# Math 46: Schedule, topics and worksheets - SPRING 2011

1Mar 28 M website, 1.1 Dimensional analysis (& review linear algebra Math 22/24) dimanal_I
30 W1.2Scalingscaling
31 Th X-hrlinear algebra! problem session on dimensional analysis dimanal_II
Apr 1 F1.3review ODE solution methods (Math 23)ode1
24 M2.1.1-2 Regular perturbation of ODEsregpert
6 W2.1.3 HW1 due. Poincaré - Linstedt method.
8 Th- (no X-hr)
9 FMatlab linksGuest lecture (Katie Kinnaird): install Matlab ahead of time. solving ODEs and plotting solutions. Use `intro46.m`.
310 M2.1.4 Asymptotic analysis, O(.) and o(.), pointwise vs uniform convergence.asympt
12 W2.2 HW2 due. Singular perturbation, dominant balancing dombal
13 Th X-hr2.4(make-up lecture) Boundary layers and uniform approximation; real world examples: bdry layer 1, 2, inviscid, shedding
14 F2.3Initial layersinitlayer
418 M 2.5WKB approximation: non-oscillatory and oscillatory cases. wkb
20 W2.5.2HW3 due. WKB eigenvalues (plot, accuracy test code: wkb_acc, shooting)wkbeig
21 Th X-hr-
22 F4.1Asymptotics of integrals. Orthogonal expansions & Fourier series
525 M4.1Uniform vs L2 convergenceL2conv
27 W4.2HW4 due. Bessel's inequality, Sturm-Liouville problems bessel
28 Th X-hr-practise problems, esp. see practise exams linked on next line.
Midterm 1 (solutions): Thursday April 28, 6-8 pm, Carson 60 (07 prac mid1, solutions), (08 prac mid1, solutions), (09 prac mid1, solutions)
29 F4.2Sturm-Liouville eigenvalue proofs reality
6May 2 M4.3.2Energy method. Integral equations
4 W4.3.4HW5 due. Volterra equations, conversion to IVPs.volterra
5 Th X-hr-
6 F4.3.4 Volterra applications, second-order IVPs, Picard's methodivpvolterra
79 M- Degenerate Fredholm equations. Worked examples for degenerate Fredholm
11 W4.4HW6 due. Symmetric Fredholm equations, Hilbert-Schmidt theorem.
12 Th X-hr- Degenerate Fredholm practise, integral equation review. degenerate
13 F4.4.3 Application: Image-deblurring in 1D (Tan pics), convolution kernels, regularization. deblur
816 M4.4.3, 6.1 Green's functions, their eigenfunction expansion. greens
18 W6.2.1-2HW7 due. Conservation laws, multivariable notation, Green's identities, heat equation on Rnsimple_pdes
19 Th X-hr-practise problems, and practise exams linked on the next line.
Midterm 2 (solutions): Thursday May 19, 6-8 pm, Carson 60 (07 prac mid2, solutions), (08 prac mid2, solutions), (09 prac mid2, solutions)
20 F6.2.3-5, 6.3Energy method for uniqueness, Laplace's and Poisson's equations, maximum principle. greenident
923 M6.5.2The Fourier transform.
25 W6.5.2HW8 due. Convolution and Fourier transform solution of ODEs and PDEs. appletconv
27 Frp.391-394How to use Table 6.2 in reverse.
1030 M- (no lecture: Memorial Day)
June 1 W-HW9 due. Review. practise questions; 07 prac final (solutions), 08 prac final (solutions), 09 prac final (solutions).
Final Exam (solutions): Friday June 3, 3-6pm, Kemeny 007.