Welcome to the 105A forum.
Thursday 22nd of September 2005 09:50:10 AM
this class rocks
THANKYOU. THANKYOU VERY MUCH...
Friday 23rd of September 2005 01:50:27 PM
Just wondering if anyone had
any advice when it comes to purchasing mathematica. Whats the cheapest
license you all have found? thanks
- wburch@ucsd.edu CLASS, ANY SUGGESTIONS?
Friday 23rd of September 2005 10:35:40 PM
In 9.9.6b, \"Maximum positive
excursion\" refers to the maximum value of x(t) in t in 0 to 2, right?
YES
Friday 23rd of September 2005 10:41:40 PM
The cheapest version of
Mathematica can be obtained from various UCSD student-runned hubs; one can
use DC++ to access it at \"ucladchub.kicks-ass.org\" -- note: a UCSD IP
address or VPN setup is required. Mathematica can also be found via P2P
software such as Kazaa, as well as a number of ftp\'s out there. Ask
Google for details.
Friday 23rd of September 2005 11:51:07 PM
I\'m running Mathematica
v5.0. For 9.10.2, the labels for the R values do not show. I\'m guessing
they\'re either Ohms or mOhm\'s. The question asks for the current, and
the label for the current would differ depending on whether the
resistances are labeled Ohm\'s or mOhm\'s--so, please clarify this minor
detail. WEIRD THAT THE OHMS SYMBOLS ARE MISSING. EVERYTHING IS IN
OHMS.
Monday 26th of September 2005 12:17:46 PM
I\'ve tried to use the lab in
CLICS to access Mathematica, and it doesn\'t seem to work. Just thought I
would let you know.HMMM. THANKS, I'LL LOOK INTO IT.
Monday 26th of September 2005 05:53:07 PM
Professor Dubin; I was in
this class last year and lost the CD that comes with the book. Is there
any other way you could post the problems?OY, THAT'S A PROBLEM,
HAVING TO COPY N QUESTIONS ONTO THE ASSIGNMENT RATHER THAN JUST THE
PROBLEM NUMBERS. BUT, I'M SUCH A NICE GUY. CHECK THE WEBSITE IN AN
HOUR OR SO....
Wednesday 28th of September 2005 09:02:18 PM
is there a written-part to
the first assignment? the questions assigned do not directly ask for a
written part, and the only question that i had to use paper for was the
kirchkoff\'s prob. but that was on a scratch piece of ketchupy Pizza Hut
napkin that i no longer have with me.. IT'S UP TO YOU WHAT YOU
WANT TO HAND IN-- YOU NEED TO ENSURE THE SOLUTIONS ARE PROPERLY EXPLAINED.
IF YOU FEEL A PIZZA HUT NAPKIN WILL HELP YOUR GRADE,
HAND IT IN. WRAPPED AROUND A PIZZA, PREFERABLY (THE TA GETS HUNGRY).
I HAVE BEEN ASSURED BY ACS THAT THE COMPUTERS IN CLICS 263 ARE RUNNING
MATHEMATICA 5.2, SO THOSE COMPUTERS SHOULD ALSO BE USEABLE BY OUR CLASS.
LET
ME KNOW IF THEY ARE NOT.
Thursday 29th of September 2005 11:48:15 PM
www.mininova.org
Search for mathematica, or Family Guy, or whatever.
Friday 30th of September 2005 07:38:21 PM
the typo in 1.2.2a is only in
the printed version, and it\'s corrected in the CD. dv/dt should be dy/dt.
(in the future, please double-check the assigned problems for typos before
posting..) THANKS FOR FINDING THE TYPO. I'LL TRY TO CATCH THEM, BUT
CAN'T PROMISE I'LL BE SUCCESSFUL. LET ME KNOW IF YOU FIND MORE.
Sunday 02nd of October 2005 09:22:23 PM
yet another typo...
in 1.3.8b \\phi = \\cos\\theta / r^2 ... and not \\cos\\theta / r ... this
mistake is, again, present in the printed version but fixed on the CD.
hm... if this continues, i suppose i (and my cohorts) might as well just
return the book. (your publisher will not like you for this, so this is a
*threat* to check for typos--at least in the assigned problems!!! think of
all the undergrads who suffer unnecessary stress from your typos!)
