15 Pages

shortest_path

Course: AMATH 4120, Fall 2009
School: Colorado
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Word Count: 8938

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y(O)p 1401 60 4 100 v 196 w(A)p 1634 60 V 188 w(B)p 1899 60 V 187 w(C)p 2126 60 V 185 w(D)p 2391 60 V 189 w(E)p 2623 60 V 137 w(T)p 1115 63 1670 4 v 1165 67 188 4 v 1165 173 4 107 v 1193 148 a(A-4)p 1350 173 V 1165 176 188 4 v 1401 178 4 115 v 130 w(B-1)p 1634 178 V 1685 148 166 60 v 1899 178 4 115 v 366 w(B-2)p 2126 178 V 118 w(E-1)p 2391 178 V 119 w(D-1)p 2623 178 V 1195 248 a(C-5)p 1401 278 4 100 v 128 w(D-7)p 1634 278 V 117 w(C-2)p 1899 278 V 118 w(E-5)p 2126 278 V 118 w(B-5)p 2391 278 V 120 w(B-4)p 2623 278 V 1195 348 a(B-6)p 1401 377 V 1634 377 V 381 w(E-4)p 1899 377 V 2126 377 V 364 w(T-6)p 2391 377 V 118 w(C-5)p 2623 377 V 1401 477 V 1634 477 V 1701 447 a(D-5)p 1899 477 V 2126 477 V 2178 447 166 60 v 2391 477 4 100 v 610 w(T-8)p 2623 477 V 0 680 a(Belo)n(w)30 b(an)n(y)g(no)r(de)h(with)g(a)f(n)n(um)n(b)r(er)h(o)n(v)n(er)e(it)i (\(curren)n(tly)f(no)r(des)h(O)f(and)h(A\),)g(consider)f(the)h(next)g (closest)f(no)r(de.)47 b(In)31 b(this)0 780 y(case,)26 b(w)n(e)g(can)g(get)g(to)g(no)r(de)h(C)f(from)g(O)g(in)h(a)f(total)g (of)g(0+5=5)e(units)j(and)f(w)n(e)g(can)g(get)g(to)h(no)r(de)f(B)g (from)g(O)h(\(through)e(A\))0 880 y(in)j(a)f(total)g(of)h(4+1=5)d (units.)38 b(\(That's)27 b(4)g(to)h(get)f(to)h(A)g(and)f(then)h(1)f (more)g(to)h(get)f(to)g(B.\))0 1029 y(W)-7 b(e)27 b(pic)n(k)f(the)h(no)...

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National Taiwan University - AST - 141
Astronomy 141 Life in the Universe Autumn Quarter 2008 Syllabus Lectures: MWF, 9:30am - 10:48am, 0120 Baker Systems Engineering (BE 0120) Professor: Scott GaudiOffice: 4057 McPherson Lab (614-292-1914) Office Hours: Tues, Wed, Thurs 11:30am-12:30pm
Colorado - AMATH - 4120
%!PS-Adobe-2.0 %Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %Title: rev1.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips rev1.dvi %DVIPSParameters: dpi=600, compress
Colorado - AMATH - 4120
%!PS-Adobe-2.0 %Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %Title: rev2.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips rev2.dvi %DVIPSParameters: dpi=600, compress
Colorado - AMATH - 4120
%!PS-Adobe-2.0 %Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %Title: hw1.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips hw1.dvi %DVIPSParameters: dpi=600, compressed
Colorado - AMATH - 4120
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Colorado - AMATH - 4120
%!PS-Adobe-2.0 %Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %Title: hw2.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips hw2.dvi %DVIPSParameters: dpi=600, compressed
Colorado - AMATH - 4120
%!PS-Adobe-2.0 %Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %Title: hw3.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips hw3.dvi %DVIPSParameters: dpi=600, compressed
Colorado - AMATH - 4120
%!PS-Adobe-2.0 %Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %Title: hw4.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips hw4.dvi %DVIPSParameters: dpi=600, compressed
Colorado - AMATH - 4120
%!PS-Adobe-2.0 %Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %Title: hw5.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips hw5.dvi %DVIPSParameters: dpi=600, compressed
Colorado - AMATH - 4120
&quot;hhush#xxu&amp;yduh#ys@6uwaSausodhk6a`hHyHBi hBDgjS0&amp;s xq bc sd dq evv ` e i c de xqr sq vc W V c ys@Ub}Bh6eBkHq}hq6aweau}Bho6V(&amp;YYsUb~yfbBB`ukHgyfBawBuwhahBwjgv c q h s he is q d cs V c x b d sq x b b `d e is ep q i c f &quot;hqhuBhcghq6woduhy
Colorado - AMATH - 4120
%!PS-Adobe-2.0 %Creator: dvips(k) 5.78 Copyright 1998 Radical Eye Software (www.radicaleye.com) %Title: hw6.dvi %Pages: 2 %PageOrder: Ascend %BoundingBox: 0 0 612 792 %EndComments %DVIPSCommandLine: dvips hw6.dvi %DVIPSParameters: dpi=600, compressed
