Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

I want to express my two variable function f using Taylor expansion. But no success yet.

Why Taylor series can not estimate my function in desired interval [-1<x,y<1]?

restart

with(Student[MultivariateCalculus]):

 

f := -5023626067733175609651265492842895195168362165*xx^5*yy^9*(1/5575186299632655785383929568162090376495104)+2207379816207475241162406248223006569040862935*xx^5*yy^8*(1/2787593149816327892691964784081045188247552)+5795161625895678368156852916105373987594511979*xx^6*(1/22300745198530623141535718272648361505980416)-539977758872163289054492124375185771143918033*xx^6*yy*(1/696898287454081973172991196020261297061888)+782685832362921584689673760969891945953777553*xx^6*yy^2*(1/5575186299632655785383929568162090376495104)+749877940244270735637721966049124917356845885*xx^6*yy^3*(1/174224571863520493293247799005065324265472)+14159347676475748959036290080103848146860867025*xx^6*yy^4*(1/11150372599265311570767859136324180752990208)-2937701213452088192123555543440803264914467299*xx^6*yy^5*(1/348449143727040986586495598010130648530944)-23673134207774883972271882396704370580007933039*xx^6*yy^6*(1/5575186299632655785383929568162090376495104)-62755544772437504320590342390381422715234113715/89202980794122492566142873090593446023921664+35696532930567486560276536615522532283474689213*yy*(1/2787593149816327892691964784081045188247552)+43423414494451507811145033075147441881593811799*yy^2*(1/22300745198530623141535718272648361505980416)+1173296429365947392287371443632107462978009165*xx^6*yy^7*(1/174224571863520493293247799005065324265472)-56566850002827011453690682806041619180254985625*yy^3*(1/696898287454081973172991196020261297061888)+57447439083834576362467553225131370438848237035*xx^6*yy^8*(1/22300745198530623141535718272648361505980416)-1277356081222180962342283013232991241852904465*xx^6*yy^9*(1/696898287454081973172991196020261297061888)-29946355461657315300256240552185966952551471*xx^7*(1/1393796574908163946345982392040522594123776)+998213736763384913910074759047227544847506773*xx^7*yy*(1/11150372599265311570767859136324180752990208)-2038600361316622246653155899145012259420048867785*yy^4*(1/44601490397061246283071436545296723011960832)+10578825782023300845453772557509072093336001*xx^7*yy^2*(1/43556142965880123323311949751266331066368)-4303517165264733669855129139552505045324631645*xx^7*yy^3*(1/11150372599265311570767859136324180752990208)-652299342907430898149182084981866414949696905*xx^7*yy^4*(1/696898287454081973172991196020261297061888)+11170081785792631086653879206603595320491089331*xx^7*yy^5*(1/11150372599265311570767859136324180752990208)+116540829629507365267125159526451609264014215*xx^7*yy^6*(1/87112285931760246646623899502532662132736)+211134394987302797546644924545169826774270265159*yy^5*(1/1393796574908163946345982392040522594123776)-14785537121406447202257499440081382142298519099*xx^7*yy^7*(1/11150372599265311570767859136324180752990208)+1970986683407627074325019523003479974617451789943*yy^6*(1/22300745198530623141535718272648361505980416)-868641325364973493898126340263842300348545855*xx^7*yy^8*(1/1393796574908163946345982392040522594123776)+216255546256559295251079313253452049445763455*xx^7*yy^9*(1/348449143727040986586495598010130648530944)-4089215965643055747590786827106386135115380275*xx^8*(1/89202980794122492566142873090593446023921664)+1869246621670048362557342074310025153518449965*xx^8*yy*(1/2787593149816327892691964784081045188247552)+18712604797880071317805036942199122521197359575*xx^8*yy^2*(1/22300745198530623141535718272648361505980416)-3479476522267890993628796487849129439635143625*xx^8*yy^3*(1/696898287454081973172991196020261297061888)-77131555128675321096947207038878222843991869993*yy^7*(1/696898287454081973172991196020261297061888)-206512033439850904054937113093163624192322042825*xx^8*yy^4*(1/44601490397061246283071436545296723011960832)+15350689937843699961175740256400109996121380375*xx^8*yy^5*(1/1393796574908163946345982392040522594123776)+157001869330425518481531763580902779395436599415*xx^8*yy^6*(1/22300745198530623141535718272648361505980416)-6686861200533386632065997818427854246215113305*xx^8*yy^7*(1/696898287454081973172991196020261297061888)-3917684154726736823398471536296978037714283086195*yy^8*(1/89202980794122492566142873090593446023921664)-285743684916570536194588196441080828723328178675*xx^8*yy^8*(1/89202980794122492566142873090593446023921664)+8094790880015327525694605814920739418439287725*xx^8*yy^9*(1/2787593149816327892691964784081045188247552)+30423874459994412977383604476886160940746185*xx^9*(1/5575186299632655785383929568162090376495104)-1197236208181378637639504269592639035279087665*xx^9*yy*(1/44601490397061246283071436545296723011960832)-72716798311978341010558827315982986191821905*xx^9*yy^2*(1/696898287454081973172991196020261297061888)+5138909461003175489938484170634052266819688725*xx^9*yy^3*(1/44601490397061246283071436545296723011960832)+1206817075246069632318716986669541278160772775*xx^9*yy^4*(1/2787593149816327892691964784081045188247552)-12993287722661922638788467553649639108437064835*xx^9*yy^5*(1/44601490397061246283071436545296723011960832)-431284328058774504067793959976795724976545555*xx^9*yy^6*(1/696898287454081973172991196020261297061888)+17639360745426635511855086638766468926126459875*xx^9*yy^7*(1/44601490397061246283071436545296