19mathcad学习资料汇编

Mathcad01()02()03()04()05()06(),0708091011121314151617181920212223Z242526272829Mathcad130Mathcad231Mathcad33233343536ExamProblemMathcadExamKeyMathcad∞n0nk1nk+()2∑=lim→0→∞nnn2+n3--()⋅lim→52→∞nn12n+3n+lim→3→1-x11x-51x3--⎛⎜⎝⎞⎟⎠lim→2-→0xx2sinx()⋅cos1x⎛⎜⎝⎞⎟⎠⋅lim→0→2(1)∞x23x⋅+33x⋅+⎛⎜⎝⎞⎟⎠x1+lim→exp1-3⎛⎜⎝⎞⎟⎠→∞x2πatanx()⋅⎛⎜⎝⎞⎟⎠xlim→exp2-π⎛⎜⎝⎞⎟⎠→0x1tanx()+sinx()1+-x3lim→14→0x12tanx()2⋅+()cotx()2lim→exp2()→∞xx21+x21-⎛⎜⎜⎝⎞⎟⎟⎠x2lim→exp2()→π4xsecx()22tanx()⋅-1cos4x⋅()+lim→12→(2)0xxlnx1+()lim+→1→π2xtanx()2x⋅π-lim-→1→0xexpx3()1-1cosx1cosx()-()⋅⎡⎣⎤⎦-lim+→4→(3)0x0x3tcost2()⌠⎮⌡d0xtt2expt2-()⋅⌠⎮⌡dlim→3→1()Mathcad,.1..2.,Ctrl+L.•.•Ctrl+.→“”.•=.1.(1)∞n11n+⎛⎜⎝⎞⎟⎠nlim→exp1()→∞n11n+⎛⎜⎝⎞⎟⎠3-n⋅lim→exp3-()→∞n11n+⎛⎜⎝⎞⎟⎠an⋅lim→expa()→(2)∞n3n2sinn!()⋅n1+lim→0→∞nn2n+n-()lim→12→∞n3n21+3n2-3n2k+3n2-lim→1k→3()∞n1nkkn2∑=lim→12→2003-2-7yt()sint()cost()⋅1sint()2+:=xt()cost()1sint()2+:=210uhu()dd10362880-→5ugu()dd5160-cos0()⋅→160-=u0:=1.,,,.2..15xhx()dd1587178291200x1+()15→10xhx()dd10362880-x1+()10→hx()ln1x+():=xgx()dd2x⋅sin2x⋅()⋅2x2⋅cos2x⋅()⋅+→gx()x2sin2x⋅()⋅:=(2)2xlnfx()()dd2simplify2-cosexp2-x⋅()()2-2cosexp2-x⋅()()⋅sinexp2-x⋅()()⋅exp2-x⋅()⋅+2exp4-x⋅()⋅+()cosexp2-x⋅()()2⋅→xlnfx()()ddsimplify2xcosexp2-x⋅()()⋅sinexp2-x⋅()()exp2-x⋅()⋅+()cosexp2-x⋅()()⋅→xhx()ddsimplify1-42-sinx()⋅2sinx()⋅expx()⋅2x⋅cosx()⋅-+2x⋅cosx()⋅expx()⋅+xsinx()⋅expx()⋅+()xsinx()⋅1expx()-()12⋅⎡⎢⎣⎤⎥⎦121expx()-()12⋅⋅→hx()xsinx()⋅1expx()-⋅:=xfx()ddsimplify2x⋅expx2()⋅cosexp2-x⋅()()⋅2sinexp2-x⋅()()⋅expxx2-()⋅[]⋅+→fx()ex2cose2-x⋅()⋅:=1.(1)f(x).•Shift+/xfx()ddkxfx()ddk,f(x).