c=[3 2 0 0 -1] c = 3 2 0 0 -1 roots(c) ans = -1.0000 -0.1508 + 0.7086i -0.1508 - 0.7086i 0.6350 polyval(c,2) ans = 63 doc fzero Overloaded functions or methods (ones with the same name in other directories) doc optim/fzero edit myfun fschange('V:\MATLAB\myfun.m'); clear myfun r=fzero('myfun',1) r = 0.7391 myfun(r) ans = 0 r=fzero(myfun,1) ??? Input argument "x" is undefined. Error in ==> myfun at 2 y=cos(x)-x; r=fzero('myfun',1) r = 0.7391 r=fzero(@myfun,1) r = 0.7391 r=fzero('cos(x)-x',1) r = 0.7391 r=fzero('cos(x)-x',3) r = 0.7391 r=fzero('cos(x)-x',77) r = 0.7391 r=fzero('cos(x)-x',-112) r = 0.7391 edit myfun fschange('V:\MATLAB\myfun.m'); clear myfun r=fzero('cos(x)-x',1) r = 0.7391 r=fzero(@myfun,1) r = 1.5708 for,at long ??? for,at long | Error: Incomplete or misformed expression or statement. format long r=fzero(@myfun,1) r = 1.57079632679490 3*pi/2 ans = 4.71238898038469 r=fzero(@myfun,4.5) r = 4.49340945790906 r=fzero(@myfun,4.6) r = 4.49340945790906 r=fzero(@myfun,4.7) r = 4.71238898038469 r=fzero(@myfun,[4.5 4.7]) ??? Error using ==> fzero The function values at the interval endpoints must differ in sign. r=fzero(@myfun,[4.4 4.7]) r = 4.49340945790906 r=fzero(@myfun,[7.6 7.8]) r = 7.72525183693771 doc ode edit myfun fschange('V:\MATLAB\myfun.m'); clear myfun tspan=[1 3] tspan = 1 3 y0=4 y0 = 4 [t,y] = ode45(@myfun,tspan,y0); t t = 1.00000000000000 1.01339672763472 1.02679345526944 1.04019018290415 1.05358691053887 1.08750527999185 1.12142364944482 1.15534201889780 1.18926038835077 1.23159800510455 1.27393562185833 1.31627323861212 1.35861085536590 1.40861085536590 1.45861085536590 1.50861085536590 1.55861085536590 1.60861085536590 1.65861085536590 1.70861085536590 1.75861085536590 1.80861085536590 1.85861085536590 1.90861085536590 1.95861085536590 2.00861085536590 2.05861085536590 2.10861085536590 2.15861085536590 2.20861085536590 2.25861085536590 2.30861085536590 2.35861085536590 2.40861085536590 2.45861085536590 2.50861085536590 2.55861085536590 2.60861085536590 2.65861085536590 2.70861085536590 2.75861085536590 2.80861085536590 2.85861085536590 2.90861085536590 2.95861085536590 2.96895814152442 2.97930542768295 2.98965271384147 3.00000000000000 y y = 4.00000000000000 3.80935023837064 3.63740383177756 3.48162281682825 3.33988318043326 3.03214031733865 2.78354568593225 2.58002305843859 2.40992936478999 2.23321498283437 2.08889438888684 1.97004474228243 1.87101263309339 1.77425314469601 1.69562687120932 1.63173037447149 1.57973339892645 1.53753066526614 1.50368280881018 1.47692123155398 1.45615453370052 1.44049841533066 1.42927754061497 1.42189573391882 1.41782199210389 1.41660401253228 1.41788012095639 1.42132572654207 1.42664502558399 1.43357916993238 1.44191705548810 1.45146748455353 1.46205445887794 1.47352242312776 1.48574392026681 1.49860344947391 1.51199477712558 1.52582421200596 1.54001521879594 1.55449887950357 1.56921245132108 1.58410122711445 1.59912069628814 1.61423128109508 1.62939772227464 1.63254043934254 1.63568403148364 1.63882826851051 1.64197292773013 plot(t,y);shg size(t) ans = 49 1 tspan=[1 0] tspan = 1 0 [t,y] = ode45(@myfun,tspan,y0); Warning: Failure at t=7.449597e-001. