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vpde_2019-20-diary [2020/02/15 10:30] trinh |
vpde_2019-20-diary [2020/03/06 09:04] trinh |
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We covered the computation of scalar integrals and work integrals, doing examples for both. We also covered various properties of curves (reversability, | We covered the computation of scalar integrals and work integrals, doing examples for both. We also covered various properties of curves (reversability, | ||
+ | |||
+ | ===== Week 2 ===== | ||
==== Lecture 4 (11 Feb 2020) ==== | ==== Lecture 4 (11 Feb 2020) ==== | ||
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We discussed how to interpret surface integrals, and how to calculate the two main surface integrals (a scalar one and a vector one). This involved writing dS as a cross product. We did an example with a sphere. | We discussed how to interpret surface integrals, and how to calculate the two main surface integrals (a scalar one and a vector one). This involved writing dS as a cross product. We did an example with a sphere. | ||
+ | |||
+ | ===== Week 3 ===== | ||
+ | |||
+ | ==== Lecture 7 (18 Feb 2020) ==== | ||
+ | |||
+ | * A short statement and discussion about the strikes. See the Owen Jones' article [[https:// | ||
+ | * Explanation of the surface integral formula | ||
+ | * Thinking about flux integrals and their interpretation (see [[https:// | ||
+ | * Chap. 7: Divergence and curl | ||
+ | |||
+ | ==== Lecture 8 (20 Feb 2020) ==== | ||
+ | * Finishing up the curl and divergence | ||
+ | * Doing more examples on (i) the computation of surfaces and normals; (ii) the computation of flux integrals | ||
+ | |||
+ | ==== Lecture 9 (21 Feb 2020) ==== | ||
+ | * Continued examples on (i) the computation of surfaces and normals; (ii) the computation of flux integrals | ||
+ | |||
+ | ===== Week 4 ===== | ||
+ | |||
+ | ==== Lecture 10 (25 Feb 2020) ==== | ||
+ | |||
+ | * We looked at the motivation of the divergence theorem (flux through a little cuboid) | ||
+ | * We stated the divergence theorem | ||
+ | * We did examples on computations using the divergence theorem | ||
+ | |||
+ | ==== Lecture 11 (27 Feb 2020) ==== | ||
+ | |||
+ | * Using the divergence theorem, we proved two versions of Green' | ||
+ | * We did examples on computations using Green' | ||
+ | |||
+ | ==== Lecture 12 (28 Feb 2020) ==== | ||
+ | |||
+ | * This was a complete problem set class, doing different examples of Green' | ||
+ | |||
+ | ===== Week 5 ===== | ||
+ | |||
+ | ==== Lecture 13 (3 Mar 2020) ==== | ||
+ | |||
+ | * We finished off the Vector Calculus portion of the term by discussing Stokes' | ||
+ | * We showed the intuition of Stokes' | ||
+ | * We did some examples on computations using Stokes' | ||
+ | |||
+ | ==== Lecture 14 (5 Mar 2020) ==== | ||
+ | |||
+ | * We played a video by Feynmann discussing the difficulty of defining magnetism (this is a precursor to help you understand the difficulty of modelling the real world!) | ||
+ | * We showed off a simulation of a 2D heat equation | ||
+ | * We derived the heat equation in 1D. | ||
+ | * We began a derivation of the wave equation in 1D. | ||
+ | |||
+ | ==== Lecture 15 (6 Mar 2020) ==== | ||
+ | * We completed the derivation of the wave equation in 1D. | ||
+ | * We showed off a simulation of a 2D wave equation | ||
+ | * We used separation of variables to introduce the topic of Fourier series. | ||
+ | |||
+ |