•Ctrl+,,Symbolcsimplify•,.:,.1..2.Mathcad:()2003-2-7xyx()ddtyt()ddtxt()dd=tyt()ddtxt()ddsimplify3cost()2⋅2-()-sint()2cost()2+()⋅→xat,()atsint()-()⋅:=yat,()a1cost()-()⋅:=tyat,()ddtxat,()ddsint()1cost()-()→2003-2-7xgxy,()∂∂ygxy,()∂∂-simplifyexpx()-expy()+()-expx()expy()+()→gxy,()lnexey+():=xfxy,z,()∂∂1sinx()2siny()2+sinz()2+()12sinx()⋅cosx()⋅→fxy,z,()sinx()2siny()2+sinz()2+:=vfuv,()∂∂19π2⋅cos12π⋅⎛⎜⎝⎞⎟⎠⋅→0=ufuv,()∂∂23π⋅sin12π⋅⎛⎜⎝⎞⎟⎠⋅19π2⋅cos12π⋅⎛⎜⎝⎞⎟⎠⋅+→2.094=vπ6:=uπ3:=xyfxy,()∂∂∂∂2x⋅cosxy+()⋅x2sinxy+()⋅-→2yfxy,()∂∂2x2-sinxy+()⋅→2xfxy,()∂∂22sinxy+()⋅4x⋅cosxy+()⋅x2sinxy+()⋅-+→yfxy,()∂∂x2cosxy+()⋅→xfxy,()∂∂2x⋅sinxy+()⋅x2cosxy+()⋅+→f(x,y)f(1)fxy,()x2sinxy+()⋅:=,..1..2.()3(2)lnx2y2+()atanyx⎛⎜⎝⎞⎟⎠=,dydx.Fxy,()lnx2y2+()atanyx⎛⎜⎝⎞⎟⎠-:=dydxFx-Fy=xFxy,()∂∂simplifyxy+()x2y2+()→yFxy,()∂∂simplifyy-x+()-x2y2+()→Dxy,()xFxy,()∂∂yFxy,()∂∂-:=Dxy,()simplifyxy+()y-x+()→xcosx()3⌠⎮⎮⌡d13cosx()2⋅sinx()⋅23sinx()⋅+→0πxfx()⌠⎮⌡d12expπ()⋅12π⋅+12+→13.641=0123369fy()πyxfx()⌠⎮⌡d1-2cosx()⋅expx()⋅12sinx()⋅expx()⋅+12cosx()⋅sinx()⋅+12x⋅+→(2):xxfx()dddd2cos13π⋅⎛⎜⎝⎞⎟⎠⋅exp13π⋅⎛⎜⎝⎞⎟⎠⋅2sin13π⋅⎛⎜⎝⎞⎟⎠2⋅2cos13π⋅⎛⎜⎝⎞⎟⎠2⋅-+→5xfx()dd529.427-=xfx()dd3.027=xπ3:=nxfx()ddn8-cosx()⋅expx()⋅32sinx()2⋅32cosx()2⋅-+→n6:=xfx()ddcosx()expx()⋅sinx()expx()⋅2cosx()⋅sinx()⋅-+→fx()sinx()ex⋅cosx()2+:=,Calculus:,:4-sinx()⋅expx()⋅8cosx()2⋅8sinx()2⋅-+,:2-sinx()⋅expx()⋅2cosx()⋅expx()⋅+8sinx()⋅cosx()⋅+,:2cosx()⋅expx()⋅2sinx()2⋅2cosx()2⋅-+,:cosx()expx()⋅sinx()expx()⋅2cosx()⋅sinx()⋅-+x,symbols/Variable/Differentiate:sinx()ex⋅cosx()2+:(1)::..(40xxlnx1+()lnx()-()⋅lim+→0→πx13cotx()⋅+()secx()lim→exp3()→0xxsinx()⋅1+1-expx2()1-lim→12→0x1x+1-31x+1-lim→32→π2xlnsinx()()π2x⋅-()2lim→1-8→∞n2nn!lim→0→∞nn1nk2k⋅1-()∏=1nk2k⋅()∏=lim→1→1∞k1k2∑=16π2⋅→∞nSn()lim→16π2⋅→Sn()1nk1k2∑=:=(4)seriesft()seriest,7,1t+13t3⋅+13t4⋅130t5⋅-118t6⋅-+→ft()sint()et⋅cost()2+