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (1.776357e-015) at time t. > In ode45 at 355 plot(t,y);shg tspan=[3 2] tspan = 3 2 [t,y] = ode45(@myfun,tspan,y0); Warning: Failure at t=2.732794e+000. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (7.105427e-015) at time t. > In ode45 at 355 tspan=[3 2.75] tspan = 3.00000000000000 2.75000000000000 [t,y] = ode45(@myfun,tspan,y0); plot(t,y);shg edit myfun fschange('V:\MATLAB\myfun.m'); clear myfun y0=[1 3] y0 = 1 3 tspan=[1 4] tspan = 1 4 [t,y] = ode45(@myfun,tspan,y0); ??? Error using ==> funfun\private\odearguments MYFUN must return a column vector. Error in ==> ode45 at 173 [neq, tspan, ntspan, next, t0, tfinal, tdir, y0, f0, odeArgs, ... y0=[1; 3] y0 = 1 3 edit myfun fschange('V:\MATLAB\myfun.m'); clear myfun [t,y] = ode45(@myfun,tspan,y0); size(t) ans = 49 1 size(y) ans = 49 2 plot(t,y(:,1));shg web('http://www.mathworks.com/search/ice.cgi?query=ode', '-browser'); ODEOPTIONS=odeset('RelTol',1e-6) ODEOPTIONS = AbsTol: [] BDF: [] Events: [] InitialStep: [] Jacobian: [] JConstant: [] JPattern: [] Mass: [] MassConstant: [] MassSingular: [] MaxOrder: [] MaxStep: [] NormControl: [] OutputFcn: [] OutputSel: [] Refine: [] RelTol: 1.000000000000000e-006 Stats: [] Vectorized: [] MStateDependence: [] MvPattern: [] InitialSlope: [] [t,y] = ode45(@myfun,tspan,y0,ODEOPTIONS); plot(t,y(:,1));shg size(t) ans = 145 1 ver ------------------------------------------------------------------------------------- MATLAB Version 7.0.0.19920 (R14) MATLAB License Number: 133330 Operating System: Microsoft Windows XP Version 5.1 (Build 2600: Service Pack 2) Java VM Version: Java 1.4.2 with Sun Microsystems Inc. Java HotSpot(TM) Client VM ------------------------------------------------------------------------------------- MATLAB Version 7.0 (R14) Simulink Version 6.0 (R14) Communications Blockset Version 3.0 (R14) Communications Toolbox Version 3.0 (R14) Control System Toolbox Version 6.0 (R14) Curve Fitting Toolbox Version 1.1.1 (R14) Excel Link Version 2.2 (R14) Financial Toolbox Version 2.4 (R14) Fixed-Point Toolbox Version 1.0 (R14) Fuzzy Logic Toolbox Version 2.1.3 (R14) Image Processing Toolbox Version 4.2 (R14) LMI Control Toolbox Version 1.0.9 (R14) MATLAB Compiler Version 4.0 (R14) Mapping Toolbox Version 2.0.2 (R14) Model Predictive Control Toolbox Version 2.0 (R14) Mu-Analysis and Synthesis Toolbox Version 3.0.8 (R14) Neural Network Toolbox Version 4.0.3 (R14) Optimization Toolbox Version 3.0 (R14) Partial Differential Equation Toolbox Version 1.0.5 (R14) Real-Time Workshop Version 6.0 (R14) Robust Control Toolbox Version 2.0.10 (R14) Signal Processing Blockset Version 6.0 (R14) Signal Processing Toolbox Version 6.2 (R14) SimMechanics Version 2.2 (R14) Simulink Control Design Version 1.0 (R14) Simulink Fixed Point Version 5.0 (R14) Spline Toolbox Version 3.2.1 (R14) Statistics Toolbox Version 5.0 (R14) Symbolic Math Toolbox Version 3.1 (R14) System Identification Toolbox Version 6.0.1 (R14) Wavelet Toolbox Version 3.0 (R14) syms x f=1/(x^6+1) f = 1/(x^6+1) ezplot(f) shg axes;shg int(f) ans = 1/12*3^(1/2)*log(x^2+3^(1/2)*x+1)+1/6*atan(2*x+3^(1/2))-1/12*3^(1/2)*log(x^2-3^(1/2)*x+1)+1/6*atan(2*x-3^(1/2))+1/3*atan(x) diff(f) ans = -6/(x^6+1)^2*x^5 diff(f,4) ans = 31104/(x^6+1)^5*x^20-38880/(x^6+1)^4*x^14+11160/(x^6+1)^3*x^8-360/(x^6+1)^2*x^2 f4=diff(f,4) f4 = 31104/(x^6+1)^5*x^20-38880/(x^6+1)^4*x^14+11160/(x^6+1)^3*x^8-360/(x^6+1)^2*x^2 ezplot(f4) shg int(f,0,1) ans = 1/12*3^(1/2)*log(2+3^(1/2))+1/6*pi-1/12*3^(1/2)*log(2-3^(1/2)) vpa(ans) ans = .90377177374877204684265435798682 digits(100) ans ans = .90377177374877204684265435798682 int(f,0,1) ans = 1/12*3^(1/2)*log(2+3^(1/2))+1/6*pi-1/12*3^(1/2)*log(2-3^(1/2)) vpa(ans) ans = .9037717737487720468426543579867867261336754320361058503394427671813302957084902096189016532895965184 vpa(pi) ans = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117068 digits(1000) vpa(pi) ans = 3.141592653589793238462643383279502884197169399375105820974944592307816406286208998628034825342117067982148086513282306647093844609550582231725359408128481117450284102701938521105559644622948954930381964428810975665933446128475648233786783165271201909145648566923460348610454326648213393607260249141273724587006606315588174881520920962829254091715364367892590360011330530548820466521384146951941511609433057270365759591953092186117381932611793105118548074462379962749567351885752724891227938183011949129833673362440656643086021394946395224737190702179860943702770539217176293176752384674818467669405132000568127145263560827785771342757789609173637178721468440901224953430146549585371050792279689258923542019956112129021960864034418159813629774771309960518707211349999998372978049951059731732816096318595024459455346908302642522308253344685035261931188171010003137838752886587533208381420617177669147303598253490428755468731159562863882353787593751957781857780532171226806613001927876611195909216420199 int(f,0,inf) ans = 1/3*pi taylor(f) ans = 1 f f = 1/(x^6+1) taylor(f,20) ans = 1-x^6+x^12-x^18 taylor(f,20,2) ans = 449/4225-192/4225*x+21264/274625*(x-2)^2-1763488/17850625*(x-2)^3+120185796/1160290625*(x-2)^4-6990251532/75418890625*(x-2)^5+348937753919/4902227890625*(x-2)^6-14467981909248/318644812890625*(x-2)^7+432552083391216/20711912837890625*(x-2)^8-1748074560528672/1346274334462890625*(x-2)^9-1023534402146211576/87507831740087890625*(x-2)^10+103145171289859104792/5688009063105712890625*(x-2)^11-7088133735088958651839/369720589101871337890625*(x-2)^12+396701322806174398533888/24031838291621636962890625*(x-2)^13-18580050837736883770380096/1562069488955406402587890625*(x-2)^14+692109990032760745548629632/101534516782101416168212890625*(x-2)^15-15318567522537518569471622244/6599743590836592050933837890625*(x-2)^16-433629528615043854732512994852/428983333404378483310699462890625*(x-2)^17+83760853778903297918757819575359/27883916671284601415195465087890625*(x-2)^18-6846656580636781014879216340393728/1812454583633499091987705230712890625*(x-2)^19 syms t f=exp(-t)+1 f = exp(-t)+1 laplace(f) ans = 1/(1+s)+1/s F=1/(s^3+s^2+1) ??? Undefined function or variable 's'. syms s F=1/(s^3+s^2+1) F = 1/(s^3+s^2+1) ilaplace(F) ans = -1/31*sum((3+11*_alpha+2*_alpha^2)*exp(_alpha*t),_alpha = RootOf(_Z^3+_Z^2+1)) F=1/(s^3+s^2+s) F = 1/(s^3+s^2+s) ilaplace(F) ans = -exp(-1/2*t)*cos(1/2*3^(1/2)*t)-1/3*3^(1/2)*exp(-1/2*t)*sin(1/2*3^(1/2)*t)+1 diary off