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| ==== Lecture 9 (21 Feb 2020) ==== | ==== Lecture 9 (21 Feb 2020) ==== | ||
| * Continued examples on (i) the computation of surfaces and normals; (ii) the computation of flux integrals | * 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. | ||
| + | |||
| + | ===== Week 6 ===== | ||
| + | |||
| + | ==== Lecture 15 (10 Mar 2020) ==== | ||
| + | |||
| + | * We began our investigation of Fourier series, starting off by defining terminology of periodic, even, and odd functions. | ||
| + | * We stated the orthogonality property of sines and cosines | ||
| + | |||
| + | ==== Lecture 16 (12 Mar 2020) ==== | ||
| + | * We derived the Fourier sine and cosine coefficients | ||
| + | * We defined the notion of a Fourier sine series or a Fourier cosine series | ||
| + | * We studied an example of estimating abs(x) using a Fourier series | ||
| + | |||
| + | ==== Lecture 17 (13 Mar 2020) ==== | ||