# Math 46: Schedule, topics and worksheets - SPRING 2007

1Mar 28 W website, 1.1 Dimensional analysisdimanal, solns
29 Th X-hrlin. algebra! problem session on dimensional analysis
30 F1.2Scalingscaling (w/ solns)
Apr 2 M1.3review ODE solution methodsode1
24 W1.4HW1 due. review 2D ODEs (phase plane), stabilityphaseplane
5 Th X-hrMatlab links numerical solution and plots of ODEs with Matlab, `intro46.m`
6 F2.1.1-2Regular perturbationregpert
9 M2.1.3-4Poincare-Linstedt method, asymptotic analysis, O(.) and o(.)
311 W2.2HW2 due. Singular perturbation dombal
12 Th X-hr-
13 F2.3Boundary layers and uniform approximation
16 M2.4Initial layers
418 W 2.5HW3 due. WKB approximationwkb
19 Th X-hr-
20 F2.6.1-2WKB eigenvalues, asymptotic expansion of integralswkbeig
23 M2.6.3Stationary phase integrals
525 W4.1HW4 due.Asymptotic expansion by parts.
26 Th X-hr-practise problems (also this)
Midterm 1: Thursday April 26, 6-8 pm, Kemeny 008. (solutions)
27 F4.1Orthogonal expansions & Fourier series
30 M4.1Uniform convergence, Bessel's inequalitybessel
6May 2 W4.2HW5 due. Sturm-Liouville problems.
3 Th X-hr-
4 F4.3.2Integral equations: Volterra equations volterra
7 M4.3.3 Degenerate Fredholm equations
79 W4.3.4HW6 due. Symmetric Fredholm equations
10 Th X-hr- Review degenerate Fredholm
11 F4.4Hilbert-Schmidt theorem, Green's functionsgreens
14 M4.4Green's functions via eigenfunction expansion. Classifying PDEs.
816 W6.1HW7 due. Integrating simple PDEs, fundamental solution, heat equation on R. simple_pdes
17 Th X-hr-practise problems and integral equation review
Midterm 2: Thursday May 17, 6-8 pm, Kemeny 008 (solutions)
18 F6.2.1-2Conservation laws, Green's identities, heat equation on Rn
21 M6.2.3-5, 6.3Energy method for uniqueness, Laplace's equation, maximum principle.
923 W6.4HW8 due. Eigenfunction (mode) expansions separable
24 Th X-hr6.5.2 (replacing Monday lecture) The Fourier transform.
25 F6.6 Convolution and Fourier transform solution of PDEs.conv
28 M (no lecture: Memorial Day)
1030 W-HW9 due. Review (practise questions)
Final Exam: Friday June 1, 8-11am, Kemeny 108 (solutions)