6/26/2014
Lecture 1 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 1
Lecture 2
By Giuseppe Tenti and annotated by Douglas Wilhelm Harder.
1. The flux o
6/26/2014
Lecture 10 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for Electrical Engineers
Lecture 10
Lecture 9 | Lecture 11
The previous lectures discussed the phenomena of vortici
6/26/2014
Lecture 14 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 14
Lecture 13 | Lecture 15
Surface Integrals of Vector Fields
To evaluate a surfac
6/26/2014
Lecture 15 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 15
Lecture 14 | Lecture 16
Differential Vector Calculus: The Operator
In Lectures
6/26/2014
Lecture 13 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 13
Lecture 12 | Lecture 14
Surface Integrals of Scalar Fields
First, consider the
6/26/2014
Lecture 12 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for Electrical Engineers
Lecture 12
Lecture 11 | Lecture 13
Now that we have parametrized surfaces, we will proceed
6/26/2014
Lecture 9 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 9
Lecture 8 | Lecture 10
Flux and Divergence of a Vector Field
Consider again a smo
6/26/2014
Lecture 8 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 8
Lecture 7 | Lecture 9
The Vorticity of a Vector Field
We will consider the veloci
6/26/2014
Lecture 11 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for Electrical Engineers
Lecture 11
Lecture 10 | Lecture 12
In the previous lecture, we discussed the parameterizat
6/26/2014
Lecture 7 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 7
Lecture 6 | Lecture 8
The Circulation of a Vector Field
Given a smooth vector fie
6/26/2014
Lecture 5 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 5
Lecture 4 | Lecture 6
Path Independence and Gradient Fields
We have already demon
6/26/2014
Lecture 4 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 4
Lecture 3 | Lecture 5
Arc Length
You will recall from Calculus that the integral
6/26/2014
Lecture 6 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 6
Lecture 5 | Lecture 7
Green's Theorem
Gradient fields are very important for appl
6/26/2014
Lecture 3 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for Electrical Engineers
Lecture 3
Lecture 2 | Lecture 4
The Line Integral
Recall that with standard integration, th
6/26/2014
Lecture 2 | MATH 212 | Department of Electrical and Computer Engineering | University of Waterloo
MATH 212 Advanced Calculus 2 for
Electrical Engineers
Lecture 2
Lecture 1 | Lecture 3
Any interval of the form
is a continuous line as a subset o