6/19/2014
Lecture 13 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 13
Lecture 12 | Lecture 14
Surface Integrals of Scalar Fields
First, consider the in
6/19/2014
Lecture 12 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 12
Lecture 11 | Lecture 13
Now that we have parametrized surfaces, we will proceed t
6/19/2014
Lecture 15 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 15
Lecture 14 | Lecture 16
Differential Vector Calculus: The Operator
In Lectures 5
6/19/2014
Lecture 8 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 8
Lecture 7 | Lecture 9
The Vorticity of a Vector Field
We will consider the velocity
6/19/2014
Lecture 14 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 14
Lecture 13 | Lecture 15
Surface Integrals of Vector Fields
To evaluate a surface
6/19/2014
Lecture 6 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 6
Lecture 5 | Lecture 7
Green's Theorem
Gradient fields are very important for applic
6/19/2014
Lecture 10 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for Electrical Engineers
Lecture 10
Lecture 9 | Lecture 11
The previous lectures discussed the phenomena of vorticity
6/19/2014
Lecture 9 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 9
Lecture 8 | Lecture 10
Flux and Divergence of a Vector Field
Consider again a smoot
6/19/2014
Lecture 11 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for Electrical Engineers
Lecture 11
Lecture 10 | Lecture 12
In the previous lecture, we discussed the parameterizatio
6/19/2014
Lecture 7 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 7
Lecture 6 | Lecture 8
The Circulation of a Vector Field
Given a smooth vector field
6/19/2014
Lecture 3 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for Electrical
Engineers
Lecture 3
Lecture 2 | Lecture 4
The Line Integral
Recall that with standard integration, the
6/19/2014
Lecture 2 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 2
Lecture 1 | Lecture 3
Any interval of the form
is a continuous line as a subset of
6/19/2014
Lecture 4 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 4
Lecture 3 | Lecture 5
Arc Length
You will recall from Calculus that the integral
wh
6/19/2014
Lecture 1 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 1
Lecture 2
By Giuseppe Tenti and annotated by Douglas Wilhelm Harder.
1. The flux of
6/19/2014
Lecture 5 | ECE 206 | Department of Electrical and Computer Engineering | University of Waterloo
ECE 206 Advanced Calculus 2 for
Electrical Engineers
Lecture 5
Lecture 4 | Lecture 6
Path Independence and Gradient Fields
We have already demonst