X( ACTUALLY, I'M HAPPY TO GET IT RIGHT IN ONE PLACE AT LEAST. THESE
MISTAKES OCCUR IN THE TEXT BECAUSE THE TEXT WAS INCORRECTLY TRANSCRIBED
FROM THE CD BY THE PUBLISHER, AND I DIDN'T CATCH THE ERRORS DURING THE
PROOFING PROCESS. AS A RESULT THE CD HAS FEWER ERRORS THAN THE PRINTED
BOOK.
I DO CHECK FOR TYPOS CAREFULLY, BUT IT'S NOT EASY TO FIND THEM ALL. IT IS
HELPFUL TO GET STUDENT FEEDBACK BECAUSE YOU SEE THINGS MY BRAIN SKIPS
OVER. FEEL FREE TO RETURN THE BOOK IF YOU LIKE. YOU MAY WANT TO TAKE A
LOOK AT THE TEXTBOOK WEBSITE (SEE THE LINK ON THE COURSE HOMEPAGE) WHERE
THERE IS A
LIST OF FOUND TYPOS. IT MIGHT PROVE USEFUL IN FUTURE WORK.
Sunday 02nd of October 2005 09:49:54 PM
Please post details on the
revised boundary conditionss for 1.3.8a, after re: the correction sent via
email to the whole class. THE PROBLEM IS NOT REVISED, ONLY THE
HINT. THE INITIAL CONDITIONS, IF THAT IS WHAT YOU WERE REFERRING TO,
REMAIN UNCHANGED.
Friday 07th of October 2005 10:20:17 AM
Whats the policy on late HW
again?LATE HOMEWORK IS PENALIZED 10% PER DAY LATE, UP TO THE CUT-OFF
DATE AFTER WHICH IT IS NOT ACCEPTED. IF IT COMES IN
BETWEEN 5-6 PM ON FIRDAY, IT IS PENALIZED 5%
Friday 07th of October 2005 11:50:47 AM
A follow up to that last
post...
On late HW, would we need to type our written parts of the solutions into
the notebook, or can we submit the .nb online (Saturday for example) and
turn in the written on Monday and still only loose %10? Best is to
type it in. Otherwise, it depends on if the work is a stand-alone written
problem, or
supporting material in the notebook. If it is the former, it will be
graded late according to when it arrives in our possession. If the latter,
it may (depending on the judgement of the grader) be graded according to
when the notebook arrives. If you can't submit such work on time, and
don't want to type it into the notebook,you could scan it and email the
scanned material.
Thursday 13th of October 2005 04:47:48 PM
Since we don\'t learn the
homework material until thursday\'s, how are we supposed to work on the
homework throughout the week? Homework should be due the following week
after learning the material. BTW it would be useful to offer a solutions
guide to the odd problems, there just isn\'t enough examples in the book
to do the homework efficiently. IT WOULD BE NICE IF WE HAD THE LUXURY
OF PUTTING OFF ASSIGNMENTS FOR A WEEK, BUT THAT WASTES TIME. IT IS
EXPECTED THAT STUDENTS WILL HAVE TROUBLE FULLY ABOSRBING THE MATERIAL IF
THEY ARE SEEING IT FOR THE FIRST TIME IN LECTURE. FIRST AND FOREMOST,
YOU ARE SUPPOSED TO READ AHEAD. (READ SECS. 2.1-2.3
FOR NEXT WEEK). SECOND, THE ASSIGNMENTS THEMSELVES ARE ONE OF THE BEST
WAYS TO LEARN THE MATERIAL. YOU MAY THINK YOU KNOW A SUV=BJECT, BUT YOU
DON'T REALLY KNOW IT UNLESS YOU CAN DO THE PROBLEMS. IN MY OPINION IT IS
BEST TO WORK ON THE PROBLEMS AT THE SAME TIME AS YOU ARE THINKING ABOUT
THE MATERIAL IN THE CLASSES, NOT WAITING A WEEK.
I AGREE A SOLUTIONS MANUAL WOULD BE NICE. I'M WORKING ON ONE.
Friday 14th of October 2005 01:53:26 AM
Where can we turn in the
written part of the homework? The syllabus says to the TA in the lab but
the lab ends at 4pm and the homework is due at 5pm so where does it go if
we want that extra hour? THE TA REMAINS IN THE LAB UNITL 5 PM
BECAUSE HE HAS HIS OFFICE HOUR THERE, FROM 4-5 PM.
