1. General review & continuation of Chapter 2 computer lab efforts
Geology Geomath
General review & continuation of Chapter 2 computer lab efforts
tom.h.wilson
Department of Geology and Geography
West Virginia University
Morgantown, WV

2. Don’t forget to hand in problems 1-20 before leaving today
Tom Wilson, Department of Geology and Geography

3. Objectives for the day
Look over the list of mathematical models used to represent geological relationships
Introduce another class of mathematical functions used to represent geological and other observations in mathematical form.
Continue using computer to visualize mathematical models, develop comprehensive solutions and help gain a broader understanding of our data and their implications.
Tom Wilson, Department of Geology and Geography

4. Mathematical models we’ve reviewed
Linear
Quadratic
General polynomial (order n)
Power laws
Exponential (or allometric)
Logarithmic
These mathematical functions allow us to represent a variety of geological data in mathematical form.
These models allow us to quantify our observations and make predictions about future behaviors.
Tom Wilson, Department of Geology and Geography

5. A couple questions for group discussion
Tom Wilson, Department of Geology and Geography

6. Using sines and cosines to represent arbitrary functions
Using sines and cosines to represent arbitrary functions. The Fourier series: a weighted sum of sines and cosines
Periodic functions and signals may be expanded into a series of sine and cosine functions

7. Note that the Fourier series shares some similarity to the order-n polynomial
Tom Wilson, Department of Geology and Geography

8. Simulate the step using a sum of sines and cosines. An impossible task?
Tom Wilson, Department of Geology and Geography

9. Try the excel file step2.xls (see link on class page)
Fourier series
Try the excel file step2.xls (see link on class page)
Sin(wt)1/3sin(3wt)1/7sin(7wt)

10. The step function is defined by the Fourier series shown below
Function of t , x, or other independent variable.
Tom Wilson, Department of Geology and Geography

11. This applet is fun to play with & educational too.
Experiment with

12. Another function to add to your tool kit.
Fourier series
The Fourier series can be expressed more compactly using summation notation
You’ve seen from the forgoing example that right angle turns, drops, increases in the value of a function can be simulated using the curvaceous sinusoids.
Another function to add to your tool kit.

13. A more comprehensive look at Problem 2.13 radioactive decay
Tom Wilson, Department of Geology and Geography

14. Problem 2.13 See page 38 of the lab guide for detailed check list.
Statement of problem
Submit two excel plots
Label plots showing values in question
Present calculations of t(a=100) as a cross check on your computer work
State result
Tom Wilson, Department of Geology and Geography

15. Today’s group problems: finding the intercept
Tom Wilson, Department of Geology and Geography

16. To do list … Hand in problems 1-20 before leaving
Continue working through the computer lab problem 2.13
Bring questions to class on Thursday
Hand in the group problems before leaving (i.e determine the intercept and Co)
Excel and book problems 2.11 and 2.12 are due this Thursday. See page 26 of lab guide for presentation format.