Colorado - AMATH - 4120
T y ad r q a V y c x fd q adi d d 4$tasgU(9bv(gbg$UpgUg$ T yad r q a 4$`asgU 9bgbp$UpgUg$(9b y c } fd q adi d d V y c T yad r q W | a i rad W ya W dd k y c d 4$`aesgt~$dUl`4$Ut4etpUg$9bpd T r x qa c r x W dd c y c W W Wd d e
National Taiwan University - AST - 141
Astronomy 141 Life in the Universe Professor Gaudi Homework #3Name _ Astronomy 294 Life in the Universe Winter Quarter 2008 Prof. Gaudi Homework #3 Due Monday November 17 in class Instructions Answer the following six questions by circling the
National Taiwan University - AST - 141
Astronomy 141 Life in the Universe Professor Gaudi Homework #4 SolutionsAstronomy 141 Life in the Universe Autumn Quarter 2008 Prof. Gaudi Homework #4 SolutionsThese questions concern the concept of targets for searches for extrasolar planet
National Taiwan University - AST - 141
Astronomy 141 Life in the Universe Professor Gaudi Homework #1Astronomy 141 Life in the Universe Autumn Quarter 2008 Prof. Gaudi Homework #1 SolutionsQuestion 1 (40 points total) Part 1 (20 points). One reason that the ancient Greeks didnt b
National Taiwan University - AST - 141
Astronomy 141 Life in the Universe Professor Gaudi Homework #2Name _ Astronomy 141 Life in the Universe Autumn Quarter 2008 Prof. Gaudi Homework #2 Due Monday, October 27 in class Instructions Answer the following six questions by circling the
National Taiwan University - AST - 141
Astronomy 141 Life in the Universe Professor Gaudi Homework #2Astronomy 294 Life in the Universe Autumn Quarter 2008 Prof. Gaudi Homework #2 SolutionsAstronomers surveying the outer solar system discover a new planet that they name Rocky. As
National Taiwan University - AST - 141
Astronomy 141 Life in the Universe Professor Gaudi Homework #1Astronomy 141 Life in the Universe Autumn Quarter 2008 Prof. Gaudi Homework #1 Due Monday, October 6 in class Instructions: Answer the following four questions by circling the corre
National Taiwan University - AST - 143
ASTRONOMY 143: The History of the UniverseFall Quarter 2008 Mon Wed Fri 1:30 - 2:48 pm Mendenhall 191Where do we come from? What are we? Where are we going? Paul Gauguin, 1897Instructor: Professor Barbara Ryden Oce: 4035 McPherson Lab (4th oo
National Taiwan University - AST - 143
National Taiwan University - AST - 143
National Taiwan University - AST - 294
ASTRONOMY 294Z: The History of the Universe Professor Barbara RydenSOLUTIONS TO PROBLEM SET # 51) [20 points] Einstein showed that mass (M ) and energy (E) are interchangeable: E = M c2 , where c is the speed of light. This implies, for instance,
National Taiwan University - AST - 294
ASTRONOMY 294Z: The History of the Universe Professor Barbara RydenSOLUTIONS TO PROBLEM SET # 41) [20 points] Today, the average density of matter in the universe is = 3 10-27 kg/m3 . If the matter consisted entirely of hydrogen atoms, how many
National Taiwan University - AST - 294
ASTRONOMY 294Z The History of the Universe Professor Barbara RydenProblem Set # 7: The Last Problem Set Due Tuesday, March 4 at class timeNAME (please print clearly):SCORE (instructor use only):Reminder: The Final Exam for this class will be
National Taiwan University - AST - 294
ASTRONOMY 294Z: The History of the Universe Professor Barbara RydenSOLUTIONS TO PROBLEM SET # 61) [20 points] Potassium-40 is an unstable atomic nucleus; it decays to argon40 with a half-life of 1.3 billion years. Suppose that a rock contains 1,00
National Taiwan University - AST - 294
ASTRONOMY 294Z: The History of the Universe Professor Barbara RydenSOLUTIONS TO PROBLEM SET # 11) [20 points] Two Martian astronomers, Marvin and Marla, are located due north and south of each other on the planet Mars. Marvin sees the Sun directly
National Taiwan University - AST - 294
ASTRONOMY 294Z The History of the UniverseWinter Quarter 2008 Tuesday &amp; Thursday, 3:00 4:48 pm Hitchcock 131Where Do We Come From? What Are We? Where Are We Going? Paul Gauguin, 1897 Instructor: Professor Barbara Ryden Oce: 4035 McPherson Lab (4