Saturday 15th of October 2005 09:53:01 PM
can you post some sample
midterm questions? also, if the midterm questions are similar to the
homework questions, can you hold a 3 or 5 hour midterm to include buffer
time for debugging? I will post last years midterm and solutions. Do
you really want to spend three hours on the midterm? Past years have not
done that and they have done OK.
Sunday 16th of October 2005 07:26:01 PM
For problem 7 in section 1.6,
is there a certain method you want us to use to solve for the potential?
Or is any method alright? ANY METHOD IS OK
Monday 17th of October 2005 02:55:22 PM
more typos and some questions.
PlotStyle->{Red,Green,Purple} in Cell2.1 doesn\'t work... M5 wants
\"graphic primitives,\" like RGB[1,0,0], for example.
in Thrm 2.1, should \"it is possible to construct a Fourier series that
equals f(t) for all t\" be \"it is possible to construct a Fourier series
that converges uniformly to f(t) for all t\"
n=SM in the paragraph above eq 2.1.17 (Gibbs Section)
THE PLOTSTYLE COMMAND ONLY WORKS IF THE ADD-ON GRAPHICS LIBRARY IS
LOADED, AS IN THE FIRST LINE OF CELL 2.1. THEOREM 2.1 IS CORRECT AS
STATED. THE FOURIER SERIES EQUALS F(T) FOR ALL T WHEN AN INFINITE
NUMBER OF TERMS
ARE KEPT. THIS IS AS OPPOSED TO FOURIER SERIES OF FUNCTIONS THAT DO NOT
SATISFY THM. 2.1. HOWEVER, YOUR STATEMENT IS ALSO TRUE. IT
NECESSITATES A DISCUSSION EARLY ON OF UNIFORM CONVERGENCE, WHICH I WANTED
TO
PUT OFF UNTIL THE SEC. ON UNIFORM AND NONUNIFORM CONVERGENCE.
(ACTUALLY, IF YOU THINK ABOUT IT LONG ENOUGH, YOU CAN CONVINCE
YOURSELF THAT THE TWO STATEMENTS OF THE THEOREM ARE THE SAME.)THANKS FOR
POINTING OUT THE
N=S M TYPO -- THAT'S ONE I WAS ALREADY AWARE OF, BUT HAVE NOT POSTED YET.
Thursday 20th of October 2005 12:11:02 AM
The link to the pdf version
of the syllabus does not work...FIXED
Thursday 20th of October 2005 11:53:13 PM
For Ection 1.6 Problem 8, you
want us just to find the particular solution for Q(t) and not do parts a
and b? NO, DO BOTH A AND B
Sunday 23rd of October 2005 06:05:20 PM
What does the midterm cover up
to? Is it up to and including Section 2.1 or 2.2? UP TO SEC. 2.1
INCLUSIVE
Thursday 27th of October 2005 12:47:50 PM
when and where will the
midterm be held at?WHAT FOLLOWS IS THE TEXT OF THE EMAIL I SENT TO ALL
STUDENTS ON OCT. 20. The midterm for physics 105A is at 2:30PM -4 PM on
Friday Oct. 28. For those of you with surnames starting
with letters in the range A - HEDBERG inclusive, the test is in UH 6126.
For the other students, the exam is
in APM B337 & B349.
Thursday 27th of October 2005 10:21:48 PM
The solutions to Homework #4
are not opening due to a \"syntax error.\" Could you please check the
file to make sure it will open. ThanksIT DOWNLOADS AND OPENS OK
FOR ME.
Monday 31st of October 2005 07:25:40 PM
can we use m5 to do the
integrals for hw5? or, by \"paper and pencil,\" did you really mean
**paper and pencil** (and integration tables) with no electronic
computational package support. YES DO ALL THE INTEGRAL WORK BY HAND,
EXCEPT
IN PROBLEM 18B. OF COURSE YOU ARE ALWAYS WELCOME TO CHECK YOUR RESULTS
USING MATHEMATICA.
Friday 04th of November 2005 02:49:20 PM
Is 105B not being offered next
quarter? THIS YEAR 105B WILL BE OFFERED IN THE SPRING RATHER THAN
THE WINTER
Sunday 06th of November 2005 08:16:34 PM
When is assignment 6 due since
Friday is a holiday? DUE MONDAY, AT 4 PM. TURN IN WRITTEN WORK AT
MY OFFICE MH 3102 (DROP BOX OUTSIDE THE DOOR)
Sunday 13th of November 2005 12:32:14 AM
Please, in the next revision
of this book, include solutions to selected problems. At the very least it
would be great if there were thorough examples for key concepts.
