Math 46: Schedule, topics and worksheets - SPRING 2011

weekdatereading daily topics & demosworksheets
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.