Phys 5041.001 (Spring 2017)http://www.physics.umn.edu/classes/2017/spring/Phys%205041.001/Mathematical Methods for Physics2017-03-24T08:01:06ZXML::Atom::SimpleFeed2017-02-01T15:24:22Z<i>This item is restricted: please visit the website to view it.</i>2017-03-22T12:45:15ZJoshua Hiltbrandcid:58451.eid:427482.updated:2017-03-22 07:45:15Homework Solutions (Updated)2017-02-17T16:08:44Z<ul>
<table width="100%">
<tr valign="top">
<td class="emptytag"></td>
<td>
<a href="/classes/2017/spring/Phys 5041.001/downloads/431732-Casimir.pdf" title="4247 Kbytes, application/pdf">Casimir.pdf</a>
<small>| <a href="/classes/2017/spring/Phys 5041.001/downloads/431732-Casimir.pdf?download=1" title="4247 Kbytes, application/pdf">Download</a></small>
</td><td align="right">
<small><i>posted 17-Feb-2017 at 10:09AM</i></small>
</td></tr>
</table>
</ul>2017-02-17T16:09:13ZOriol T. Vallscid:58451.eid:431712.updated:2017-02-17 10:09:13Casimir Force paper (Updated)2017-01-17T15:31:29Z<p>Instructor office hours are on Th at 4:45 (after the Colloquium) and Fr at 1:25, at McNamara 148-2 via 160. TA office hours will be on Th 12:35 in PAN 442</p>2017-01-17T15:31:29ZOriol T. Vallscid:58451.eid:423612Office hours2016-12-08T20:48:00Z<p>PHYSICS 5041 SPRING 2017</p>
<p>I- Objectives of the course:</p>
<p>The main objective of the course is to help students develop the level of <br />
understanding, skill, and ease in the use of mathematical techniques for <br />
problem solving which is required<br />
of professional physicists. The purpose is to give students <br />
not only the abilities they need, <br />
but also to instill in them the equally necessary<br />
confidence in their ability to handle advanced mathematics.</p>
<p>The course will emphasize "how to get it done", not mathematical rigor.<br />
It will also emphasize the blending of analytic, symbolic and (occasionally)<br />
numerical techniques, as used by practicing physicists in contemporary research,<br />
rather than their separate aspects.</p>
<p>II- Prerequisites:</p>
<p>This course is intended for Physics graduate students. Many advanced <br />
undergraduates take it also. It should be useful as well<br />
to students majoring in other <br />
scientific or engineering subjects.</p>
<p>Prospective students unsure about their preparation should contact the<br />
instructor. Permission will be liberally given to all genuinely interested<br />
people.</p>
<p>The course is not mandatory for anybody, and therefore it is rather informal.</p>
<p>III- Class meetings and Office hours:</p>
<p>The course is currently scheduled to have four 50 minute<br />
meetings on MTWF at 8:00 in room 110 PAN. There are no recitations but<br />
the Wednesday lectures will begin with an extended period of<br />
student questions and discussion. This is not intended in any way to discourage<br />
students from asking questions at any other time during the lectures, but only<br />
to allow for the deeper questions (often requiring longer answers) which arise<br />
during studying and problem solving attempts.</p>
<p>Instructor office hours (in McNamara 1480-2, accessible via<br />
Suite 160) will be on Th at 4:40 (after the colloquium)<br />
and Fr at 1:25. The TA will also hold office hours, in PAN 442,<br />
on Th at 12:35.</p>
<p>IV- Textbooks:</p>
<p>No particular book will be followed in the lectures, but students should expect<br />
to need to do a fair amount of book reading to supplement their class notes.<br />
Many textbooks cover the subjects that will be discussed. Two books are<br />
recommended: for general purposes, Arfken & Weber "Methods of Mathematical <br />
Physics" contains an encyclopedic assortment of topics (many of<br />
which will be covered in class, not necessarily in the same way). <br />
Nearly all standard mathematical<br />
methods that physicists are expected to know how to use are covered. <br />
It is available for FREE in electronic form at: </p>