One case where examples would\'ve helped: Section 2.3.6, \"case of
degeneracy, can also be easily handled using similar techniques, and is
left to the exercises...\"
Here most of us lack a strong mathematical background to understand the
\'techniques\' (especially at points where several seemingly trivial steps
are omitted to save space). Also, it is rather unlikely that we can figure
out the degenerate case from the exercises for two key reasons:
1. most are already struggling to barely understand the non-degenerate
case.
2. few of us can actually find a technique for the degenarate case, given
that there are no solutions to check out work for the simplier
non-degenarate case.
Several of my friends and I can testify that the lack of examples and
solutions has made our hard efforts to learn very frustrating and
unrewarding :( I apologize for the long post. THANKS FOR THE USEFUL
COMMENTS. SELECTED SOLUTIONS WILL EVENTUALLY BE POSTED ON THE BOOK
WEBSITE, AS AN ONLINE SOLUTIONS MANUAL. NOT EVERY SPECIAL CASE CAN BE
HANDLED
WITH AN EXAMPLE IN THE BOOK ITSELF, OR THE BOOK WOULD BE MUCH TOO LONG.
HOWEVER, YOUR
COMMENTS ABOUT DEGENERACY ARE WELL FOUNDED AND I WILL EVENTUALLY INCLUDE
EXAMPLES ON
THE WEBSITE. NOTE THAT FINDING INDEPENDENT HOMOGENEOUS SOLUTIONS FOR THE
CASE OF
DEGENERACY IS COVERED IN SEC. 1.6.2.
Sunday 13th of November 2005 04:29:30 PM
I believe that the course text
is best used when supplemented with other texts. For the case of
degenerate ODE\'s, consult Shankar\'s Basic Training in Mathematics (yes,
by the same Shankar who wrote the legendary QM classic, Principles of
Quantum Mechanics). His book is quite excellent, since after reading each
section, one can quite effortlessly solve the problems (and answers are
provided). For more practice, check out Schaum\'s Notes Differential
Equations for problems with solutions. Moreover, Arfken\'s coverage of
Green\'s functions in terms of eigenfunction expansions... makes much more
sense than Dubin S2.4ff. THOSE ARE EXCELLENT TEXTS, AND I AGREE THEY
ARE USEFUL ADJUNCTS TO THE COURSE. I ALSO LIKE POWERS, BOUNDARY VALUE
PROBLEMS. ARFKEN MAY BE A LITTLE ADVANCED FOR AN UNDERGRAD. CLASS.
EIGENFUNCTION
EXPANSIONS ARE ALSO COVERED IN THIS BOOK, BUT NOT UNTIL CHAP. 4. (NOTE
THAT EIGENFUNCTION EXPANSIONS ARE NOT NECESSARILY THE BEST WAY TO
REPRESENT A GREEN'S FUNCTION, AKTHOUGH THEY HAVE THEUR USES.
REPRESENTATION IN TERMS OF HOMOGENEOUS
SOLUTIONS IS SOMETIMES PREFERABLE, AS IS A NUMERICAL REPRESENTATION (NOT
COVERED IN ANY OF THE ABOVE). I
THINK IT'S BEST TO COVER SEVERAL DIFFERENT APPROACHES. ANOTHER GOOD
REFERENCE FOR ANALYTIC DESCRIPTION OF GREEN'S FUNCTIONS IS JACKSON,
CLASSICAL
ELECTRODYNAMICS.
Sunday 13th of November 2005 03:05:35 PM
Professor YOU should have
graded our tests not the TA! I graded problem 1, the TA graded
problem 2. If you have complaints about the grading, first see the TA
to try to resolve it, and if you are not satisfied, come see me. For
the midterm, just come see me directly on problem 1, since I graded
it.
Sunday 13th of November 2005 07:53:38 PM
is there a homework7 due this
friday? if so, it is not posted yet. would be nice if it is due on monday
instead, so that we can at least have a weekend to spend on it.
THE NEXT HOMEWORK WILL BE DUE NEXT MONDAY, SO YOU HAVE A WEEK BETWEEN
ASSIGNMENTS.
