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Why Taylor series can not estimate my function in ...

Asked by: mehdibgh 235
taylor student-multivariatecalculus
November 30 2023
0  2

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 showin...

Asked by: Quadri Robiu OLAIDE 0
October 23 2023
0  1

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

How to use plot3d...

Asked by: abdulganiy 140
plot3d plotting incomplete-question
October 02 2023
0  3

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

How do I test against the specified tolerance?...

Asked by: abdulganiy 140
numeric differential-equations duplicate-question
August 29 2023
0  1

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

why 'solve' can not obtain results...

Asked by: NIMA112 20
solve rootfinding fsolve
August 26 2023
1  22

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

How to plot the values of x and y...

Asked by: kencom1 100
plotting
June 27 2023
0  2

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

3D plot of robot and Wankel engine using a single...

by: Mahardika Mathematics 35 Maple 2016
April 17 2023
1  2

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...

 

Where the error in the following code?...

Asked by: khalil20232023 15
homework differential-equations duplicate-question
April 15 2023
1  0

alpha1 := .8; alpha2 := .6; eq1 := fracdiff(x(t), t, alpha1)-t^2*x(t)+y(t)-2*t = 0; eq2 := fracdiff(y(t), t, alpha2)-2*z(t)+2*(t+1) = 0; eq3 := z(t)-y(t)-2*t*x(t)+t^4-t-1 = 0; N := 4; x0 := 0; y0 := 0; z0 := 1; XT1 := D[xt](eq1); XT2 := D[xt](eq2); XT3 := D[xt](eq3); XT1[0] := x0; XT2[0] := y0; XT3[0] := z0; for n to N do XT1[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT1))), t); XT2[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT2))), t); XT3[n] := unapply(simplify(rhs(subs({seq(D[xt](x(t)), j = 0 .. n-1), seq(D[xt](y(t)), j = 0 .. n-1), seq(D[xt](z(t)), j = 0 .. n-1)}, XT3))), t) end do; xseries := add(XT1[n](t)*t^(n*alpha1)/factorial(n*alpha1), n = 0 .. N); yseries := add(XT2[n](t)*t^(n*alpha2)/factorial(n*alpha2), n = 0 .. N); zseries := add(XT3[n](t)*t^(n*alpha2)/factorial(n*alpha2), n = 0 .. N); x_sol := unapply(xseries, t); y_sol := unapply(yseries, t); z_sol := unapply(zseries, t); print(x_sol); print(y_sol); print(z_sol)

proc (t) options operator, arrow; 1.000000000+1.119174954*XT3[1](t)*t^.6+.9076036841*XT3[2](t)*t^1.2+.5964840410*XT3[3](t)*t^1.8+.3354346720*XT3[4](t)*t^2.4 end proc

 (1)

``

Download Ex2_FDAEs.mw

I can not explore the error when I run this code b...

Asked by: khalil20232023 15
homework differential-equations fractional-derivative
April 10 2023
1  1

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];

plot of dna helix using as parametric surface

by: Mahardika Mathematics 35 Maple 2016
parametric plotting helix
April 09 2023
1  1

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

ENJOY...

 

Creating Graph Equation of Water Drop Wave in...

by: Mahardika Mathematics 35 Maple 2016
implicit plotting
April 03 2023
1  0

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

plots using only single implicit functions

by: Mahardika Mathematics 35 Maple 2016
animation implicit plotting
March 29 2023
1  5

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 

How can I handle this error?...

Asked by: OLOWE RUTH 5
syntax differential-equations
March 22 2023
1  4

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?

Non zero Christoffel display ...

Asked by: albivaldmaple 20
tensor physics christoffel
March 08 2023
2  1

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...

Asked by: NIMA112 20
solve fsolve
February 28 2023
1  0

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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