Chapter Comments
- In Calculus I (differential calculus) you studied how to analyze functions of one variable (i.e., functions of the form y=f(x)). Note that the list of section titles below gives a list similar to the tools you used in Calculus I: domain and range will be discussed in §15.1, then limits and continuity, derivatives, tangent lines (including differentials and approximations), and extreme values. In Calculus IV you will be using many of the same strategies you have used before, but now with functions of more than one variable. Adding dimensions adds complications, but the content of Calculus IV draws very heavily on skills you already have from previous courses.
- One of the most challenging aspects of Calculus IV (multivariable calculus) is visualizing the objects being studied. To try to facilitate this process for you, we have tried to provide more graphics than most textbooks do. Be sure to study the pictures so that you can learn to think in 3-space.
Chapter Contents
- §15.1 Functions of Several Variables
- §15.2 Limits and Continuity
- §15.3 Partial Derivatives
- §15.4 Tangent Planes and Linear Approximations
- §15.5 The Chain Rule
- §15.6 Directional Derivatives and the Gradient Vector
- §15.7 Maximum and Minimum Values
- §15.8 Lagrange Multipliers
Chapter 15 Sample Test Items and
Sample Solutions
This document is part of the Math 2443: Calculus and Analytic Geometry IV course designed for the Independent Study Department in the College of Continuing Education at the University of Oklahoma, Norman.
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