:=11x⋅+13x3⋅+13x4⋅130x5⋅-+Ox6()+x,symbols/Variable/ExpandtoSeries:sinx()ex⋅cosx()2+(3)0π2x1a2sinx()2⋅b2cosx()2+1+⌠⎮⎮⎮⌡d1202⋅π⋅→b3:=a2:=0π2xexpαx⋅()sinβx⋅()⋅⌠⎮⎮⌡dexp12π⋅α⋅⎛⎜⎝⎞⎟⎠β-cos12π⋅β⋅⎛⎜⎝⎞⎟⎠⋅αsin12π⋅β⋅⎛⎜⎝⎞⎟⎠⋅+⎛⎜⎝⎞⎟⎠α2β2+()⋅βα2β2+()+→01xxlnx1+()⋅⌠⎮⌡d14→x1sinx()m⌠⎮⎮⎮⌡dx1sinx()m⌠⎮⎮⎮⌡d→xx3expx()⋅⌠⎮⎮⌡dx3expx()⋅3x2⋅expx()⋅-6x⋅expx()⋅6expx()⋅-+→2x→0tsint()t2⋅sin3t3()lim→13→0tsint()et⋅sin3t()lim+→13→∞t14t-⎛⎜⎝⎞⎟⎠tlim→exp4-()→0xsinx()xcosx()⋅-sinx()3lim→13→∞ttnet-⋅lim→0→0tln3t21+()tsint()⋅lim→3→1xx11x-lim→exp1-()→1x1x-()tanπ2x⋅⎛⎜⎝⎞⎟⎠⋅lim→2π→0xln1x⎛⎜⎝⎞⎟⎠⎛⎜⎝⎞⎟⎠xlim+→1→∞x2πatanx()⋅⎛⎜⎝⎞⎟⎠xlim→exp2-π⎛⎜⎝⎞⎟⎠→1x2πacosx()⋅⎛⎜⎝⎞⎟⎠1xlim-→0→(5)0πx1fx()2+⌠⎮⌡d14.156=0πf(x).0πxπfx()2⋅⌠⎮⌡d18π⋅exp2π⋅()⋅25π⋅expπ()⋅+38π2⋅+1140π⋅+→243.932=Sn()1nk1k2∑=:=n1000050000,100000..:=6Sn()⋅3.141497163947213.141573555129573.1415820433013=Mathcad,tong,.fxy,()yx2y2+:=3f(x,y){(x,y)|yxy^2,1ysqrt(3)}.I815→I01xxx2--xx2-yx⌠⎮⎮⌡d⌠⎮⎮⌡d:=yxx2-=gxy,()x:=00.510.50.5Ax()Bx()xBx()Ax()-:=Ax()xx2-:=2f(x,y){(x,y)|x^2+y^2x}.0ax0ax-y1x-y-⌠⎮⌡d⌠⎮⌡d9-2→a3:=01y01y-xfxy,()⌠⎮⌡d⌠⎮⌡d16→0ax0ax-y1x-y-⌠⎮⌡d⌠⎮⌡d12a2⋅13a3⋅-→0ay0ay-xfxy,()⌠⎮⌡d⌠⎮⌡d12a2⋅13a3⋅-→0ax0ax-yfxy,()⌠⎮⌡d⌠⎮⌡d12a2⋅13a3⋅-→fxy,()1x-y-:=1f(x,y){(x,y)|x0,y0,x+ya}.0111x-x.,.1.,(),2..Shift+7.,Mathcad,,3..()55u=f(x,y).02x02x-y02x-y-zfxy,z,()⌠⎮⌡d⌠⎮⌡d⌠⎮⌡d88315→fxy,z,()xy2+()z2⋅:=5u=f(x,y,z){(x,y,z)|0x2,0y2-x,0z2-x-y}.I112exp4()⋅exp2()-→I1121y1y2xfxy,()⌠⎮⎮⌡d⌠⎮⎮⌡d12y12xfxy,()⌠⎮⌡d⌠⎮⌡d+:=I12exp4()⋅exp2()-→I12x1x2yfxy,()⌠⎮⎮⌡d⌠⎮⎮⌡d:=012341230.521x12xfxy,()yexy⋅⋅:=4f(x,y){(x,y)|1/xy2,1x2}.I1simplify1-2ln2()⋅112π⋅3⋅+→I113xxxyfxy,()⌠⎮⌡d⌠⎮⌡d33xx3yfxy,()⌠⎮⌡d⌠⎮⌡d+:=I0.10688=I112π⋅3⋅12ln2()⋅-→I13yyy2xfxy,()⌠⎮⌡d⌠⎮⌡d:=01231213xxx01x0xyxy+x2y2+()⌠⎮⎮⎮⌡d⌠⎮⎮⎮⌡d12ln2()