Sunday 13th of November 2005 07:51:52 PM
just curious: what\'s the
difference between who grades which problem on the midterm? I'M
UNSURE MYSELF. IN PRINCIPLE, THERE IS NO DIFFERENCE AS LONG AS THERE IS
CONSISTENCY. I'M MERELY POSTING THE COMMENTS AS THEY COME. I'M UNDER
THE IMPRESSION THAT SOME PROPLE MAY HAVE ISSUES WITH THE WAY THE
GRADING HAS BEEN DONE, HENCE MY COMMENT ABOVE.
Sunday 13th of November 2005 08:51:48 PM
is 2a) supposed to be solved
via the method of section 2.4.3 (matrix inversion) instead of section
2.4.2? DON'T USE MATYRIX INVERSION, DO THE PROBLEM ANALYTICALLY
USING HOMOGENEOUS SOLUTIONS AS IN 2.4.2
Sunday 13th of November 2005 08:57:56 PM
prob 2.4.2i -- the condition
G\'[0]=0 (along with the others) forces G=0... was a trivial solution
intended or is one of the boundary conditions a typo? NO, G IS
NONZERO. THE ODE IS THIRD
ORDER SO THREE BOUNDARY CONDITIONS ARE NECESSARY. NO TYPOS. EXCEPT, WHEN
YOU PLOT, PLOT G(X,1/2) NOT G(X-X0).
Sunday 13th of November 2005 11:47:08 PM
do u mean G(t,0) 2.4.2i
instead of G(t,1/2) ? the 1/2 seems arbitrary.. I MEAN G(T,1/2).
IT IS ARBITRARY, BUT YOU NEED TO CHOOSE SOME VALUE OR OTHER FOR X0 IN
ORDER TO MAKE A PLOT. YOU CAN TRY X0 = 0 TOO IF YOU LIKE.
Sunday 13th of November 2005 10:45:15 PM
I used eqn 2.3.85 to solve for
the Green\'s function in Problem 2a. Is this wrong because I don\'t use
any of the initial conditions? I just find the roots and plug them in.
Also as in a general question, how do I graph when I have imaginary values
in my function? The Re function only works for numbers not
expressions. 2.3.85 is only correct for ODEs with constant
coefficients. Derive the green's function from first principles, using
the jump condition. Re[] works on all complex functions.
Monday 14th of November 2005 10:58:07 AM
For Problem 3 i), I took the
Green\'s function I found in problem 2 and multiplied it by the f(x)=xe^-x
and integrated that from infinity to negative infinity to get a particular
solution. Where do the initial conditions come in for this part?
WHAT YOU FOUND WAS A PARTICULAR SOLUTION. NOW ADD IN A HOMOGENEOUS
SOLUTION TO THE ODE WITH COEFFICIENTS CHOSEN TO MATCH THE ICS/BCS
Wednesday 16th of November 2005 10:18:48 PM
For HW 7, Qn 7(b), the
question in the book and in the electronic version is different. Do we
follow the one that is on the cd? USE THE VERSION ON THE CD (WITH
FORCE F(X) =X ADDED)
Friday 18th of November 2005 04:47:57 PM
hi, i have a specific question
regarding M5\'s evaluation of functions:
1. If I were to program a function for the fourier sine coefficients that
has the arguments of the function and the limits of integration, FcSin[f_,
a_, b_] := Integrate[2/L Sin[n Pi x/L] f, {x, a, b}]; ... would it be
equivalent to Cell 3.2 in the book once i feed in the initial conditions
f=y_0. I\'ve tried it for that case and a few others. They all work, so
I\'m wondering whether I got lucky all the time or if there are
exceptions/limitations to applying encapsulation and basic object oriented
programming to M5.
and i also have a general question:
2. I believe that M5 evaluates functions based on the most recent
definition of a function involving an argument with an underscore.
