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-1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 270 1 {CSTYLE " " -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 271 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 272 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 273 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 11 274 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }1 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 275 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 276 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 277 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 278 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 13 "MATH 2280 - 1" }}{PARA 278 "" 0 "" {TEXT -1 22 "FIRST MAPLE ASSIGNMENT" }}{PARA 257 "" 0 "" {TEXT -1 16 "Due May 26, 2005" }}{PARA 265 "" 0 "" {TEXT -1 1 "\n" } {TEXT 276 29 "(taken from Prof. Treibergs, " }{TEXT 308 27 "www.math.u tah.edu/~treiberg" }{TEXT 309 1 ")" }}{PARA 266 "" 0 "" {TEXT -1 1 "\n " }{TEXT 275 375 "In this first assignment, we will learn some of Mapl es capabilities for solving differential equations. If you have neve r used Maple before, you should introduce yourself to the program usin g Prof. Korevaar's tutorial. You can find a link to it on the course \+ webpage (http://www.math.utah.edu/~bobby/2280/), download the document in the .mws format and open it with Maple." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 256 187 "Carefully read through the following and answer the questions at the end about indoo r temperature variations. This material can be found in section 1.5 A pplication (page 56) of our text." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }} {PARA 0 "" 0 "" {TEXT 257 116 "First let's see some of Maple's capabil ites when solving differential equations. For example, we saw in clas s that:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 258 "" 0 "" {TEXT 258 1 " " }{TEXT 259 19 "y(x) = (-x-1) + e^x" }{TEXT 260 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 261 15 "solves the ODE:" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 259 "" 0 "" {TEXT -1 0 "" }{TEXT 262 0 "" }{TEXT 263 11 "y'-y-x = 0." }}{PARA 0 " " 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }{TEXT 264 67 "Le t's check this with Maple. It is a good idea to clear variables." } {MPLTEXT 1 0 5 " " }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "res tart:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "y:=\nx->(-x-1)-exp (x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%\"yGf*6#%\"xG6\"6$%)operator G%&arrowGF(,(9$!\"\"\"\"\"F.-%$expG6#F-F.F(F(F(" }}}{EXCHG {PARA 260 " " 0 "" {TEXT -1 26 "If we want some values of " }{TEXT 265 4 "y(x)" } {TEXT -1 4 " or " }{TEXT 266 5 "y'(x)" }{TEXT -1 26 " we can use the f ollowing:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 184 "y(0);D(y)(0);\n# the #-sign tells Maple to ignore this line\n# \+ this is a good tool when trying to tell\n# someone what you are doing \+ in this step \n# i.e. finding the values y(0) and y'(0)" }}{PARA 11 " " 1 "" {XPPMATH 20 "6#!