General review continuation of Chapter 2 computer lab

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

Return homework and discuss Keep all returned homework assignments: 1) for study and 2) to cross check with the grade summary Questions on the homework? 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. • Use the computer to visualize mathematical models and help us get a broader understanding of our data 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

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

Fourier series • Try the excel file step 2. xls

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/

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

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

For the day … • Continue working through the computer lab problems • Bring questions to class on Tuesday • Hand in the group problems before leaving