Example: if I were to define
j[r]=r^2; g[r_]=Integrate[j[r] Log[r],r] ... then M5 would plug j[r] into
the integral in g[r_] as in g[2] = Integrate[j[r] Log[r],r]/.r=2 ... i.e.,
evaluate the integral and then plug in 2. The same idea would apply in a
general case, and thus it would be redundant to put an underscore_ after
both the j[r_] and g[r_]. Instead, an underscore_ is required only in
g[r_].
i\'d like this comment to be answered in the forum because others in the
course seem to be similarly confused regarding the usage of underscores in
function argumentation_. thank you. WELL, THAT'S QUITE A MOUTHFUL! OK,
AS TO COMMENT 1, YES, FUNCTIONS CAN THEMSELVES BE ARGUMENTS OF OTHER
FUNCTIONS (THESE OTHER FUNCTIONS ARE THEN 'FUNCTIONALS', FUNCTIONS OF
FUNCTIONS. MATHEMATIUCA CAN DEAL WITH FUNCTIONALS VERY NICELY.). I WOULD
HAVE WRITTEN YOUR INTEGRATION FUNCTIONAL, SLIGHTLY DIFFERENTLY, AS
FcSin[f_, {a_, b_}] := Integrate[2/L Sin[n Pi x/L] f[x], {x, a, b}]
.
THEN IS ONE DEFINES A FUNCTION G[R_] = R^2; AND CALLS
FcSin[G,{1,2}], the integrals are done over G.
AS TO THE USE OF UNDERSCORES, REMEMBER THAT WITHOUT THE UNDERSCORE
THE FUNCTION IS DEFINED ONLY FOR THAT SPECIFIC VALUE OF THE ARGUMENT. IF
YOU DEFINE J[R], AND THEN ASK FOR J[X] SOMEWHERE ELSE, YOU WILL FIND IT IS
NOT DEFINED.HOWEVER, IF YOU DEFINE J[R_], IT IS DEFINED FOR ANY R. YOUR
EXAMPLE ONLY WORKS BECAUSE YOUR INTEGRATION VARIABLE WAS r. IF YOU HAD
WRITTEN
g[X_] = Integrate[j[X] Log[X],X]
, THE FUNCTION WOULD NOT
HAVE WORKED UNLESS j WAS DEFINED WITH AN UNDERSCORE AS j[R_] = R^2.
Saturday 19th of November 2005 06:30:11 PM
in equation 3.1.30, why is
there an extra minus sign (in front of the double integral) when you
obtained the solution by direct integration? THE MINUS SIGN
ALREADFY APPEARS IN EQ. (3.1.29). THE SOURCE TERM HAS A MINUS SIGN IIN
FRONT OF IT BECAUSE WE TOOK IT OVER TO THE RHS OF THE EQUATION.
Saturday 19th of November 2005 06:36:56 PM
in m5 -- is BeginPackage /
EndPackage the only way to create something similar to an external
library? also, the equivalent to the c commands, include() or require(),
would be just calling the package? I DON'T KNOW IF ITS THE ONLY WAY
TO MAKE AN EXTERNAL PACKAGE, BUT I CAN TELL YOU THAT ALL EXTERNAL
"ADD-ON" PACKAGES USE THE BEGINPACKAGE ENDPACKAGE SYNTAX. THE
EQUIVALENT TO INCLUDE OR REQUIRE IN MATHEMATICA IS GET, OR <<. THIS
READS IN A SPECIFIED EXTERNAL FILE OR SET OF FILES. IT'S WHAT WE USE
TO LOAD ADD-ON PACKAGES.
Sunday 20th of November 2005 01:44:32 AM
are there supposed to be some
rather large deviations at the endpoint x=Pi for the seperation of
variables y(x,t)=yeq(x) + delta y(x,t) method of solution versus
NDSolve\'s? if so, is this attributed to the Gibb\'s effect?
WHEN INITIAL CONDITIONS DO NOT MATCH THE BOUNDARY CONDITIONS, A GIBBS
PHENOMENON OCCURS. THE LARGE-WAVENUMBER OSCILLATION QUICKLY DECAYS
AWAY IN THE HEAT EQUATION SOLUTION.
Sunday 20th of November 2005 05:30:58 PM
hi, can you explain what you
mean by when an initial condition does not match the boundary condition?
do you mean when the boundary conditions are homogenous but the initial
conditions are not, then the gibbs phenomenon would arise? if so, would it
be localized to a particular region that can be predetermined by either
the bc/ic\'s (if that\'s the case, how would one do that in general)?
thanks. HERE'S AN EXAMPLE. SAY THE BOUNDARY CONDITIONS ARE T=1 AT
X=0 AND T=2 AT X=L, BUT THE INITIAL CONDITIONS ARE T=1 + 2X/L. THE
BOUNDARY CONDITION MATCHES THE INITIAL CONDITION AT X=0, BUT NOT AT
X=L. A GIBBS PHENOMENON ARISES IN THE SOLUTION AT X=L. THE MORE TERMS
ONE KEEPS IN THE FOURIER SUM, THE NARROWER THE REGION OVER WHICH THE
OSCILLATIONS OCCUR.