723011960832)-2146702909675882809503682033933399905335826325*xx^9*yy^9*(1/11150372599265311570767859136324180752990208)+1587967252519403636411870604735180043125989625*xx^9*yy^8*(1/5575186299632655785383929568162090376495104)+76828297887427851822683521168415270943435162685*yy^9*(1/2787593149816327892691964784081045188247552)+220816865194317615868568855814620996552449073*xx*(1/5575186299632655785383929568162090376495104)-9205355621994819342146712860571987786619361601*xx*yy*(1/44601490397061246283071436545296723011960832)-104255809907916433055923335622932126645726549*xx*yy^2*(1/696898287454081973172991196020261297061888)+27484692689867334306687311759874973819976026005*xx*yy^3*(1/44601490397061246283071436545296723011960832)+1583056855557692418384969876461998197073089695*xx*yy^4*(1/2787593149816327892691964784081045188247552)-36304948749180317956941914133403396762716230691*xx*yy^5*(1/44601490397061246283071436545296723011960832)-590212436135125327923049635849260481403670583*xx*yy^6*(1/696898287454081973172991196020261297061888)+27046038795224386955728969793334632924015008227*xx*yy^7*(1/44601490397061246283071436545296723011960832)+2168816628024980374461014350770096009019357665*xx*yy^8*(1/5575186299632655785383929568162090376495104)-2255097230860381206152749351617455809672044745*xx*yy^9*(1/11150372599265311570767859136324180752990208)+35122173917479363738100862234581108137514304171*xx^2*(1/22300745198530623141535718272648361505980416)-17449701902039745490242163912540688306429882361*xx^2*yy*(1/696898287454081973172991196020261297061888)-11540959773500599403794316292492996114189538863*xx^2*yy^2*(1/5575186299632655785383929568162090376495104)+27287439738914744607616926917914225474665410565*xx^2*yy^3*(1/174224571863520493293247799005065324265472)+929769947314964740179937673332890647768037984465*xx^2*yy^4*(1/11150372599265311570767859136324180752990208)-100809382380090436397261413740272360141145204891*xx^2*yy^5*(1/348449143727040986586495598010130648530944)-930314746723434588666177195703059675161177190255*xx^2*yy^6*(1/5575186299632655785383929568162090376495104)+36390552938954376406834468187448925576623439893*xx^2*yy^7*(1/174224571863520493293247799005065324265472)+1872760743346397986120124413411813119412045269675*xx^2*yy^8*(1/22300745198530623141535718272648361505980416)-35643509355104072817665294345590475660747146425*xx^2*yy^9*(1/696898287454081973172991196020261297061888)-125283292999146417157156696376640452081866835*xx^3*(1/1393796574908163946345982392040522594123776)+5011420945327438626354964312196465908094234685*xx^3*yy*(1/11150372599265311570767859136324180752990208)+29341459645317546529685572705520876577051855*xx^3*yy^2*(1/87112285931760246646623899502532662132736)-15637727799880882327290754576104647826715168925*xx^3*yy^3*(1/11150372599265311570767859136324180752990208)-851688199122087410134053760306093104684621525*xx^3*yy^4*(1/696898287454081973172991196020261297061888)+23458516464006675395891679247259419002768896835*xx^3*yy^5*(1/11150372599265311570767859136324180752990208)+39584968580329795728950940517214770307434335*xx^3*yy^6*(1/21778071482940061661655974875633165533184)-20361225581568567923686744589522827658576624955*xx^3*yy^7*(1/11150372599265311570767859136324180752990208)-1174244552874873223035231031480900497934023075*xx^3*yy^8*(1/1393796574908163946345982392040522594123776)+941109349474535911451616661821106567867537125*xx^3*yy^9*(1/1393796574908163946345982392040522594123776)-48412290717709997717153300332089796247538326265*xx^4*(1/44601490397061246283071436545296723011960832)+17196469545705046799299985950707233685621881055*xx^4*yy*(1/1393796574908163946345982392040522594123776)-9551461763890264957289963973620923748598225435*xx^4*yy^2*(1/11150372599265311570767859136324180752990208)-26051472095770585704126329008135447818638784275*xx^4*yy^3*(1/348449143727040986586495598010130648530944)-765302392604646459013613426858243443467023490875*xx^4*yy^4*(1/22300745198530623141535718272648361505980416)+94251624724512021502035994822030873708141367565*xx^4*yy^5*(1/696898287454081973172991196020261297061888)+843981485493394825713526892530506348990296828805*xx^4*yy^6*(1/11150372599265311570767859136324180752990208)-33218490572036542393092937176469859040906121155*xx^4*yy^7*(1/348449143727040986586495598010130648530944)-1758702445038817232726176779731884586549332868025*xx^4*yy^8*(1/44601490397061246283071436545296723011960832)+31380186488931551370058361496245928395816772575*xx^4*yy^9*(1/1393796574908163946345982392040522594123776)+184838927094446995029201369223921105703104647*xx^5*(1/2787593149816327892691964784081045188247552)-6817973449093402642853212701104432585928821163*xx^5*yy*(1/22300745198530623141535718272648361505980416)-113510140727511300460098712979462156361337425*xx^5*yy^2*(1/348449143727040986586495598010130648530944)+23570688854853763073042723518782612790921757535*xx^5*yy^3*(1/22300745198530623141535718272648361505980416)+1613038118657167505912389296857854524947676825*xx^5*yy^4*(1/1393796574908163946345982392040522594123776)-44608078263668464626393951292252447406629869273*xx^5*yy^5*(1/22300745198530623141535718272648361505980416)-588774433706353379897742534304221654039246663*xx^5*yy^6*(1/348449143727040986586495598010130648530944)+47950825635610780986659544491454706340397108297*xx^5*yy^7*(1/22300745198530623141535718272648361505980416):

