# Vector Calculus Independent Study Path

## Unit 3: Scalar Valued Functions

Scalar valued functions of several variables are fundamental to the study of vector calculus. For one thing, it is possible to break any vector valued function up into component functions, each of which is scalar valued. For another, they are the most direct generalization of the single variable functions you studied in calculus, and have all of the wonderful applications that you've come to love and expect (for example, max/min problems). In this unit, you will learn:
• How to graph scalar valued functions of two variables.
• How to find the level sets of scalar valued functions of two or three variables.
• How to calculate partial derivatives.
• How to compute the gradient.
• How to find the tangent plane to a graph.
• How to use the chain rule.
• How to calculate directional derivatives.
For more detailed instructions, see the Xdvi or PDF pages.

## Suggested Procedure

• Read and do some problems from
• Rogers Chapters 8, 9, 10, and 11,
• Marsden and Tromba chapter 2 (if you have the 4th edition, read section 3.1 as well), or
• Simmons sections 19.1 through 19.6
• Take the Sample Test, Xdvi or PDF.
• Take a unit test.

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watko@athena.mit.edu