Surfaces and Transformations

Partial Derivatives and vectors are essential to two important concepts in multivariable calculus-surfaces in 3 dimensional space and transformations from one coordinate system into another.  Thus, in this chapter, we combine the ideas of the first two chapters in order to study and explore surfaces and transformations.  

In so doing, we will introduce several concepts which will be important in the chapters on integration which are to follow.  We will also discover some very interesting and elegant results about surfaces.  In particular, we will introduce the concept of intrinsic properties of a surface, which will include some of the concepts that have greatly influenced mathematics over the past 100 years.

Summary and Review

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