Sunday 20th of November 2005 06:27:10 PM
hi, for problem 3.1.7, there
appears to be gibbs phenomenon at the x=Pi endpoint in the plot of the
deviation of the solution by SOV and the solution from ndsolve. how does
one relate the initial condition dy/dt(x,0)=x^2 sin x to the boundary
conditions. or, in general, how does a initial condition involving a time
derivative of y relate to the boundary conditions involving just the
function y. thanks. NO GIBBS PHENOMENON IN THIS SOLUTION. THE BOUNDARY
CONDITIONS MATCH THE INITIAL CONDITIONS, SINCE THE INITIAL CONDITION
HAS DY/DT = 0 AT BOTH ENDS, AND Y=0.
Sunday 20th of November 2005 07:56:37 PM
what is the mass density (or
mass) of the rope in prob 3.1.9? IT DOESN"T MATTER.
Monday 21st of November 2005 02:05:20 AM
For problem 3.1.7b I\'m
looking for the equilibrium solution, y(x). I have the second derivative
of y(x,t) = -f(x). I solve by direct integration. Now I have y(x) but
depending on which boundary condition I use I get different constants for
this equation.Which one should I use? USE THE BOUNDARTY CONDITIONS
THAT WERE STATED IN THE PROBLEM.
Thursday 24th of November 2005 06:29:44 PM
the solution to problem
3.2.1d appears to be trivial, since the a_n (n!=0) term is proportional to
Sin(n pi). and, the homogenous neumann boundary condition in y forces a_0
to be 0. but, a trivial solution would not satisfy phi\'(x,1)=1 ...
what\'s wrong? help!FIRST, HAPPY THANKSGIVING. SECOND, CHECK TO SEE
IF A SOLUTION EXISTS! (SEE EQ. 3.2.3)
Thursday 24th of November 2005 06:41:19 PM
is prob 3.2.4 a \"grounded
conducting cylinder,\" (as printed in the book) where phi(a,theta)=0 or a
\"long conducting cylinder\" (as printed on the CD), where
phi(a,theta)=constant=which? THE CYLINDER IS BOTH LONG AND
GROUNDED.
Thursday 24th of November 2005 06:53:37 PM
it appears that m5 can\'t
quite ndsolve/dsolve laplace\'s equation. is there another way that we can
check our solutions? YOU ARE RIGHT THAT M5 DOES NOT SOLVE
POISSON'S EQUATION. YOU CAN CHECK YOUR SOLUTION BY MAKING SURE THAT IT
SOLVES LAPLACE'S EQUATION TERM-BY TERM (BY SUBSTITUTION) AND BY
ENSURING THAT YOUR SOLUTION MATCHES THE BOUNDARY CONDITIONS.
Thursday 24th of November 2005 05:21:03 PM
in the An equation below the
paragraph below 3.2.14, should there be an extra factor of 2/a for the
cosine series?
if not, then should 3.2.12 not have an extra factor of 2/b?
(holidays = time to get reading for this class done.) YES, THERE IS A
TYPO IN THE EQUATION AFTER 3.2.14. THERE SHOULD BE AN EXTRA FACTOR OF 2/A.
FORTUNATELY, THE INTEGRAL IN THE EQUATION IS ZERO, SO ALL THE AN'S ARE
ZERO ANYWAY, FOR N>0
Saturday 26th of November 2005 10:54:53 PM
in cell 4.41, for the
parametric plot, the third \"coordinate\" is cos(t) phi ... shouldn\'t
cos(t) be sin(t) + cos(t) in general? so, in cell 4.41, you applied the
initial condition dc(t)/dt =0 ()? YES
Saturday 26th of November 2005 04:27:26 PM
hi,
above cell 3.22, you claim that only the m=0 spherical harmonics enter
the equation because of cylindrical symmetry. i don\'t see the cylindrical
symmetry in this problem, nor do i see how cylindrical symmetry relates to
spherical harmonics in general...