National Taiwan University - AST - 294
ASTRONOMY 294Z: The History of the Universe Professor Barbara RydenSOLUTIONS TO PROBLEM SET # 31) [20 points] You are given a ticket for running a red traffic light. For an observer halted at the light, the light emitted has a wavelength 0 = 700 n
National Taiwan University - AST - 294
ASTRONOMY 294Z: The History of the Universe Professor Barbara RydenMIDTERM EXAM: SOLUTIONSShort-Answer Problems 1) Arrange the following scientists in order of when they lived, earliest to latest: Isaac Newton, Aristarchus, Nicolaus Copernicus. Ar
National Taiwan University - AST - 294
ASTRONOMY 294Z The History of the Universe Professor Barbara RydenProblem Set # 6 Due Tuesday, February 26 at class timeNAME (please print clearly):SCORE (instructor use only):Only four questions on this problem set! However, the final questi
National Taiwan University - AST - 294
ASTRONOMY 294Z: The History of the Universe Professor Barbara RydenPRACTICE MINI-EXAMShort Answer Problems 1) Who lived first: Kepler or Copernicus? Copernicus. (Kepler modified the Copernican model by adding elliptical orbits.) 2) If the density
National Taiwan University - AST - 294
ASTRONOMY 294Z The History of the Universe Professor Barbara RydenProblem Set # 4 Due Tuesday, February 5 at class timeNAME (please print clearly):SCORE (instructor use only):Reminder: The midterm exam will be on Thursday, February 7, at clas
National Taiwan University - AST - 294
ASTRONOMY 294Z The History of the Universe Professor Barbara RydenProblem Set # 3 Due Tuesday, January 29 at class timeNAME (please print clearly):SCORE (instructor use only):1) [20 points] You are given a ticket for running a red traffic lig
National Taiwan University - AST - 294
ASTRONOMY 294Z: The History of the Universe Professor Barbara RydenSOLUTIONS TO PROBLEM SET # 71) [20 points] The age of the universe (that is, the time since the Big Bang) is 14 billion years. The age of the Solar System is 4.56 billion years. Th
National Taiwan University - AST - 294
ASTRONOMY 294Z The History of the Universe Professor Barbara RydenProblem Set # 5 Due Tuesday, February 19 at class timeNAME (please print clearly):SCORE (instructor use only):1) [20 points] Einstein showed that mass (M ) and energy (E) are i
National Taiwan University - AST - 822
1Wednesday, September 21: IntroductionThis course deals with continuum radiation processes of astrophysical interest. (Processes that produce spectral lines, rather than continuum radiation, are dealt with in Astronomy 823: Theoretical Spectrosco
National Taiwan University - AST - 822
1Monday, November 21: Inverse Compton ScatteringWhen I did the calculations for the scattering of photons from electrons, I chose (for the sake of simplicity) the inertial frame of reference in which the electron was initially at rest. However, a
National Taiwan University - AST - 822
1Wednesday, November 16: Return of SynchrotronBoth bremsstrahlung and synchrotron radiation can be emitted by hot ionized gas. How can you tell whether the light you observe from a distant galaxy is bremsstrahlung or synchrotron? One way of disti
National Taiwan University - AST - 822
AST 822: Electromagnetic RadiationProblem Set 6: due Wednesday, November 23 1) A highly relativistic electron initially has Lorentz factor 0 1. It is moving in a magnetic field of constant flux density B with a pitch angle . What is (t) as the elect
National Taiwan University - AST - 822
11.1ASTRONOMY 822: Electromagnetic RadiationProblem Set 4: due Wednesday, October 261) Commercial radio stations often broadcast their programs using 2 to 12 dipole antennas arranged in long rows:a) Why do they use this arrangement, rather th
National Taiwan University - AST - 822
