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What time do you prefer?

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Total Members Voted: 2

Voting closed: March 29, 2015, 06:59:57 AM

Author Topic: Review lecture April 13  (Read 921 times)

Victor Ivrii

• Elder Member
• Posts: 1793
• Karma: 0
Review lecture April 13
« on: March 19, 2015, 06:59:57 AM »
1) Please pick up you TT2; if you have questions do it during my office hours

2) Now you approximately know where are you standing. I recall that your Final Mark will be equal HA+TT1 + TT2 +  FE + Bonus which constitute respectively 20%, 20%, 20%, 40% of the mark (and Bonus is up to 10 points on the Top). TT1, TT2, and Bonus Marks are on BlackBoard exactly as they will be counted (and so will be a Final Exam Mark).

On the other hand, HA will be counted as the sum of 7 best but scaled to 20 from 35 (which means 4/7 factor).

3) There is a number of unanswered HA and Web Bonus problems on the Forum and you can get your Bonus Points. During last week of classes I will run a Review and you can get Class Bonus Points actively participating.

4) I also plan an extra lecture April 13 before exam. I am running poll on Forum to select a better time slot. Note that you can select several slots

5) Finally I will add HA10 but still keep HA as the  sum of 7 best but scaled to 20 from 35 (which means 4/7 factor). Thus not 2 but 3 worst marks (including unsubmitted) will be dropped. I asked clarification and was told since 1) it is minor 2) everyone can only benefit from this change (and nobody loses if he/she just ignores it) it does not require  class vote. HA10 itself will be placed on Web page during coming weekends.
« Last Edit: April 04, 2015, 07:19:29 AM by Victor Ivrii »

Victor Ivrii

• Elder Member
• Posts: 1793
• Karma: 0
Review lecture April 13 and CheatSheet
« Reply #1 on: April 04, 2015, 07:16:45 AM »
Review lecture: April 13, 10:00-12:00, BA2135 (booking confirmed)

The following CheatSheet will be the last page of the Exam booklet

Appendix: Some useful formulas.
Not exam problems

• The two dimensional  Laplacian in polar coordinates:
\begin{equation*}
\Delta  f =\frac {\partial^2 f}  {\partial r^2}  +\frac{1}{r}  \frac{\partial f}   {\partial r}  + \frac{1}{r^2} \frac {\partial^2 f}  {\partial \theta^2}.
\end{equation*}
• The Stokes theorem
\begin{equation*}
\int _D  \frac {\partial f } {\partial x_i}  \, dx = \int_{\partial D}f  n_i \, d \sigma
\end{equation*}
where $n$ (with components $n_i$) is the unit normal vector pointing outside.
• The complex Fourier series of a periodic function $f(x)$  of period $2l$,  defined on the interval $(-l,l)$ is
$$f(x)= \sum_{n=-\infty}^{+\infty} c_n e^{\pi i nx/l}$$
with the coefficients $c_n$ given by the formula
\begin{equation*}
c_n=\frac{1}{2l} \int_{-l}^{l} f(x) e^{-\pi i nx/l} dx
\end{equation*}
•   The Fourier transform of a function  $f(x)$ is defined by
\begin{equation*}
\hat{f} (k) = \int_{-\infty}^\infty e^{-ikx} f(x) dx.
\end{equation*}
The inverse Fourier transform is
\begin{equation*}
f(x) = \frac{1}{2\pi} \int_{-\infty}^\infty e^{ikx} \hat{f} (k) dk.
\end{equation*}
Here some of its properties:
a. if  $g(x) =f(ax)$ , then $\displaystyle{ \hat{g} (k) =\frac{1}{|a|} \hat f( \frac{k}{a}).}$

b. if $g(x) =f(x-a)$, then $\hat g(k) = e^{-iak} \hat f(k)$.

c. if $h= f*g$, then $\hat h(k) =\hat f(k) \hat g(k)$.

dif $f(x)=e^{-x^2/2}$, then  $\hat f(k) =\sqrt{2\pi} e^{-k^2/2}$.

« Last Edit: April 07, 2015, 03:50:48 PM by Victor Ivrii »