Vector Calculus Independent Study Unit 3 Scalar Valued Functions
Short Description
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 …
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Vector Calculus Independent Study
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 expecof the wonderful applications that you’ve come
to love and expect (for example, max/min problems).
In this unit you should/will learn:
1. Graphing
How to graph z = f(x; y).
How to nd cross sections (x = c or y = c).
How to nd levels sets z = c.
How to use symmetry to graph functions.
How to nd the domain of de nition of a function.
How to nd the level sets of w = f(x; y; z).
2. Partial derivatives
The limit de nition: @f
@x = limh!0
f(x+h;y).f(x;y)
h
How to compute…
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