ASTRONOMY 822 Electromagnetic RadiationProblem Set 2 due Wednesday, October 12 at class time 1) Consider a plane electromagnetic wave of the form E = ey E0 cos(kx - t) ^ and B = ez E0 cos(kx - t) . ^ The wavelength of the light is measured to be =
National Taiwan University - AST - 822
ASTRONOMY 822 Electromagnetic RadiationProblem Set 3 due Wednesday, October 19 at class time 1) A particle of charge q is moving at a constant speed v q along a straight line. You are located so that the particle's distance at closest approach is b
National Taiwan University - AST - 822
1Monday, October 3: Stellar AtmospheresThere exist entire books written about stellar atmospheres; I will only give a brief sketch of the simplest approximations used in studying stellar atmospheres. In particular, I want to discuss that most use
National Taiwan University - AST - 822
1Monday, November 28: ComptonizationWhen photons and electrons coexist in the same volume of space, their scattering interactions can transfer energy from photons to electrons (Compton scattering) or from electrons to photons (inverse Compton sca
National Taiwan University - AST - 822
1Monday, October 17: Multi-particle SystemsFor non-relativistic charged particles, we have derived a useful formula for the power radiated per unit solid angle in the form of electromagnetic radiation: dP q2 2 2 [a sin ] , = d 4c3 q (1)where q
National Taiwan University - AST - 822
1Monday, October 24: Special Relativity ReviewPersonally, I'm very fond of classical physics. As we've seen recently, you can derive some very useful electromagnetic formulae without taking into account quantum mechanics or special relativity. Ho
National Taiwan University - AST - 822
1Monday, September 26: Radiative TransferAs light travels through the universe, things happen to it. By interacting with charged particles, photons can gain energy; they can lose energy; they can change their direction of motion. Photons can also
National Taiwan University - AST - 822
1Monday, November 7: Synchrotron Radiation for BeginnersAn accelerated electron emits electromagnetic radiation. The most effective way to accelerate an electron is to use electromagnetic forces. Since electrons have mass, they can also be accele
National Taiwan University - AST - 822
1Monday, October 31: Relativistic Charged ParticlesAs I was saying, before the midterm exam intervened, in an inertial frame of reference K there exists an electric field E and a magnetic field B at a spacetime location (r, t). Another inertial f
National Taiwan University - AST - 822
1Monday, October 10: PotentialsI've already remarked on the similarity between the electrostatic force between two point charges, q1 q2 (1) F = 2 , r and the gravitational force between two point masses, F = -G m1 m2 . r2 (2)The similarities be
National Taiwan University - AST - 822
AST 822: Electromagnetic RadiationProblem Set 5: due Wednesday, November 9 1) An observer in the inertial frame of reference K sees a particle moving in the xy plane, with velocity ux = u cos and uy = u sin . The inertial frame of reference K is mo
National Taiwan University - AST - 822
ASTRONOMY 822 Electromagnetic RadiationProblem Set 1 due Wednesday, October 5 at class time1) If you could construct a box opaque to neutrinos, then at a temperature T , the thermal neutrinos inside the box would have the specific intensity I (T )
National Taiwan University - AST - 143
National Taiwan University - AST - 143
National Taiwan University - AST - 143
National Taiwan University - AST - 143
ASTRONOMY 143: The History of the Universe Professor Barbara RydenPRACTICE MINI-EXAMWITH SOLUTIONSShort-Answer Problems 1) Which has the greater energy: a photon of infrared light or a photon of ultraviolet light? ULTRAVIOLET light has the great
National Taiwan University - AST - 143
National Taiwan University - AST - 143
National Taiwan University - AST - 143
National Taiwan University - AST - 143
National Taiwan University - AST - 143