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PS2soln

# PS2soln - f LocT/wm g —————_l MATH 412 Problem...

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Unformatted text preview: f LocT/wm g —————__l._._ MATH 412: Problem Set 2 due Thursday, February 7, 2008 1. Strauss 2.2 #2 - energy and momentum for wave equation 2. Strauss 2.2 #5 — damped wave equation 3. Consider the following transport-decay equation for Mrs, t): at + can: 2 —,\u Where A > D is a constant. By making an appropriate change of variables similar to What we discussed in class, convert this to an ordinary differential equation (ODE). Then solve that equation, remembering that any constants could be functions of the other variable. From this obtain a solution ii(rr:, t). Show also that this equation can be solved by making the following change of dependent variable (the function itself): w(m,t) = n(a‘,t)e)‘t How do you interpret this? 4. Strauss 2.3 #6 - comparison principle for heat equation HINT: deﬁne w(mj t) : nix, t) — ii(:r, t), and use the Maximum Principle for the heat equation (p.42) 5. Strauss 2.3 #8 - radiative boundary condition 6. Strauss 2.4 #1 - diﬁnsion equation 7. Strauss 2.4 #11 - even and odd initial conditions Version 1.1 P” :‘g‘Q/ﬁfkwyg wﬁ’wak) I @252; Z Dawé/ML SLMHH‘F 4Myﬂx\$\$®r€~ Q? (53/494 L457 3 _ LHXM¥+IL 6 y}: / . 2 ‘ M 2/6 Die/M 4%”? '1 Maﬁ 4545444“ ‘ E I E V 4'" er/ 1:: M3“? ﬂak;— OCR—k2»!— "‘_Z_. LCJMJG Mfg“ :M-x—X’ Mkkkiﬂﬁék:éé% W ’2’ gwlvw's; \$55? Whgﬁxxl”fU/P F>© (a’dﬁ‘rzbu'rx BONE GAO/>7 (/ﬂ/ﬁ’ HC§M+MKX3 w‘o/Q Mk ‘AUC 9/ {>3 6 gag—(EMPKgO/K : _ )2 )2 34; J, E z édv‘ 904\$“ "CﬂMWC/X "I" ﬁacf/ J7, PL )3 Lﬂm 3L _,L a ' dé Wit/K “5 Vﬂxﬁﬂ/y/A/ " '— ﬂébg/ ’7 >0 32 27/ Q 0 L43L;9[ i "2 E étd‘eueg Am 33-72556 \$692 w‘ 9 We 5% Wamuw \$ 141ka 74,. +9“) 7521; M/A7+\ 4 vkﬂ (#742 EC; MﬂZ—A f. K/ﬂg‘?) ym'r“U'-€ ...
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PS2soln - f LocT/wm g —————_l MATH 412 Problem...

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