Math 53 Syllabus

Course outline.

In single variable calculus, you studied functions of a single variable, limits, and continuity. You then learned about derivatives, which describe how functions change, and which can be used to help find maxima and minima of functions. You then learned about integrals which describe the aggregate behavior of a function over an interval, such as the area under a curve or the average of a varying quantity. The derivative and the integral are then tied together in the fundamental theorem of calculus, one version of which relates the integral of the derivative of a function over an interval to the values of the function at the endpoints of the interval.

While single variable calculus is extremely useful, in many applications one needs to consider functions of more than one variable. For example, in understanding the weather, the temperature is a function of three variables: latitude, longitude, and altitude. In this course we will generalize the ideas from single variable calculus mentioned above to functions of two or three variables. (Most of what we will do can also be extended to functions of any number of variables, although this requires a bit more abstraction, and the thorough understanding of two and three variables that we will develop in this course will provide the intuition for understanding functions of more than three variables, should you encounter them later.)

Since the heart of the course comes at the end, we will move somewhat rapidly through the early, warm-up material, in order to devote sufficient time to the Big Theorems that come later.

Lecture schedule and homework assignments.

Below each lecture is the corresponding homework assignment; homework from a Tuesday lecture is due on Friday, and homework from a Thursday lecture is due the following Monday.

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