\"#" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#!\"#" }} }{EXCHG {PARA 261 "" 0 "" {TEXT -1 48 "Now we can input the above ODE. The expression " }{TEXT 267 12 "diff(y(x),x)" }{TEXT -1 12 " stands \+ for " }{TEXT 268 5 "y'(x)" }{TEXT -1 2 ", " }{TEXT 269 14 "diff(y(x),x ,x)" }{TEXT -1 12 " stands for " }{TEXT 270 6 "y''(x)" }{TEXT -1 5 " e tc." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 20 "d iff(y(x),x)-y(x)-x;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}} {EXCHG {PARA 262 "" 0 "" {TEXT -1 25 "Hence our above equation " } {TEXT 271 4 "y(x)" }{TEXT -1 19 " satisfies the ODE." }{MPLTEXT 1 0 1 "\n" }}{PARA 263 "" 0 "" {TEXT -1 37 "Suppose that we wished to show t hat " }{TEXT 272 11 "z(x)= x e^x" }{TEXT -1 13 " satisfies " } {TEXT 273 26 "x^2 z'' - x(x+1)z' + z = 0" }{TEXT -1 3 " ," }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 16 "z:= x->x*exp(x);" }}{PARA 11 "" 1 " " {XPPMATH 20 "6#>%\"zGf*6#%\"xG6\"6$%)operatorG%&arrowGF(*&9$\"\"\"-% $expG6#F-F.F(F(F(" }}}{EXCHG {PARA 267 "" 0 "" {TEXT -1 65 "The follow ing should evaluate to zero if the above is a solution:" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 45 "x^2*diff(z(x),x,x) -x*(x+1)*diff(z(x),x)+z(x);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#,(*&)% \"xG\"\"#\"\"\",&*&F'F(-%$expG6#F&F(F(*&F&F(F+F(F(F(F(*(F&F(,&F&F(F(F( F(,&F+F(F.F(F(!\"\"F.F(" }}}{EXCHG {PARA 264 "" 0 "" {TEXT -1 117 "Thi s is too complicated. MAPLE can simplify expressions in a number of wa ys. One way to try is to call the operation " }{TEXT 274 12 "simplify( % )" }{TEXT -1 134 ". % is MAPLE's way of referring to the previously displayed experession. Simplification yields zero, so the expression \+ is a solution." }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "simplify( %);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 268 "" 0 "" {TEXT -1 133 "Next let's try some ODE specific tools in Maple. T o begin, we call up the ODE library. We store the DE in question in t he variable " }{TEXT 277 3 "eq1" }{TEXT -1 28 ". We use the function \+ name " }{TEXT 278 4 "u(x)" }{TEXT -1 12 " instead of " }{TEXT 279 4 "y (x)" }{TEXT -1 47 " as this already has a meaning in this session." } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 14 "with(DE tools):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 31 "eq1:=diff(u(x),x )-2*x*u(x)-x=0;" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq1G/,(-%%diffG6 $-%\"uG6#%\"xGF-\"\"\"*(\"\"#F.F-F.F*F.!\"\"F-F1\"\"!" }}}{EXCHG {PARA 269 "" 1 "" {TEXT -1 0 "" }{TEXT 280 53 "Now we use Maple's tool s to get the general solution:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 12 "dsolve(eq1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#/-%\"uG6#%\"xG ,&#\"\"\"\"\"#!\"\"*&-%$expG6#*$)F'F+F*F*%$_C1GF*F*" }}}{EXCHG {PARA 270 "" 0 "" {TEXT -1 163 "Goodness folks, it look like I might be out \+ of a job! This is TOO easy. But wait, Maple will also find the parti cular solution, let's store this in the variable " }{TEXT 281 4 "sol1 " }{TEXT -1 1 ":" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 27 "sol1:=d solve(\{eq1,u(0)=0\});" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%%sol1G/-% \"uG6#%\"xG,&#\"\"\"\"\"#!