Toronto Math Forum
APM3462015F => APM346Lectures => Topic started by: Victor Ivrii on September 18, 2015, 12:59:05 AM

During first two hours we covered Chapter 1. Basically it is a guided tour into PDE realm. This material will be left out of Home Assignments (exception: HA1 covering some classification: what is the order of equation? What are linear/semilinear/quasilinear/nonlinear equations? and some very simply solvable equations). Those would be one question in Quiz 1 and not represented in Term Tests or Final at all. However understanding is important: why we need to study PDEs, how they emerge, and not only on their own but also with BVP (boundaryâ€“value problems), IVP (initial value problems) and IBVP (initialboundary value problems). Why some equations come from the physical universe (and not only) but some others seem to be nothing more but mathematical artefacts (which is not always true). This Chapter is important because it gives a purpose to our class. You may want to review it later when you learn more in the class (and may be several times).
Later you may want to review Chapter 14 (Section 14.1 (http://www.math.toronto.edu/courses/apm346h1/20159/PDEtextbook/Chapter14/S14.1.html), Section 14.2 (http://www.math.toronto.edu/courses/apm346h1/20159/PDEtextbook/Chapter14/S14.2.html), Section 14.3 (http://www.math.toronto.edu/courses/apm346h1/20159/PDEtextbook/Chapter14/S14.3.html)) which is another guided tour into PDE realm (Conservation laws, Maxwell equations, Quantum Mechanical Equations), which we definitely will not cover.
We started Chapter 2. So far we covered the part of Section 2.1 (http://www.math.toronto.edu/courses/apm346h1/20159/PDEtextbook/Chapter2/S2.1.html) (namely, Subsections 2.1.12.1.3). So far we did no new math (just some very basic ODEs) but we were thinking different, looking at these things from the different angle. So complexity is not from mathematics involved but from the change of perspective. It is very important: new mathematical constructions we'll do later will require this new perspective. So, despite mathematical simplicity watch carefully! You may be lost very soon otherwise.