g := .5*(1+tanh(f)):

plot3d(g, xx = -1 .. 1, yy = -1 .. 1, color = red, style = surface)

 

 

h := Student:-MultivariateCalculus:-TaylorApproximation(g, [xx, yy] = [0, 0], 35):

plot3d(h, xx = -1 .. 1, yy = -1 .. 1, color = red, style = surface)

 

 

Download taylorProblem.mw

How will I use maple 2016 to solve ODEs and showing the steps involved because this will increase my understanding in it. 

Dear Colleagues,

I wish to use plot3d to the attached code but always encoutered error. However, pointplot3d runs perfectly. Please I need your assistance in this regards.

Thank you all and best regards.K2_Problem_2_two_body_kepler_e=0.mw

Good day everyone.

I am trying to write a code with variable stepsize involving tolerance. two vectors are declare for the errors. However, I don't know how to declare the two errors in comparison with the tolerance. Please kindly help. Also, any other modification to the entire code is also welcomed. Thank you all and best regards.

The code is as attached.

Variable_step_size_Falkner.mw

Hi everyone.

Could you please help me to obtain the results by 'solve'?

Is there any way such as numerical methods in this regard?

Fung.mws

Good day everyone, 

How can I extract the values of x and y for plotting? 

The worksheet is attached below. Thanks

dont_get_it.mw

TODAY I GOT AN INSPIRATION TO CREATE 3D GRAPH EQUATION OF WALKING ROBOT (ED-209) IN CARTESIAN SPACE USING ONLY WITH SINGLE IMPLICIT EQUATION.

ENJOY...

 

How to Create Graph Equation of Wankel Engine on Cartesian Plane using Single Implicit Function run by Maple Software

Enjoy...

