INTRODUCTION to VECTOR CALCULUS calculus 3
This video is the first in a series of videos which serve as an introduction to vector calculus and calculus 3. These videos are intended as supplemental material for the course MATH2021 which I am presently teaching at the University of Sydney.
0:00 Introduction and chit chat
2:48 Main topics of the video
3:22 Definition of a vector field
3:36 Weather map
3:45 Examples of vector fields
4:21 Remarks about vector fields in three dimensions
4:48 Vector fields in physics
6:33 Vector fields from smooth functions
6:45 Definition of the grad vector
6:59 Definition of the gradient field
7:12 Example of computing the gradient field of a function
7:54 Second example of computing the gradient field of a function
8:46 Definition of a conservative vector field
9:08 Example of determining whether a vector field is conservative
10:16 Second example of determining whether a vector field is conservative
11:45 Remarks about conservative vector fields
12:35 An important model for non-conservative vector fields
14:14 Vector fields which spiral or curl, are not conservative
15:06 Review
15:45 Closing remarks
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These videos are separate from my research and teaching roles at the Australian National University, University of Sydney, and Beijing University.
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