Demystifying the Equations of Sedimentary Geology Larry Lemke Environmental Science Program Department of Geology
GOALS Alleviate student apprehensions –Build confidence –Establish effective habits Refresh and review –Reinforce key concepts –Connections with math, physics, and chemistry
Presentation Format Goals and Objectives Three approaches I use –Surgical strike reviews –Unit analyses –Perturbation interrogation Discussion: Dealing with Student Math-a-phobia –Strategies –Experiences
1. Surgical Strike Reviews Explain what you’re doing and why you’re doing it Use at the beginning of class Keep it brief – 10 minutes tops! Stay focused – only target what you’ll actually use in the day’s lecture. Revisit in subsequent lectures 5 to 10-minute review of relevant math principles targeted for a specific lecture What:
2. Unit Analysis Use routinely after presenting or deriving a new equation. Use common units to move toward generic (Mass, Length, Time) units: Assigning fundamental units of Mass, Length, and Time to analyze an equation What:
Unit Analysis Apply to derived quantities or units, such as centipoises for dynamic viscosity: Assigning fundamental units of Mass, Length, and Time to analyze an equation What:
3. Perturbation Interrogation Use in combination with Unit Analysis. Use with simple quantities: F=ma Works great with ratios: How does an equation change when its individual components increase or decrease? What:
3. Perturbation Interrogation One More Example Engelund & Hansen nondimensional sediment flux Express coefficients as constants Shields parameter or “Sheilds Stress” “What does this equation tell me?”
3. Perturbation Interrogation One More Example Shear stress – proportional to water depth (h) and stream gradient (S) Substituting into canceling
3. Perturbation Interrogation One More Example Substituting into: Will sediment flux increase or decrease if… …the water depth (h) increases? …the stream gradient (S) increases? …the grain diameter (D) increases?
Discussion Your experiences Your solutions