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Unformatted text preview: Calculus : Math 21C, Fall 2010 Summary of topics covered after Midterm 2 1. Functions of several variables Plots. Graph z = f ( x, y ) of a function f ( x, y ) of two variables. Contour plots of level curves f ( x, y ) = c . Level surfaces f ( x, y, z ) = c of a function of three variables. Sets, limits and continuity. Open and closed sets in R 2 and R 3 . Interior points and boundary points. Limits and continuity of functions of several variables. (Intuitive ideas and examples only. No ϵ- δ definitions or proofs will be required for the final.) Derivatives. Interpretation of the derivative as the local linear approxima- tion of a function. Theorem. If the partial derivatives of a function exist and are continuous, then the function is differentiable. Chain rule. Chain rule for functions of several variables. For example, d dt f ( x ( t ) , y ( t ) , z ( t )) = ∂f ∂x ( x ( t ) , y ( t ) , z ( t )) dx dt ( t ) + ∂f ∂y ( x ( t ) , y ( t ) , z ( t )) dy dt ( t ) + ∂f ∂z ( x (...
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This note was uploaded on 03/18/2011 for the course MATH 21C taught by Professor Milton during the Spring '08 term at UC Davis.
- Spring '08