Vectors allow us to study curves in the *xy*-plane and in 3 dimensional space, but we cannot yet use vectors to study surfaces and solids in 3 dimensional space. Thus, in this
chapter, we introduce the primary tool in the study of surfaces and
solids*-functions of 2 variables*. Of particular importance in this introduction to functions of 2 variables will be the concept of a
*partial derivative*, and we will use the partial derivative to study concepts related to functions of 2 variables, such as tangent planes, extrema, and saddle points.

Moreover, we will also see that partial derivatives are important beyond their use in studying the geometry of a surface. Indeed, much of the science of the last century has been presented in the form of
*partial differential equations*. Thus, we will see that partial derivatives are also important in the types of equations and models that have dominated mathematics and science for over a century.

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