 

restart;

Frac_C := proc (expr, a, t, alpha) local ig, m, tau;

m := ceil(alpha);

ig := (t-tau)^(m-alpha-1)*(diff(eval(expr, t = tau), tau$m));

`assuming`([(int(ig, tau = a .. t))/GAMMA(m-alpha)], [a < t]);

end proc;
r := .5;

k := .7;

eq1 := Frac_C(x, 0, t, r)-y(t) = 0;

eq2 := Frac_C(y, 0, t, k)-x(t)-2*t = 0;

eq3 := x(0)-y(1) = 0;

eq4 := Frac_C(x, 0, t, r)-(eval(diff(y(x), x), x = 1)) = 0;

eq5 := Frac_C(x, 0, t, r)-(eval(diff(y(x), x, x), x = 1)) = 0;

eq6 := eval(diff(y(x), x), x = 0)-x(1)-2 = 0;

eq7 := y(0) = 0;

N := 5;

x[c] := [seq(a[i], i = 0 .. N)];

y[c] := [seq(b[i], i = 0 .. N)];

for n to N do

subs([seq(x(i) = x[c][i], i = 0 .. n), seq(y(i) = y[c][i], i = 0 .. n)], {eq1, eq2, eq3, eq4, eq5, eq6, eq7});
soln := solve({eq3, eq4, eq5, eq6, eq7, seq(coeff(lhs(eq), t, j) = 0, eq in {eq1, eq2})}, {a[n+1], b[n+1]});

x[c][n+1] := eval(a[n+1], soln);

y[c][n+1] := eval(b[n+1], soln);

end do;

x[s] := add(x[c][i]*t^(i-1), i = 1 .. N+1);

y[s] := add(y[c][i]*t^(i-1), i = 1 .. N+1);

x[s];

y[s];

CREATING GRAPH EQUATION OF "DNA" IN CARTESIAN SPACE USING PARAMETRIC SURFACE EQUATION RUN ON MAPLE SOFTWARE

ENJOY...

 

How to Create Graph Equation of Water Drop Wave in Cartesian Space using single Implicit Function only run by Maple Software

The Equation is:   z = - cos( (x2+y2)0.5 - a)  with paramater a is moving form 0 to 2pi 

Enjoy...

Plese Click link below to see full equation in Maple software

Water_Drop_Wave.mw

Creating Graph Equation of An Apple in Cartesian Space using single Implicit Function only run by Maple software

Enjoy...

Please click the link below to see full equation on Maple file:

2._Apel_3D_A.mw

 

Creating Graph Equation of A Candle on Cartesian Plane using single Implicit Function only run by Maple software

Enjoy...

3D_Candle.mw

Sea_Shells.mw

 

 

 

Today I'm very greatfull to have Inspiration to create Graph Equation of 3D Candle in Cartesian Space using single 3D Implicit Function only, run by Maple software.

Enjoy... 

Candle_1.mw

 

Today I got an inspiration to create graph equation of "Petrol Truck" using only with Single Implicit Equation in Cartesian space run by Maple Software

Maple software is amazing...

Enjoy...

 

CREATING 3D GRAPH EQUATION OF BACTERIOPHAGE USING ONLY WITH SINGLE IMPLICIT EQAUTION IN CARTESIAN SPACE RUN BY MAPLE SOFTWARE

MAPLE SOFTWARE IS AMAZING...

ENJOY...

 

GRAPH EQUATION OF A FEATHER

AND THE EQUATION IS:

ENJOY...

I like this Equation and post it because it is so beautiful...

Click this link below to see full equation and download the Maple file: 

Bulu_Angsa_3.mw

 

GRAPH EQUATION OF "383" CREATED BY DHIMAS MAHARDIKA

ENJOY...

with(plots):

DHIMAS MAHARDIKA EQUATION

plots:-implicitplot(15-8.*cos(y)^(79/2)-32.*cos(y)^(37/2)+96.*cos(y)^(33/2)-96.*cos(y)^(29/2)+4.*cos(x)^(61/2)+4.*cos(x)^(31/2)-12.*cos(x)^(27/2)+12.*cos(x)^(23/2)+24.*cos(y)^29-48.*cos(y)^27+16.*cos(y)^8-64.*cos(y)^6+96.*cos(y)^4-4.*cos(x)^(19/2)-6.*cos(x)^19-4.*cos(x)^(57/2)+32.*cos(y)^(25/2)+24.*cos(y)^25+8.*cos(y)^(75/2)-cos(x)^38+cos(y)^50-64.*cos(y)^2+4.*cos(x)^2-6.*cos(x)^4+4.*cos(x)^6-cos(x)^8+12.*cos(x)^21-6.*cos(x)^23, x = -15 .. 15, y = -15 .. 15, numpoints = 50000, thickness = 4, colour = blue)

 

NULL

Download 383.mw

 

Drawing Eifel Tower using Implicit Equation in Cartesian Space 

I'm trying to solve a system of differential equations and encountered this error: Error, (in fsolve) {f1[0], f1[1], f1[2], f1[3], f2[0], f2[1], f2[2], f2[3]} are in the equation, and are not solved for. How can this error be rectified?

Hello everyone

I create a curved space ( with Physics) and create a metric tensor of 

a sphere . I see some Christoffel correcly . Is it possible to visualize all non zero Christoffel in one shot ?

Thank's a lot

Best Regards

restart; with(Physics)

Physics:-Setup(mathematicalnotation = true)

[mathematicalnotation = true]

(1)

Physics:-Setup(spacetimeindices, dimension = 2, signature = "++")

[dimension = 2, signature = `+ +`, spacetimeindices = greek]

(2)

Physics:-Coordinates(X)

{X}

(3)

ds2 := Physics:-`^`(dx1, 2)+Physics:-`*`(Physics:-`^`(sin(x1), 2), Physics:-`^`(dx2, 2))

dx1^2+sin(x1)^2*dx2^2

(4)

NULL

Physics:-Setup(metric = ds2)

[metric = {(1, 1) = 1, (2, 2) = sin(x1)^2}]

(5)

NULL

NULL

g_[]

g[mu, nu] = (Matrix(2, 2, {(1, 1) = 1, (1, 2) = 0, (2, 2) = sin(x1)^2}, storage = triangular[upper], shape = [symmetric]))

(6)

Physics:-Christoffel[`~k`, i, j]

Physics:-Christoffel[`~k`, i, j]

(7)

Physics:-Christoffel[`~1`, 2, 2]

-sin(x1)*cos(x1)

(8)

Physics:-Christoffel[`~2`, 1, 2]

cos(x1)/sin(x1)

(9)

Physics:-Christoffel[`~1`, 1, 1]

0

(10)

Download Approfondimento_1_-_Calcolo_Sfera_2D.mw

how I can solve these equations?

Fung.mws

 

restart:

with(LinearAlgebra):

with(VectorCalculus):

Q:=a_11*(E_r)^2+a_22*(E_theta)^2+a_33*(E_z)^2+2*a_12*E_r*E_theta+2*a_13*E_r*E_z+2*a_23*E_theta*E_z:

psi:=0.5*c*(Q+0.5*Q^2):

F:=matrix([[B*R/r,0,0],[0,r/R,0],[0,0,1/B]]):

#b:=matrix([[B^2*R^2/r^2,0,0],[0,r^2/R^2,0],[0,0,1/B^2]]):

b:=matrix([[B*(r^2-A)/r^2,0,0],[0,B*r^2/(r^2-A),0],[0,0,1/B^2]]):

sigma_r:=-p+diff(psi,E_r)*b[1,1]:

sigma_theta:=-p+diff(psi,E_theta)*b[2,2]:

sigma_z:=-p+diff(psi,E_z)*b[3,3]:

#H:=p_o+subs(r=r_o,diff(psi,E_r)*b[1,1]):

H:=p_o+subs(r=sqrt(B*(R_o)^2+A),diff(psi,E_r)*b[1,1]):

E_r:=0.5*(((B*r^2-B*A)/r^2)-1):

E_theta:=0.5*((B*r^2/(r^2-A))-1):

E_z:=0.5*((1/B^2)-1):

H:

p:=subs(r=sqrt(B*(R_o)^2+A),H):

x0:=simplify((sigma_r-sigma_theta)/r):

y0:=simplify(sigma_z*r):

x1:=int(x0,r):

y1:=2*Pi*int(y0,r):

Digits:=50:

p_i:=1.858e3:

p_o:=0:

R_i:=1:

R_o:=10:

a_11:=165.857:

a_22:=47.028:

a_33:=145.448:

a_12:=46.747:

a_13:=0.799:

a_23:=14.587:

c:=0.0004e6:

F_a:=0:

x2:=subs(r=sqrt(B*R^2+A),x1):

y2:=subs(r=sqrt(B*R^2+A),y1):

eq1:=subs(R=R_o,x2)-subs(R=R_i,x2):

eq2:=subs(R=R_o,y2)-subs(R=R_i,y2):

Eq1:=simplify(eq1):

Eq2:=simplify(eq2):

solve({Eq1=p_o-p_i,Eq2=F_a},{A,B});

 

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