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FinalReview - FINAL REVIEW MATH 53 ANTON GERASCHENKO...

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FINAL REVIEW - MATH 53 ANTON GERASCHENKO Studying tips : (0) Look at the midterm 1 and midterm 2 review sheets. You are responsible for that material too. (1) Try doing the quizzes again (without looking at the solutions). Try doing the quizzes that other GSIs have posted. (2) Look at the summaries in the appropriate sections of the worksheets. Try doing the questions in the worksheets; they take much less time than the problems, but still test your understanding. (3) Look at the chapter reviews in the book. It doesn’t take much time to do the concept checks and the True-False quizzes. (4) Try doing the old midterms. Remember that you can submit a write-up of an old midterm problem for an extra credit point. (5) This review sheet doesn’t cover parameterizing curves or surfaces because I can’t think of any way to summraize everything you should know. I recommend trying to come up with lots of different surfaces and trying to parameterize them. In particular, you should be quite good at parameterizing surfaces of revolution. Vector Calculus: Derivatives: You’ve learned three types of derivatives. The notation is supposed to help you remember the formulas. You think of the operator as the “vector” ( ∂x , ∂y , ∂z ) . (Gradient) You apply gradient to a function to get a vector field: f := (bigg ∂f ∂x , ∂f ∂y , ∂f ∂z )bigg = ( f x , f y , f z ) The direction of the gradient is the direction of maximal increase of f . To get the rate of change of f in the direction of a unit vector u , you take D u f = u ·∇ f . Perhaps the most useful fact about the gradient is that it is always normal to the level curves or level surfaces of f .
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