\"\"*&#F,F-F,-%$expG6#*$)F)F-F,F,F," }}} {EXCHG {PARA 271 "" 0 "" {TEXT -1 92 "Here is a better way to check th e solution, rather than expliciting inputing we did earlier:" } {MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 18 "odetest (sol1,eq1);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#\"\"!" }}}{EXCHG {PARA 272 "" 0 "" {TEXT -1 28 "Here's example 5 on page 63:" }}{PARA 273 "> \+ " 0 "" {MPLTEXT 1 0 50 "eq2:=dsolve(x*D(v)(x)+6*v(x)-3*x*v(x)^(4/3),v( x));" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq2G/,(*&\"\"\"F(*$)-%\"vG6 #%\"xG#F(\"\"$F(!\"\"F(F.F1*&)F.\"\"#F(%$_C1GF(F1\"\"!" }}}{EXCHG {PARA 274 "" 1 "" {TEXT -1 0 "" }{TEXT 282 61 "Here's another command \+ to get Maple to simplify the answer: (" }{TEXT 283 38 "does anyone kno w what the proc(x) is?)" }{TEXT 284 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 13 "solve(eq2,v);" }}{PARA 11 "" 1 "" {XPPMATH 20 "6#f*6# %\"xG6\"F&F&*&\"\"\"F(*&)9$\"\"$F(),&F(F(*&F+F(%$_C1GF(F(F,F(!\"\"F&F& F&" }}}{EXCHG {PARA 275 "" 0 "" {TEXT -1 66 "The following is creates \+ slope fields as the ones we saw in class." }{MPLTEXT 1 0 0 "" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 22 "eq3:=D(w)(x)-w(x)-x=0;" }} {PARA 11 "" 1 "" {XPPMATH 20 "6#>%$eq3G/,(--%\"DG6#%\"wG6#%\"xG\"\"\"- F+F,!\"\"F-F0\"\"!" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 127 "DEpl ot(eq3,w(x),x=-2..2,\{seq([w(0)=k/3],k=-6..0)\}, color=black,linecolor =[red,magenta,blue,green,cyan,coral,navy],arrows=LINE);" }}{PARA 13 " " 1 "" {GLPLOT2D 256 256 256 {PLOTDATA 2 "6,-%'CURVESG6]dl7$7$$!3qE$>j 5\"3I?!#<$!3jt-suF*$!3a<;htg:w5F-7$7$$!3SRX!*=8 .?=F*$!3&4'*>wsu;+\"F-7$$!3E8l^\\g\"*er?J5w5F-7$7$$!3M7qdWh** 4;F*$!3e'>ohDI<+\"F-7$$!3'H4lAf)*ya\"F*$!3f%pj@fZg2\"F-7$7$$!3yJ.^Fi(* *R\"F*$!33M>#f_)y,5F-7$$!3;EGvxe'oL\"F*$!33d*4CK*)f2\"F-7$7$$!3n7MZZA( **=\"F*$!3AmJe:(\\=+\"F-7$$!3%zz5iA+\"F-7$$!3oDec+#>v9*F]o$!3Gx15IQ'e2\"F-7$7$$!3 Wio$)*3],q(F]o$!3&Gv'oU;)>+\"F-7$$!3'oHEa,#pOqF]o$!3KQ^k0izv5F-7$7$$!3 !R2*z'3L1g&F]o$!3yUJ-:G0-5F-7$$!3%>huEq#oD\\F]o$!3Q[(3L.Dd2\"F-7$7$$!3 RpC@omI,NF]o$!3t\"fU-yF@+\"F-7$$!3,V$!3J#)\\>W5dv5F-7$7$$\"3N Gh+m:QnpF_r$!3'=4b`3_2\"F-7$7$ $\"33iTjo;6!4*F]o$!3@n5wUQn-5F-7$$\"3Am%=Cvcs&)*F]o$!3&R#3d0S5v5F-7$7$ $\"3W)\\4<2q>\"F*$!3>dQa\"f$*\\2\"F- 7$7$$\"3=yL9Bc_G8F*$!3!QN2*y8!H+\"F-7$$\"3Lz(>@[;$39F*$!3OPXUpk([2\"F- 7$7$$\"3pD4!*Q(R#Q:F*$!3b\")*y\"Rd-.5F-7$$\"3=z6%z*\\l>;F*$!3i4H:4@vu5 F-7$7$$\"3cr9CzJ#zu\"F*$!3$4(3G=z:.5F-7$$\"3l!ez\"*=C5$=F*$!3C?50I*>Y2 \"F-7$7$$\"3vc0\"QRuv&>F*$!3u&fKIb)H.5F-7$$\"3!GW*=1cUU?F*$!3U&H*H&HzW 2\"F-7$7$$!3/dg/vh\">.#F*$!3YuD(>;H0C*F*7$$!3'H%R&\\#Q3o>F*$!3n$HB:p$p \")**F*7$7$$!3ppJA#oB>#=F*$!3-iVbiC;T#*F*7$$!3'H)y>'oBqv\"F*$!351:%4Rg 5)**F*7$7$$!3R5%=eO[>h\"F*$!3'>GsbKG=C*F*7$$!3#\\pB5PYfa\"F*$!3<'eBz_% R!)**F*7$7$$!3aJx#H,\"*>S\"F*$!3.Z[Md*GDC*F*7$$!3UEaL#4^[L\"F*$!34@5:' *Qpz**F*7$7$$!3'*\\96bC0#>\"F*$!3V(=r\"[nEV#*F*7$$!3lgFd=qtB6F*$!3p!oC `5c*y**F*7$7$$!3d,N?6dL@)*F]o$!3-m@N!HWSC*F*7$$!3=J\"\\)4F.E\"*F]o$!36 -P9j&y\"y**F*7$7$$!3'*o^h(*GNAxF]o$!31@!4#)Rk[C*F*7$$!3L!