Introduction to 3c 16 3 Part 3
Exploring 3c 16 3 Part 3 reveals several interesting facts. Establishing that conservative vector fields are the only ones independent of path and that work integrals of conservative fields ...
3c 16 3 Part 3 Comprehensive Overview
The fundamental theorem of line integrals, stated in general and proved for smooth curves in 2-space. We look at several work integrals along 2 different paths connecting the same starting and ending points. Some definitions: simple curves, closed curves, simple closed curves, and simply connected regions.
Parametrizing surfaces that are graphs of of functions of x and y or r and theta. We also look at
Summary & Highlights for 3c 16 3 Part 3
- The test for a conservative vector field. We work through the test in 2-space; there is a similar test in
- Verifying a vector field is conservative, finding a potential function, and using that to evaluate a work integral.
- A brief discussion of the vocabulary: conservative vector fields and potential functions and their relationship to the conservation of ...
- Looking at why our regions need to be simply connected.
- Another example of verifying that a vector field is conservative and finding a potential function.
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