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