Multivariable Calculus

You have all learned single variable calculus: the differential and integral calculus of functions of a single variable, f left parenthesis x right parenthesis . This is a very important area of mathematics, and it has widespread applications in applied math, physics, chemistry, engineering, environmental science, biology, economics, finance, and the list goes on. But there are limits to the applications of functions of a single variable, which essentially describes a universe in which there is one dimension, such as movement along a line, or a problem in which everything depends on only one input. The real world that we live in has three spatial dimensions; when an engineer is constructing a bridge, he or she certainly must understand how loads and support elements change in all three dimensions (if not, I recommend that you do not drive over that bridge). Multivariable calculus extends the concepts, techniques, and applications of calculus to functions of two or three (or more) variables: f left parenthesis x comma y right parenthesis space o r space f left parenthesis x comma y comma z right parenthesis . As in single variable calculus, the two main divisions of this subject are differential and integral calculus. Here in Math 1C we will study differential multivariable calculus. If you take the subsequent course, Math 1D, you will study integral multivariable calculus, parts of which are also referred to as vector calculus. The last major topic that we will cover in Math 1C, a topic in calculus in general, not specifically multivariable calculus, is the study of infinite sequences and series.

In our studies, these are our broad learning outcomes:

Students will solve problems involving applications of functions of multiple variables and series.
Students will develop conceptual understanding of sequences and series and functions of multiple variables and their rates of change. They will learn to demonstrate and communicate this understanding in a variety of ways, such as: reasoning with definitions and theorems, connecting concepts, and connecting multiple representations, as appropriate.
Students will demonstrate the ability to model lines and planes in space and calculate partial and directional derivatives of functions of multiple variables.

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