MA 501
Advanced Mathematics for Engineers and Scientists I
FA11 SAS 2106 9:10-10:00 MWF
Lubkin
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Dates |
Topics Schedule will be
revised often during the semester; if it's in gray, it's tentative |
Read this before class |
Homework * with
plots. |
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8/17, 19 |
course
policies review of ordinary differential equations |
Appendix A.1-2 |
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8/22-26 |
review: ODE review: Euler's
formula review:
roots of a complex number orthogonality
of vectors and functions introduction
to Maple |
6.1 |
HW1 A.2/ 4,
10, 12, 20, 24, 26, 30, 40 and make
Maple graphs of 4 of the solutions (your choice). You will need to choose
values for the constants in order to plot. much
easier than a typical HW set due Wed
8/31 |
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8/29-9/2 Tues is last day to
add |
periodic functions Fourier series Gibbs phenomenon odd and even functions
periodic extensions |
2.1-2.4 |
HW2 6.1/2
(use the definitions), 21 2.1/2* (some
will have to be sketched by hand!), 8 Spend 30
minutes exploring the Falstad Fourier series applet. 2.2/1-4*
(plot by hand!), 6*, 7*, 8*, 10*, 11* (For 6-11, do both parts (a) and (b),
but you only need to plot N=1, 2, 4, 8, 16. You can also do N = 32 if you
want. For each problem, plot f and the partial sums all on the same axes.)
Hint: You will have to think about problems10-11, because careless use of
Maple will mislead you! 2.3/6*
(pick parameter values for plotting), 20ab due Fri
9/9 |
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9/7, 9 no classes Monday |
Fourier series applet wave equation separation of variables eigenvalues,
eigenfunctions IC, BC |
3.1-3.3 |
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9/12-16 |
superposition 1D wave applet heat equation |
3.5 3.6 |
HW3 3.1/1-6, 7abe 3.3/2**, 4**, 6**, 11, 12a-d 3.5/2**, 4**, 9*, 12** due Mon 9/26 |
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9/19-23 |
no class no office hours catch up on reading the chapters! |
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9/26-30 |
various BC in the heat equation wave and heat eq in 2D Laplace equation |
3.7, 3.8 6.2 |
HW4 3.6/2**, 4**, 16 3.8/2*, 4*, 8 3.10/2* due Wed 10/5 |
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10/3, 5 |
Monday class canceled
(illness) wave and heat eq in 2D inner products in 2D |
3.5, 3.6, 3.7 |
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10/10-14 Friday last day to drop |
review Monday midterm Wednesday go over exam Robin BC |
3.6 |
HW5
3.6/5, 6** 3.7/2**, 12** 6.2/12, 14, 16, 18, 23*, 26* due Wed 10/19 |
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10/17-21 |
inner product with a weight Sturm-Liouville theory Laplace equation on a disk Euler equations (ODE) |
6.1, 6.2 A.3, 4.1, 4.4 |
HW6 A.3/ 32 6.1/ 6 4.4/ 2*, 4*, 8*, 12*, 14*, 21, 22* Make plots in both height and contour format. Use
plot3d and contourplot, and make sure your coordinates plot correctly! due Wed 10/26 |
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10/24-28 |
wave equation on a disk, radially symmetric Bessel functions pebble in a pond wave equation on a disk, not symmetric |
4.2, 4.7, 4.8 4.3, 6.3 |
HW7 4.7/ 18*, 20* (pick values for the constants for your
plots) 4.8/ 26*, 30* 4.2/ 3**, 4**, 6** due Wed 11/2 |
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10/31-11/4 |
Laplace transforms ODE using Laplace transforms convolution |
8.1, 8.2, 8.3, Appx. B4 |
Project 1 3.8/11** 4.2/10, 11** 6.3/1** work in teams of 2 or 3 with all names on the
same paper due Fri 11/11 |
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11/7-11 |
erf and erfc step and delta
functions PDE using Laplace transforms cartoon physics: the falling infinite string complex Fourier series Fourier integral + transform properties of FT |
7.1, 7.2 2.6 7.8 |
HW
8 8.1/ 8, 16, 24, 26, 30, 40 8.2/ 24, 30, 40 Method: First get used to using the
tables, then you can check your
answers in Maple. 8.3/ 2**, 10**, 15, 16** due Friday 11/18 |
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11/14-18 |
PDE using the Fourier transform D'Alembert's solution midterm Friday |
3.4 7.3, 7.4, 7.8 |
HW 9 7.2/ 2*, 4*, 38, 50, 53, 54 7.3/ 2**, 4**, 8 (this is called the
advection equation), 17**, 22** 7.4/ 2**, 26** 7.8/ 52 due 12/2 |
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11/21 |
Gaussian kernel of diffusion equation multiple use of
transforms |
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Project 2 due
after end of classes |
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11/28-12/2 |
multiple use of transforms systems of PDE finite difference methods review |
9.1 |
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Mon Dec 12, 8-11 am |
final exam |
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