<p><a href="http://primo.lib.umn.edu/primo_library/libweb/action/display.do?tabs=detailsTab&ct=display&fn=search&doc=umn_aleph006591280&indx=1&recIds=umn_aleph006591280&recIdxs=0&elementI">http://primo.lib.umn.edu/primo_library/libweb/action/display.do?tabs=detailsTab&ct=display&fn=search&doc=umn_aleph006591280&indx=1&recIds=umn_aleph006591280&recIdxs=0&elementI</a> d=0&renderMode=poppedOut&displayMode=full&frbrVersion=&fctN=facet_frbrgroupid&dscnt=0&vl%282404505UI0%29=any&fromSitemap=1&onCampus=false&query=any%2Ccontains%2Cmathematical%20methods%20for%20physicists&frbg=502847&fctV=502847&loc=local%2Cscope%3A%28tcsearch%29&dym=true&dstmp=1370356334995&highlight=true&lang=eng&cs=frb&vl%281UIStartWith0%29=contains&group=GUEST&vl%28freeText0%29=mathematical%20methods%20for%20physicists&vid=TWINCITIES&institution=TWINCITIES</p>
<p>The second book, Bender & Orszag "Advanced Mathematical Methods for Scientists <br />
and Engineers", is shorter and more advanced, but very useful. Buy it if<br />
you can. The Springer edition is identical (except for a slightly different <br />
title) to the earlier McGraw-Hill edition. Save money and buy it used. <br />
The book is a "keeper", which should remain in the students' bookshelf for a long <br />
time after the course is over. Bender & Orszag covers<br />
methods with a reputation for being "advanced" or "difficult", in such a way as<br />
to make these topics very accessible. According to Garrison Keillor, this is a<br />
very well-written scientific book, see<br />
<a href="http://dir.salon.com/books/col/keil/2001/02/20/harvard_grad/index.html">http://dir.salon.com/books/col/keil/2001/02/20/harvard_grad/index.html</a> .</p>
<p>There are many other books with roughly the same scope: if you<br />
already own one of them, you may not need anything else. </p>
<p>Other materials:</p>
<p>Students need to have access to a symbolic mathematical package such as<br />
Mathematica or Mathlab. All Physics students have such access through the<br />
Physics Department servers. Other students should contact the instructor.<br />
Students will be expected to develop<br />
familiarity with symbolic software packages during the course, and some previous<br />
experience, while not required, is a plus.</p>
<p>V- Major topics that will be discussed include:</p>
<p>a.- Applications of Complex Analysis to integration and series summation.<br />
b.- Asymptotic series. Their generation. Numerical summation. Borel summation. <br />
c- Divergent series. Pade approximants.<br />
d.- Fourier series. FFT. <br />
e.- Integral Transforms (Fourier & Laplace). <br />
f.- Multiple delta functions; response functions.<br />
g.- Operational methods: Green functions. Boundary Conditions in PDE<br />
h.- Integral equations. <br />
i - Differential equations. Series solutions. <br />
j.- Asymptotic behavior of solutions. Singular solutions<br />
to differential equations.</p>
<p>Additional topics, depending on student interest, may be covered if time allows.</p>
<p>VI- Homework:</p>
<p>The objectives of the course can only be attained through practice. Therefore<br />
homework is a very important part of the course. A set of problems will be<br />
handed out every Monday and solutions will be due one week later. No late<br />
homework will be accepted. If illness or other valid reason prevent a <br />
student from doing a set, an adjustment will be made in the denominator of the<br />
homework percentage. Making an intelligent effort to solve the homework is<br />
mandatory: this is enforced as explained below. Getting the answers right the<br />
first time is of course not what is mandatory: trying to get answers is.</p>
<p>Sample solutions will be posted at the course web site shorty after the<br />
deadline for handing in the solutions. Sets will be graded: Each problem will be <br />
assigned, in addition to the standard grade based on how correct the solution <br />
is, a second "attempt" grade on a binary scale: a "1" if a serious attempt was <br />
made to solve the problem (even if the attempt was unsuccessful) and "0" <br />
otherwise.</p>
<p>It is quite acceptable, and for most people a good idea, for students to get<br />
together in groups to do the homework, but each student should hand in his or<br />
her own version of the work and be prepared to defend it. When doing<br />
