General review & continuation of Chapter 2 computer lab efforts Geology 351 - Geomath General review & continuation of Chapter 2 computer lab efforts tom.h.wilson tom.wilson@mail.wvu.edu Department of Geology and Geography West Virginia University Morgantown, WV

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

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

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

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

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

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

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

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)

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

This applet is fun to play with & educational too. Experiment with http://www.falstad.com/fourier/

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.

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

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

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

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.