*zk2#*[9qF]o$ !31ZoGb%et(**F*7$7$$!3k_P+HfeBcF]o$!3+s7MI,tX#*F*7$$!3?L*p/')HF!\\F]o$ !37'faJs#\\w**F*7$7$$!3iKt\"f=X]_$F]o$!3DSgR9[kY#*F*7$$!3wzow(GW2z#F]o $!3)y#)*4R!yb(**F*7$7$$!3Wt&yKkTnU\"F]o$!3#*f_lu?hZ#*F*7$$!3+b;;Y^@&y' F_r$!3@31%)y2hu**F*7$7$$\"3A#f`9'488nF_r$!3$[T&yiej[#*F*7$$\"3Gv$\\<1] RV\"F]o$!3H`/r!*pet**F*7$7$$\"3?tNann5pFF]o$!3ukr8#\\?(\\#*F*7$$\"3uM1 91FoYNF]o$!3Q.(e8O-D(**F*7$7$$\"3dMH\\4kim[F]o$!33j$Hgnq3D*F*7$$\"3$ou !)*z$*ofcF]o$!3/0lYx@Nr**F*7$7$$\"3#)Rs]H$eQ'pF]o$!3%*oS]q:4_#*F*7$$\" 3.:fvvP)Hx(F]o$!3=*z\"*HGJ,(**F*7$7$$\"3<78Nq!)yg!*F]o$!3fef4A))Q`#*F* 7$$\"38;8q].e'))*F]o$!3`4**RJS$)o**F*7$7$$\"3N*)ozP+u:6F*$!3Wf4A@'oZD* F*7$$\"3$3K()eV\\+?\"F*$!3o3\\FKUXn**F*7$7$$\"3;.E@W'**F*7$7$$\"3kDSGin^W5$ >%pYZf#*F*7$$\"3dEq811VM=F*$!3$zbwS=[F'**F*7$7$$\"3H]fIzS.a>F*$!37lC^# of7E*F*7$$\"3D\\Sp?f'f/#F*$!3+.M)4F*$!3,!Rr*>yS,#*F*7$7$$!3xN&p#)3^S#=F*$!39/+s6X-m %)F*7$$!3)o^^,G'*[v\"F*$!3Y?G&>rU1?*F*7$7$$!3_EQ+5k99;F*$!3!Q!3k+8$oY) F*7$$!3yy#QoK[Pa\"F*$!3y??.Bf$)*>*F*7$7$$!3,\"32/,jUS\"F*$!34?l\">v#on %)F*7$$!3%p2c[4zDL\"F*$!3]/jvrW)*)>*F*7$7$$!3KVc-5>S%>\"F*$!3uJ\\>3@eo %)F*7$$!3Hn&eOc(Q@6F*$!3'G*yZ:^3)>*F*7$7$$!3A3QRy=kX)*F]o$!3<(Q5+!H`p% )F*7$$!3`C)eEaE<5*F]o$!3UPCmBV8(>*F*7$7$$!3a\"33e%)4vu(F]o$!3ey\"Gb(*Q 0Z)F*7$$!3tx]XfAL*)pF]o$!3+YY9[#Gh>*F*7$7$$!3UZ.Oh]j\\cF]o$!3fTcrLXgr% )F*7$$!3TQL6G2ow[F]o$!3+$=d**oi]>*F*7$7$$!3?T&[*p-._NF]o$!3m0'f8;MFZ)F *7$$!3=rct.#fPw#F]o$!3#*=KJiI$R>*F*7$7$$!3FqZ0P*3ZX\"F]o$!3sF.SuG$RZ)F *7$$!3n'o*R3Aa0lF_r$!3)o\\s#\\Vt#>*F*7$7$$\"3+&3_D*F*7$7$$\"3c'oicoD!RFF]o$!3d\\Po[+ cw%)F*7$$\"3R@:-)yjnd$F]o$!3-v!*)\\<2,>*F*7$7$$\"3i1_FV\"3a$[F]o$!3&)4 h%48,!y%)F*7$$\"3Mv%)>Yw!4p&F]o$!3u9ns#4m')=*F*7$7$$\"3Atz'4UX9$pF]o$! 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l-%%VIEWG6$;$!+++++AFa_\\l$\"+++++AFa_\\l;$!+;yx76F]g\\l$\"+m\"yx7&Fa_ \\l-%+AXESLABELSG6$Q\"x6\"Q%w(x)Fhi^l" 1 2 0 1 10 0 2 9 1 4 2 1.000000 45.000000 45.000000 0 0 "Curve 1" "Curve 2" "Curve 3" "Curve \+ 4" "Curve 5" "Curve 6" "Curve 7" "Curve 8" }}}}{EXCHG {PARA 276 "" 0 " " {TEXT -1 129 "If you have never used this feature before, it might b e instructive to change some of the above parameters to see what happe ns.\n\n" }{TEXT 285 39 "MATH 2280 - 1 FIRST MAPLE LAB QUESTIONS" } {TEXT -1 295 "\n\nClick on the left most tool bar button to open a bla nk Maple windo w. On the top line type your name and the assignment n umber. Keep your solutions organized, annotate (using the #-sign) and use enough text to properly analysis the problems. Hand in a printed hard copy of your solutions.\n\n" }{TEXT 286 2 "1." }{TEXT -1 89 " Us e Maple to solve any one of the problems 1-25 on page 54 of section 1. 5 in our text.\n\n" }{TEXT 287 3 "2. " }{TEXT -1 576 "(Computer Projec t in Section 1.5, pages 56-58) The last few pages of Prof. Korevaar's tutorial (linked to the course webpage) analyizes this project and wo uld be a good reference if you have questions or are stuck on how to s tart. Read through the discussion in the text before starting the pro ject.\n\nSCENERIO:\nThe dog days of summer are approaching and with it the annoyance of having to pay a large electricity bill for running t he AC. Let's try to figure out when our house will be the hottest so \+ we could try to avoid being home at these times to reduce our AC uasge .