homework in a group make sure you contribute your fair share and do any<br />
freeloaders a favor by ruthlessly expelling them from the group.</p>
<p>VII- Exams and grades:</p>
<p>There will be a final exam on Friday, May 12, 1:30-4:30 pm, a date and time<br />
determined by the University and the Department, which cannot be changed. There will be a<br />
one one-hour midterm tentatively scheduled for March 10. This date could be<br />
changed. There could be instead (if a clear majority of the students prefer it)<br />
two one-hour midterms. The exam grades will be based on each individual <br />
student successful solution of the problems that will be posed.<br />
<br />
The grades will be determined by two factors: </p>
<p>The regular portion of the grade, R, will be composed of: Successful homework<br />
solutions (20%), the midterm (30%, or 20% each if there are two) and the final <br />
(50% or 40% weight depending on number of midterms). R is expressed as a <br />
percentage.</p>
<p>The second, participation, P, grade will be computed as<br />
follows: 80% from the number of homework problems seriously<br />
attempted (seriously attempted means a solution handed in showing substantial <br />
work, even if it was partly or totally incorrect), and<br />
20% from class participation (asking questions etc) as judged by the<br />
instructor. Any diligent student should get a P near 100%. </p>
<p>The overall grade T is determined by the square root of P times R. <br />
T=sqrt(R*P). This means for example, that a student getting P=1 (100%), which <br />
is quite doable, and a regular "exams and homework" grade of 64% (a C <br />
according to the formula below) would have the grade transformed into 80% <br />
(a B/B+).</p>
<p>Letter grades will be based on overall grade T with 5% intervals corresponding<br />
to +/- increments, that is 15% increments corresponding to every letter. <br />
Thus, one needs 45% to get a D, 55% to get C-, 70% to get B-, 85% to get A-.<br />
This scheme awards A+ to students getting 95% or higher. The University, for<br />
some bizarre reason, does not recognize the A+ grade, students earning one will<br />
have a plain A in their official transcripts, but will receive an email from<br />
the Instructor (which they can frame if they wish) informing them. The<br />
University does not recognize the D- grade either, and any such would<br />
become and F. Students taking the course on an S/F basis must earn at least a <br />
C-, a D level grade is not satisfactory. <br />
<br />
Conduct:</p>
<p>Every student is expected to behave professionally and honestly. (See<br />
<a href="http://www.finop.umn.edu/groups/ppd/documents/index/AAcontents.cfm">http://www.finop.umn.edu/groups/ppd/documents/index/AAcontents.cfm</a> for the<br />
University conduct code). </p>
<p>No cheating or other unprofessional behavior will be tolerated. <br />
Handing in solutions copied from another person, or found in the web, would<br />
be, besides cheating, evidence of stupidity, of lack of interest<br />
in learning, and of inability to keep minimum professional standards.<br />
The minimum penalty for cheating is an automatic F for the course. All cases <br />
will be considered for whatever maximum the Supreme Court allows.<br />
</p>
<p>Web site:</p>
<p>To find this web site go to the Physics department main page at<br />
<a href="http://www.physics.umn.edu">http://www.physics.umn.edu</a> and follow the link to class pages and then to 5041.<br />
Updates of this syllabus and other announcements will be found here.<br />
Students should periodically check the site, as they are responsible<br />
for knowing the course announcements and other information posted.<br />
Brief solutions to each homework set will also be posted at the web site<br />
in .pdf format.</p>
<p>Legal stuff:</p>
<p>For anything not covered above, all relevant University Policies will be <br />
followed. A very comprehensive index of such policies is at <br />
<a href="http://www.policy.umn.edu">http://www.policy.umn.edu</a></p>2017-01-17T15:29:41ZOriol T. Vallscid:58451.eid:419502.updated:2017-01-17 09:29:41Syllabus (Updated)