THE M=0 HARMONICS ARE INDEPENDENT OF PHI. THE BOUNDARY CONDITIONS
ARE ALSO INDEPENDENT OF PHI, SO ONLY THE M=0 HARMONICS ENTER THE
SOLUTION.
also, aside from l=0,1 the figures for the other l values in cell 3.21
look like wave-fitting around a circle. (n lambda = 2 pi r) this reminds
me of fitting de broglie waves around a circle to (somewhat more
rigorously) arrive at the bohr quantum condition. is there any significant
relation in this coincidence? (the waves also look like closed orbit
diagrams from Goldstein).
SPHERICAL HARMONICS FORM A COMPLETE AND
ORTHOGONAL SET OF FUNCTIONS ON THE SURFACE OF A SPHERE. SO YES, THEY ARE
LIKE WAVES ON A SPHERE. SINCE THEY ARE ALSO EIGENFUNCTIONS OF THE ANGULAR
PART OF THE LAPLACIAN OPERATOR, THEY APPEAR IN MANY CONTEXTS INCLUDING
SHRODINGER'S EQUATION.
Sunday 27th of November 2005 06:13:35 PM
What is the second initial
condition for 4.4.2c? i.e., does the trampoline start out with an initial
velocity or not? TAKE IT AS DZ/DT = 0 INITIALLY.
Wednesday 30th of November 2005 11:07:56 PM
this is a detail that is
still not clear to many students. can you clearly explain the difference
between
f[x_]= ...
f[x_]:= ...
IN THIS FIRST DEFINITION, THE RIGHT HAND SIDE IS EVALUATED AND THE RESULT
IS ASSIGNED TO THE FUNCTION F[X]. IN THE SECOND EXAMPLE, THE RIGHT HAND
SIDE IS NOT EVALUATED, BUT THE DEFINITION OF THE RHS IS REMEMBERED AND IS
ASSIGNED TO THE FUNCTION F[X]. EVALUATION OF THE RHS THEN OCCURS ONLY WHEN
F[X] IS CALLED IN A LATER STATEMENT. THIS IS USEFUL FOR FUNCTIONS SUCH AS
F[X_] := FINDROOT[G[Y]==0,{Y,X}] THAT ONLY WORK FOR SPECIFIC NUMERICAL
VALUES OF ITS ARGUMENT.
f[x]= ...
f[x]:= ...
WITHOUT THE UNDERSCORE THE FUNCTION IS DEFINED ONLY FOR THAT SPECIFIC
VALUE OF THE ARGUMENT. IF YOU DEFINE F[X], AND THEN ASK FOR F[2], YOU WILL
FIND IT IS NOT DEFINED.HOWEVER, IF YOU DEFINE F[X_], IT IS DEFINED FOR ANY
X.
?
Thursday 01st of December 2005 03:53:55 PM
for 3.2.4, the boundary
condition that phi(a,theta)=0 seems to render a trivial (constant)
solution---since the An\'s are 0 from that condition and the Bn\'s are 0
from the finite at origin condition. I am not sure how to match the theta
boundary conditions---or if they even matter at all in this case, since
the solution is just constant (from the previously mentioned boundary
condition). then again, it doesn\'t make sense that the potential at the
phi(a,theta)=0 but that at phi(r,alpha)=V0=phi(r,0). moreover, a solution
must exist since the BC\'s are Dirchlet.. confused here. please
help! PHI(A,THETA) IS NONZERO ON THE SECTOR -- THERE THE POTENTIAL
IS ONE VOLT. PHI IS ZERO OUTSIDE THE SECTOR. SO PHI(A,THETA) =
V0(THETA) WHERE V0(THETA) IS SOME FUNCTION OF THETA. YOU NEED TO
DESCRIBE THAT FUNCTION AS A FOURIER SERIES, AND USE THESE COEFFICIENTS
IN YOUR LAPLACE EQUATION SOLUTION.
Thursday 01st of December 2005 10:56:38 PM
i\'m having difficulty
seeing the physical meaning of the plot3d graphs. for example, the
potential inside the sphere in cell 3.24..... looks more like a cool 3d
object to me than anything of physical significance. THE HEIGHT OF
THE SURFACE IS THE VALUE OF THE POTENTIAL. YOU CAN SEE THE POTENTIAL
VARIES ROUGHLY LINEARLY FROM ONE POLE TO THE OTHER AS YOU MOVE ALONG THE
AXIS OF
THE SPHERE.