Fysikens Matematiska Metoder, Tillägskurs



Lektion 1:
Introduction and overview: what is the course about (see e.g. the  WIKIPEDIA pages on variational calculus and Green's functions). Variational problems (examples). Hamilton's principle. Euler-Lagrange equations ([Var] p1-6 and/ or [KS] Section 8.1).

Lektion 2: Derivation of Euler-Lagrange equations. Functionals depending on several variables.  Example from mechanics: mathematical pendulum, Newton's equations in spherical coordinates. Variational problems for functions in several variables. Example: equilibrium form of a membrane with fixed boundary.  ([Var]  2.1, [KS] 8.1). Comments: I my lectures I presented several examples from classical mechanics. You can find a detailed description of all these examples, and a lot more, in the lecture notes on David Tong (I'll refer to is as [T]) which I highly recommend. In these notes you can also find a list of standard textbooks on classical mechanics. The examples I talked about are in Sections:  [T] 2.3 ("pendulum") 2.5.1 ("beat on a rotating hop"),

Lektion 3: (Most of the material I discussed in todays class - and much more - can be found in Tong's compendium [T] referred to above). Newton's mechanics (parts of [T] 1.2 and 1.3). Lagrangian formulation: Examples: Hyperbolic coordinates ([T] 2.2.2.), the pendulum (2.3), bead on a rotating hoop (2.5.1), double pendulum (2.5.2 and 2.6.1), spherical pendulum (2.5.3), particles in electromagnetic field (2.5.7), Hamilton's principle. Introduction to Hamiltonian mechanics (parts of [T] 4., im particular 4.1.2 and 4.1.3). Comment: The examples mentioned above all are possible exam problems.

Lektion 4: The structure of a physical theory: classical vs. quantum mechanics. Poisson brackets. Comment: Most of what I discussed last time and today can be found in [T], 4.1-4.3.

100329: I apologize that I could not cancel the lecture today in time (I was not here due to a mistake I made, I am really sorry). I will instead have an extra lecture short before the exam: Monday, April 12, 15.15-17.00h, room anounced here soon.

Next lecture: tomorrow (Thuesday March 30) 8.15h in FB53.

Lektion 5: What are Green's functions, why are they useful, how are they computed, examples (ODE examples; heat equation; string).
(Chapters 5.1 and 5.3 in [KS]; parts of Green.pdf).  Remark: I just put the numerical homework problem for this year out. Please note the deadline for this problem!
Senast uppdaterad: Dec 13, 2010