\n\n" }{TEXT 288 2 "a." }{TEXT -1 294 " Solve equation (3) on page 57 by hand using what we learned about linear first-order equations (you might need to use he integral tables in the text too). You should ge t equation (4) on page 57, include this worked out solution with your \+ lab. Notice that your constant of integration is the " }{TEXT 289 3 " c_0" }{TEXT -1 48 " in the text, you can use the initial condition " } {TEXT 290 3 "u_0" }{TEXT -1 22 " to find it's value.\n\n" }{TEXT 291 2 "b." }{TEXT -1 13 " Use Maple's " }{TEXT 292 6 "dsolve" }{TEXT -1 62 " to find the answer to (3). It is best to input the function " } {TEXT 293 4 "A(t)" }{TEXT -1 187 " first and then solve the ODE on the bottom of page 56. It's ugly, but check (use Maple if you can) that \+ this is the same as the answer you found by and and the same as (4) on page 57.\n\n" }{TEXT 294 3 "c. " }{TEXT -1 223 "Now we use parameter \+ values to get an honest function. The value for omega is still Pi/12, but choose some appropriate sounding numbers for the average temperat ure, the high and low and when these occur, to get values for " } {TEXT 295 11 "a_0,a_1,b_1" }{TEXT -1 97 ". You'll need to use equatio n (2) on page 56 to turn these numbers into the ones you input into " }{TEXT 296 4 "A(t)" }{TEXT -1 318 ". Make sur e you annotate these in your write up so I see what you choose. I should see something like: \n\n#\n# Average Temperature = \n# Temperature variation = \n# Phase D elay = \n#\n> omega := Pi/12.0;\n> a0:=\n> a1:=\n> b1:=\n> A:=t-> a0 + a1*cos(omega*t) + b1*sin(omega*t);\n# let's assume that your house is well insulated" }}{PARA 277 "" 0 "" {TEXT -1 10 "> k:=0.2\n\n" } {TEXT 297 3 "d. " }{TEXT -1 85 "Solve equation (3) again, you should \+ get something that looks like (5) on page 57.\n\n" }{TEXT 298 2 "e." } {TEXT -1 52 " Identify the part of your solution that remains as " } {TEXT 299 1 "t" }{TEXT -1 78 " approaches infinity. You should get an equation similar to (6) on page 57.\n\n" }{TEXT 300 2 "f." }{TEXT -1 58 " Rewrite your answer to the above in the form:\n\n " } {TEXT 301 23 "u(t) = A + Bcos(Ct+D)\n\n" }{TEXT -1 45 "page 185 in you r text will be helpful here.\n\n" }{TEXT 302 2 "g." }{TEXT -1 23 " Plo t your solution to " }{TEXT 303 2 "d." }{TEXT -1 12 " along with " } {TEXT 304 4 "A(t)" }{TEXT -1 76 " in a graph resembling figure 1.5.11 \+ on page 58 using the initial condition " }{TEXT 305 4 "u(0)" }{TEXT -1 6 "=70.\n\n" }{TEXT 306 2 "h." }{TEXT -1 231 " Create a graph simil ar to figure 1.5.10 using initial temperatures: 50, 55,...,75,80. Inc lude the slope field also on the plot. Label on the picture by hand w here the daily outside temperature are at their maximum and minimum.\n \n" }{TEXT 307 2 "i." }{TEXT -1 164 " What did you learn? When you s hould you try to avoid your house? Do you think it is possible that e ven in July you could avoid turning on the AC for a few days?" }}}} {MARK "0 2 0" 16 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }