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Our last month will be combining the multivariate calculus with vector calculus and this culminates in several important theorems which tie all of Calculus III topics together into several beautiful and useful packages!
learn Calculus III or needing a refresher in some of the topics from the class. These notes do assume that the reader has a good working knowledge of Calculus I topics including limits, derivatives and integration.
learn Calculus III or needing a refresher in some of the topics from the class. These notes do assume that the reader has a good working knowledge of Calculus I topics including limits, derivatives and integration.
Fundamental Theorem of Calculus. Along this theme, this course provides a basis to extend what you have learned in Cal 1 and Cal 2 into the three dimensional (and sometimes higher dimensional) setting.
Textbook. First published in 1991 by Wellesley-Cambridge Press, this updated 3rd edition of the book is a useful resource for educators and self-learners alike. It is well organized, covers single variable and multivariable calculus in depth, and is rich with applications.
2. Let D =fxx(x,y)fyy(x,y) f2xy(x,y) IF (a) D > 0 AND fxx <0, f(x,y) is local max value (b) D > 0 AND fxx(x,y)>0 f(x,y) is local min value. 3. Determine if any boundary point gives min or max. Typically, we have to parametrize boundary and then reduce to a Calc 1 type of min/max problem to solve.
Contents CHAPTER 0 Highlights of Calculus 0.1 Distance and Speed ==Height and Slope 1 0.2 The Changing Slope of yDx2 and yDxn 9 0.3 The Exponential yDex 15 0.4 Video Summaries and Practice Problems 23 0.5 Graphs and Graphing Calculators 45 CHAPTER 1 Introduction to Calculus
