# Math 46: Schedule, topics and worksheets - SPRING 2008

1Mar 26 W website, 1.1 Dimensional analysis
27 Th X-hrlin. algebra! problem session on dimensional analysis dimanal_I, dimanal_II
28 F1.2Scalingscaling (w/ solns)
31 M1.3review ODE solution methodsode1
2Apr 2 W2.1.1-2HW1 due. Regular perturbationregpert
3 Th X-hrMatlab links numerical solution and plots of ODEs with Matlab, `intro46.m`. Also consider Intro to Matlab workshop, 4-6pm.
4 F2.1.3Poincare-Linstedt method.
7 M2.1.4asymptotic analysis, O(.) and o(.), pointwise vs uniform convergence.
39 W2.2HW2 due. Singular perturbation, dominant balancing dombal
10 Th X-hr-
11 F2.3Boundary layers and uniform approximation (real world examples: bdry layer 1, 2, inviscid, shedding)
14 M2.4Initial layersinitlayer
416 W 2.5HW3 due. WKB approximation: non-oscillatory and oscillatory cases. wkb
17 Th X-hr-
18 F2.5.2WKB eigenvalues (plot, accuracy test code: wkb_acc, shooting)wkbeig
21 M4.1Orthogonal expansions & Fourier series
523 W4.1HW4 due. Uniform vs L2 convergenceL2conv
24 Th X-hr-practise problems (also this)
Midterm 1 (solutions: Thursday April 24, 6-8 pm, Kemeny 105 (prac exam, solutions)
25 F4.2Bessel's inequality, Sturm-Liouville problems bessel
28 M4.2Sturm-Liouville eigenvalue proofs reality
630 W4.3.2HW5 due.Energy method. Integral equations: Volterra equations volterra
May 1 Th X-hr-Volterra applications, Picard's methodivpvolterra
2 F4.3.4Degenerate Fredholm equations degenerate Fredholm practise
5 M4.3.4Symmetric Fredholm equations, Hilbert-Schmidt theorem. Worked examples for degenerate Fredholm
77 W-HW6 due. Application: Image-deblurring in 1D, convolution kernelsdeblur
8 Th X-hr-
9 F4.4 Deblurring, regularization, Green's functions. greens
12 M4.4.3Greens functions, their eigenfunction expansion.
814 W6.1HW7 due. Classifying PDEs, integrating simple PDEs, fundamental solution, heat equation on R. simple_pdes
15 Th X-hr-practise problems, integral equation review, practise midterm 2 (solutions).
Midterm 2: Thursday May 15, 6-8 pm, Kemeny 105 (solutions)
16 F6.2.1-2 Conservation laws, multivariable notation, Green's identities, heat equation on Rn
19 M6.2(no lecture; Alex away)
921 W6.2.3-5, 6.3HW8 due Energy method for uniqueness, Laplace's and Poisson's equations, maximum principle. greenident
22 Th X-hr6.5.2 (replacing Memorial day) The Fourier transform.
23 Fr6.5.2Convolution and Fourier transform solution of ODEs and PDEs. appletconv
26 M (no lecture: Memorial Day)
1028 W-HW9 due. Review (practise questions, practise final, solutions)
Final Exam: Saturday May 31, 8-11am, Haldeman 028 (solutions)