This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 (...
View
Full
Document
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
 MILTON
 Calculus

Click to edit the document details