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Geomath

Geomath. Geology 351 -. Differential Calculus (part 2). tom.h.wilson tom.wilson@mail.wvu.edu. Dept. Geology and Geography West Virginia University. Finish reading Chapter 8. Also don’t forget to hand in the fitting lab problem (option 1 or 2) before leaving today.

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Geomath

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  1. Geomath Geology 351 - Differential Calculus (part 2) tom.h.wilson tom.wilson@mail.wvu.edu Dept. Geology and Geography West Virginia University Tom Wilson, Department of Geology and Geography

  2. Finish reading Chapter 8 Also don’t forget to hand in the fitting lab problem (option 1 or 2) before leaving today. Problems 8.13 and 8.14 are tentatively due next Thursday. Bring questions to class on Tuesday Tom Wilson, Department of Geology and Geography

  3. Product and quotient rules - How do you handle derivatives of functions like or ? The products and quotients of other functions Tom Wilson, Department of Geology and Geography

  4. Removing explicit reference to the independent variable x, we have Going back to first principles, we have Evaluating this yields Since dfdg is very small we let it equal zero; and since y=fg, the above becomes - Tom Wilson, Department of Geology and Geography

  5. The quotient rule is just a variant of the product rule, which is used to differentiate functions like Which is a general statement of the rule used to evaluate the derivative of a product of functions. Tom Wilson, Department of Geology and Geography

  6. The quotient rule states that The proof of this relationship can be tedious, but I think you can get it much easier using the power rule Rewrite the quotient as a product and apply the product rule to y as shown below Tom Wilson, Department of Geology and Geography

  7. We could let h=g-1 and then rewrite y as Its derivative using the product rule is just dh = -g-2dg and substitution yields Tom Wilson, Department of Geology and Geography

  8. Multiply the first term in the sum by g/g (i.e. 1) to get > Which reduces to the quotient rule Tom Wilson, Department of Geology and Geography

  9. Take a few moments to through the examples on your worksheet Tom Wilson, Department of Geology and Geography

  10. A brief look at derivatives of trig functions.Consider dsin()/d.Start with the following - Take notes as we go through this and the derivative of the cosine in class. Tom Wilson, Department of Geology and Geography

  11. Functions of the type Recall our earlier discussions of the porosity depth relationship Tom Wilson, Department of Geology and Geography

  12. Between 1 and 2 kilometers the gradient is -0.12 km-1 Tom Wilson, Department of Geology and Geography

  13. As we converge toward 1km, /z decreases to -0.14 km-1 between 1 and 1.1 km depths. Tom Wilson, Department of Geology and Geography

  14. When we ask “What is the gradient at exactly 1km? We are asking – “What is ? Tom Wilson, Department of Geology and Geography

  15. Computer evaluation of the derivative This is an application of the rule for differentiating exponents and the chain rule Tom Wilson, Department of Geology and Geography

  16. Basic rule for differentiating exponential functions Sketch and discuss The rule for differentiating exponential functions incorporates the chain rule Tom Wilson, Department of Geology and Geography

  17. Work through the Excel Exercise In the lab exercise c = 1. Tom Wilson, Department of Geology and Geography

  18. Have a look at limits.xls Derivatives of trig and other functions Tom Wilson, Department of Geology and Geography

  19. Finish reading Chapter 8 Don’t forget to hand in the fitting lab problem (option 1 or 2) before leaving today. Problems 8.13 and 8.14 are tentatively due next Thursday. Bring questions to class on Tuesday Tom Wilson, Department of Geology and Geography

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