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Chapter 14Partial Derivatives
14-1 Functions of Several Variables14-2 Limits and Continuity14-3 Partial Derivatives14-5 The Chain Rule14-6 Directional Derivatives
GradientsTangent Planes and Normal Lines
14-7 Maximum and Minimum Values
The following notes are for the Calculus D (SDSU Math 252)classes I teach at Torrey Pines High School. I wrote andmodified these notes over several semesters. Theexplanations are my own; however, I borrowed severalexamples and diagrams from the textbooks* my classes usedwhile I taught the course. Over time, I have changed someexamples and have forgotten which ones came from whichsources. Also, I have chosen to keep the notes in my ownhandwriting rather than type to maintain their informalityand to avoid the tedious task of typing so many formulas,equations, and diagrams. These notes are free for use by mycurrent and former students. If other calculus students andteachers find these notes useful, I would be happy to knowthat my work was helpful. - Abby Brown
SDUHSD
Abby Brown
Calculus III/DSDSU Math 252
www.abbymath.comSan Diego, CA
* , 6th & 4th editions, James Stewart, ©2007 & 1999Brooks/Cole Publishing Company, ISBN 0-495-01166-5 & 0-534-36298-2.(Chapter, section, page, and formula numbers refer to the 6th edition of this text.)
, 5th edition, Roland E. Larson, Robert P. Hostetler, & Bruce H. Edwards,
Calculus: Early Transcendentals
*Calculus ©1994D. C. Heath and Company, ISBN 0-669-35335-3.
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Example: Related Rates The radius of a right circular cylinder is increasing at the rate of 6 inches per minute and the height is decreasing at the rate of 4 inches per minute. What is the rate of change of the volume and surface area when the radius is 12 inches and the height is 36 inches?
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