The Undergraduate Program Committee
Date: May 12, 1999
Lecture | Topics/Sections | Some Standard Examples/Concepts |
---|---|---|
Day 1 | Overview of expectations for course, revised syllabus and discussion. Circuit problem. | |
Day 2 | Electric circuits. Series solution to first order ODEs. | |
Day 3 | Taylor Series, geometric series. | |
Day 4 | Discussion of homework. Absolute vs conditional convergence. Integral tests. | |
Day 5 | Ratio test, comparison test. | |
Day 6 | The mathematician's view of simple closed circuits. Reality versus its model. (General second order ODE with constant coefficients. Homogeneous and inhomogeneous. Main theorem of ODE's.) | |
Day 7 | Matrix version of the circuit problem. Comparison with diagonal matrices. Exponential of matrix. | |
Day 8 | Matrix algebra, properties of a matrix not dependent on coordinates, computation of eigenvalues. Solve Wednesday's circuit problem. | |
Day 9 | Relax and review. | |
Day 10 | The heat equation on a wire. Setting it up. | |
Day 11 | Turning the heat equation into an eigenvalue problem. Possible solutions. | |
Day 12 | Student presentation of models. Three ways to look at a chime. | |
Day 13 | General discussion of Fourier series. Idea of vector spaces of functions, linear independence, completeness, etc. | |
Day 14 | Discussion of colloquium with Beth Bradley. [on an application of the wave equation.] | |
Day 15 | Bring your solutions to the wave equation for your chime. Student presentations of solutions. Oscilloscope will do Fourier analysis and tell you what frequencies are present. | |
Day 16 | Guest demo: Building guitars using the wave equation. The round drumhead. Mook's vibrating membrane. | |
Day 17 | Guest presentation: analysis of oboe sounds and questions for speaker. In class modelling problem: human voice. | |
Day 18 | Relax and review. | |
Day 19 | Set up of Schrodinger's equation. Probability distributions. Discussion of symmetry issues for that and the spring model. Idea of symmetry group. | |
Day 20 | Separation of variables. Eigenvalue problem associated to hydrogen. | |
Day 21 | The group of rotations, invariant subspaces, representations. | |
Day 22 | Student presentation of homework problems | |
Day 23 | Schur's lemma, intro to spherical polynomials | |
Day 24 | the spherical polynomials, intro to last assignment | |
Day 25 | Homework: compute the allowable eigenvalues for hydrogen. Can you adjust parameters so that they match the real ones? | |
Day 26 | Demo: look at Balmer lines. Discussion of final exam. | |
Day 27 | Surveys,-pass out take-home; collect homework from Schrodinger's equation (all). | |
Day 28 | ||