Welcome to this webpage!
<br><br>
<a href="syllabus-MAP4341.html">Syllabus</a>
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<b>Homework assignments:</b><br>
<b><font color=red> Note that late HW is not accepted!</font></b><br><br>


<b><font color=green> Graded HW assignments</font></b>:<p>
<a href="hw1.pdf">HW1</a> (<b>due Wed Feb 6</b>)<p>
<a href="hw2.pdf">HW2</a> (<b>due Mon Feb 25</b>)<p>
<a href="hw3.pdf">HW3</a> (<b>due Wed April 2</b>) <p>
<a href="hw4.pdf">HW4</a> (<b>due Mon April 21</b>).<br><br> 

<b><font color=green> Practice exams</font></b>:<p>
practice1: 1.4.1, 1.4.5, 1.4.7, 1.5.9,2.4.4,2.5.1,2.5.3,2.5.8<p>
practice2: 3.3.12, Sketch and calculate the 
Fourier series, Fourier sines series, Fourier cosine series of f1(x)=x^2, and f2(x)=|x|, 
(x in [-L,L] for Fourier series but x in [0,L] for Fourier sine or cosine series), 4.4.1,4.4.2.<p>
practice3: 4.6.1, 5.8.3, 5.8.11, 9.3.8, 9.3.14, 9.3.26<p>
practice4: 9.5.8, 12.6.6, 12.6.7a and d,12.6.8d,12.6.10

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<b><font color=green> Weekly ungraded HW assignments</font></b> (not collected):<br>

Wk 1 (ends Fr 1/11): read p4 (Conservation of heat energy, exact), 1.2.1, 1.2.2, 1.2.3, 1.2.5 (read p 9: diffusion
of a chemical pollutant first),1.3.2, 4.2.2, read section 4.3 (<b>mandatory</b>), 4.3.1.<p>
Wk 2 (ends Fr 1/18): 2.3.1 (c),2.3.2 (e)2.3.3 (b),2.3.5<p>
Wk 3 (ends Fr 1/25): MLK on Mon 1/21. 2.3.7, 2.4.2, 2.4.4, 2.5.1(d),2.5.3<p>
Wk 4 (ends Fr 2/1): 3.2.1 (b,c), 3.2.2(a,b), 3.2.4, 3.3.1(c),3.3.4.<p>
Wk 5 (ends Fr 2/8): no HW<p>
Wk 6 (ends Fr 2/15):3.3.5, 3.3.7, 3.3.13,4.4.1, 4.4.2 <p>
Wk 7 (ends Fr 2/22):4.6.1, 4.6.2, show that EM plane waves in vacuum propagate in the k-direction at the speed of light c.<p>
Wk 8 (ends Fr 2/29): no HW.<p>
Wk 9 (ends Fr 3/7): 5.3.3, 5.3.4, 5.8.1, 5.8.8<p>
Wk 10 (ends Fr 3/14): Spring Break.<p>
Wk 11 (ends Fr 3/21): 9.3.1,9.3.7,9.3.9,9.3.10.<p>
Wk 12 (ends Fr 3/28): 9.5.4, 9.5.7, 9.5.11.<p>
Wk 13 (ends Fr 4/4): Read section 9.5.9 and in particular understand how to obtain
Poisson's formula (<b>mandatory</b>), 9.5.13, 9.5.15., 9.5.16.<p>
Wk 14 (ends Fr 4/11): 12.2.2, 12.2.5 (c),12.2.7,12.2.8.<p>
Wk 15 (ends Fr 4/18): See practice4 above.<p>
Wk 16 (ends Fr 4/25): Last day of class and Exam IV on Wed 4/23.<p>
</ul>
<p>

<b>Announcements:</b><br>
<ul>

  <li> Exam I is on <b> Fr Feb 8 </b>. No calculators, books or
  formula sheets are allowed or needed. Only bring pen and blank paper. 
  There will be a review on <b>Wed Feb 6</b>, where you can ask me any questions you may have and where we will discuss solutions to a practice exam that I will post beforehand.
<li> Exam II is on <b>Wed Feb 27</b> in class. Same
  format as Exam I. This exam covers everything discussed on Fourier series (chap 3) although I don't expect you
  to prove the convergence thm for instance, and everything dicussed on the wave equation, excluding
  D'Alembert's principle, and waves in dimension higher than 1 (like the EM waves we studied in class). 
  The review session, including a discussion of a practice exam, will be in class
  on <b>Mon Feb 25</b>. 
<li> Exam III  is on <b>Fr 4/4</b>. It covers applications of the wave equation (see previous discussion of the material
  of Exam II), Sturm-Liouville theory and Green's functions for BVP for ODE's. This includes the concept of
  distributions, and sec 9.3, but not 9.4 or 9.5.  
  The review session, including a discussion of a practice exam, will be in class on <b>Wed 4/2</b>.

<li> Exam IV  is on <b>Wed 4/23</b>. It covers everything we saw on Green's functions for PDE's (sec 9.5 and material
  from class) and on the method of characteristics and traffic flow (sec 12.6 and material from class). 
  The review session, including a discussion of a practice exam, will be in class on <b>Mon 4/21</b>.

<li> When we will study the wave equation we will discuss the following <a href="morley.pdf">paper</a> which
  shows that wave propagation which is radially symmetric and distortionless is only possible in dimension 1 or 3.
  Fortunately for us, we don't live in 1-dim space where such wave propagation is always without attenuation.<br>
<b>Typo's in the paper</b>: p70: * In (RW) v -> v_r * Together with delta > 0 -> Together with alpha > 0 * In (4): + => -
  * p71: in (4'): + => -
  <li> An affordable reference text (about $15) on Fourier series is: Fourier Series, by Georgi P. Tolstov,
  Dover Publications, 1976.

<li> Answer to case study discussed in class (light first turns red, then 1 min later it turns
green again; 2 shock waves occur) with
u(rho)=70(1-rho/400). Fist shock wave (when  light has turned red) is uniform and propagates from (x,t)=(0,0) with 
velocity -17.5mph. Second shock wave (when light has turned green again) is not uniform and propagates from
(x,t)=(-7/18,1/45) with velocity given by ODE: dx/dt=17.5+0.5x/(t-1/60). Solving for x(t) yields
x(t)=35(t-1/60)-(7sqrt{5}/2)sqrt{t-1/60}. This is 0 when t=1/15h or 4 min. Thus the light should stay green for 4-1=3 min
in order for the shock wave to make it past the light.
</ul>