# Math 46: Schedule, topics and worksheets - SPRING 2009

weekdatereading daily topics & demosworksheets
1Mar 30 M website, 1.1 Dimensional analysis (& review linear algebra) dimanal_I
Apr 1 W1.2Scalingscaling
2 Th X-hrlinear algebra! problem session on dimensional analysis dimanal_II
3 F1.3review ODE solution methods (Math 23)ode1
26 M2.1.1-2 Regular perturbation of ODEsregpert
8 W2.1.3 HW1 due. Poincare-Linstedt method.
9 Th X-hrMatlab links numerical solution and plots of ODEs with Matlab, `intro46.m`.
10 F2.1.4asymptotic analysis, O(.) and o(.), pointwise vs uniform convergence.asympt
313 M2.2 Singular perturbation, dominant balancing dombal
14 Tu-[if needed: 4-6pm Matlab intro session by Academic Computing, sign up]
15 W2.3 HW2 due. Boundary layers and uniform approximation (real world examples: bdry layer 1, 2, inviscid, shedding)
16 Th X-hr2.4(moved from Friday) Initial layersinitlayer
17 F-(no lecture; Alex away)
420 M 2.5WKB approximation: non-oscillatory and oscillatory cases. wkb
22 W2.5.2HW3 due. WKB eigenvalues (plot, accuracy test code: wkb_acc, shooting)wkbeig
23 Th X-hr-
24 F4.1Orthogonal expansions & Fourier series
527 M4.1Uniform vs L2 convergenceL2conv
29 W4.2HW4 due. Bessel's inequality, Sturm-Liouville problems bessel
30 Th X-hr-practise problems, esp see practise exams linked on next line.
Midterm 1 (solutions): Thursday April 30, 6-8 pm, Kemeny 108 (prac exam, solutions), (prac exam, solutions)
May 1 F4.2Sturm-Liouville eigenvalue proofs reality
64 M4.3.2(no lecture; Alex away)
6 W4.3.4 moved OH 4-5pm. Energy method. Integral equations
7 Th X-hr- HW5 due. Volterra equations, conversion to IVPs. volterra
8 F4.3.4 Volterra applications, second-order IVPs, Picard's methodivpvolterra
711 M- Degenerate Fredholm equations. Worked examples for degenerate Fredholm
13 W4.4HW6 due. Symmetric Fredholm equations, Hilbert-Schmidt theorem.
14 Th X-hr- Degenerate Fredholm practise, integral equation review. degenerate
15 F4.4.3 Application: Image-deblurring in 1D (Tan pics), convolution kernels. Regularization, Green's functions. deblur
818 M4.4.3, 6.1 Greens functions, their eigenfunction expansion. greens
20 W6.2.1-2HW7 due. Conservation laws, multivariable notation, Green's identities, heat equation on Rn
21 Th X-hr-practise problems, practise midterm 2 (solutions); practise midterm 2 (solutions).
Midterm 2: Thursday May 21, 6-8 pm, Kemeny 108 (solutions)
22 F6.2.3-5, 6.3Energy method for uniqueness, Laplace's and Poisson's equations, maximum principle. greenident
925 M6.2 (no lecture: Memorial Day)
27 W6.5.2HW8 due. The Fourier transform.
28 Th X-hr6.5.2 (replacing Memorial day) Convolution and Fourier transform solution of ODEs and PDEs. appletconv
29 Frp.391-394How to use Table 6.2 in reverse.
10Jun 1 M-HW9 due. Review. practise questions, practise final (solutions), practise final (solutions).
Final Exam: Friday June 5, 11:30am-2:30pm, Kemeny 108 (solutions)