conservation of total energy including heat.
  
  
• Week 8. The gas laws. Adiabatic, isothermal and general diabatic changes. Work done in compression or expansion. Computation of specific heats of an ideal gas. Thermal expansion of a gas at constant pressure.
  
  
• Week 9. Phase changes using water as the example. Latent heat. Thermodynamic equilibrium.
  
  
• Weeks 10-12. Introduction to Thermodynamics. The (zero), first and second laws of thermodynamics. Adiabats of an ideal gas and the entropy change between adiabats.
  
  
• Weeks 13-15. The generalization of entropy. Reversible and irreversible changes. Spontaneous change and irreversibility. The Carnot cycle. The conversion of heat to work and the limits on its efficiency. An introduction to the thermodynamic potentials U, H, F and G.