Equations

Main.Equations History

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March 24, 2021, at 04:29 AM by 10.35.117.248 -
Changed lines 28-29 from:
|| log10 ||Base-10 Log || log10(x*y)=0 ||
|| log ||Natural Log || log(x*y)=0 ||
to:
|| log10() ||Base-10 Log || log10(x*y)=0 ||
|| log() ||Natural Log || log(x*y)=0 ||
April 19, 2018, at 03:31 PM by 10.37.1.116 -
Changed line 33 from:
|| tanh() ||Hyperbolic Tanget || tanh(x*y)=0 ||
to:
|| tanh() ||Hyperbolic Tangent || tanh(x*y)=0 ||
Added lines 43-44:

All trigonometric functions are in radians (not degrees).
Changed line 9 from:
The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.  Equations may be in the form of equalities (=) or inequalities (>,<).  For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.
to:
The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.  Equations may be in the form of equality (=) or inequality (>,>=,<,<=) constraints.  For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.
Changed line 9 from:
The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.  For equations may be in the form of equalities (=) or inequalities (>,<).  For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.
to:
The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.  Equations may be in the form of equalities (=) or inequalities (>,<).  For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.
June 16, 2015, at 06:48 PM by 45.56.3.184 -
Deleted lines 0-1:
!! Equations
Changed line 48 from:
(:table border=1 width=50% align=left bgcolor=#EEEEEE cellspacing=0:)
to:
(:table border=1 width=100% align=left bgcolor=#EEEEEE cellspacing=0:)
December 04, 2008, at 03:02 PM by 158.35.225.227 -
Deleted lines 21-23:
|| - ||Unary minus || -(x-y) = 0 ||
|| - ||Unary minus || -(x-y) = 0 ||
|| - ||Unary minus || -(x-y) = 0 ||
October 30, 2008, at 03:46 PM by 158.35.225.230 -
Added line 69:
Added line 71:
October 30, 2008, at 03:17 PM by 158.35.225.230 -
Changed lines 70-72 from:
     (y+2/x)^(x*z) * (log(tanh(sqrt(y-x+x^2))+3))^2 = 2+sinh(y)+acos(x+y)+asin(x/y)
to:
     (y+2/x)^(x*z) * &
   
(log(tanh(sqrt(y-x+x^2))+3))^2 &
   
= 2+sinh(y)+acos(x+y)+asin(x/y)
October 30, 2008, at 03:16 PM by 158.35.225.230 -
Changed line 11 from:
There are currently 26 operands for parameters or variables.  They are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.  For equations may be in the form of equalities (=) or inequalities (>,<).  For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.
to:
The available operands are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.  For equations may be in the form of equalities (=) or inequalities (>,<).  For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.
October 30, 2008, at 03:14 PM by 158.35.225.230 -
Changed line 15 from:
|| !,#,% ||Comment ||!! equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2]  ! comment ||
to:
|| !,#,% ||Comment ||% equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2]  ! eqn1 ||
October 30, 2008, at 03:13 PM by 158.35.225.230 -
Changed line 15 from:
|| !,#,% ||Comment || ! equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2]  ! comment ||
to:
|| !,#,% ||Comment ||!! equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2]  ! comment ||
October 30, 2008, at 03:12 PM by 158.35.225.230 -
Changed line 15 from:
|| !,#,% ||Comment || ! comment ||
to:
|| !,#,% ||Comment || ! equation #1 (:html:)<br>(:htmlend:) 0 = x[1] + x[2] ! comment ||
October 30, 2008, at 03:11 PM by 158.35.225.230 -
Deleted line 15:
|| = ||Equality || x=y ||
October 30, 2008, at 03:10 PM by 158.35.225.230 -
Changed line 13 from:
|| border=1 width=50%
to:
|| border=1 width=80%
Changed lines 15-17 from:
|| = ||Line Continuation || 0 = x[1] & (:html:)<br>(:htmlend:) + x[2] ||
to:
|| !,#,% ||Comment || ! comment ||
|| = ||Equality || x=y ||
|| &
||Line Continuation || 0 = x[1] & (:html:)<br>(:htmlend:) + x[2] ||
October 30, 2008, at 03:09 PM by 158.35.225.230 -
Changed line 15 from:
|| = ||Line Continuation || 0 = x[1] & \n + x[2] ||
to:
|| = ||Line Continuation || 0 = x[1] & (:html:)<br>(:htmlend:) + x[2] ||
October 30, 2008, at 03:08 PM by 158.35.225.230 -
Changed line 13 from:
|| border=1 width=30%
to:
|| border=1 width=50%
Added line 15:
|| = ||Line Continuation || 0 = x[1] & \n + x[2] ||
October 28, 2008, at 09:16 PM by 158.35.225.230 -
Added lines 43-44:
|| erf() ||Error function || erf(x*y)=0 ||
|| erfc() ||Complementary error function || erfc(x*y)=0 ||
September 25, 2008, at 07:34 PM by 158.35.225.230 -
Changed lines 11-12 from:
There are currently 21 operands for parameters or variables.  They are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.
to:
There are currently 26 operands for parameters or variables.  They are listed below with a short description of each and a simple example involving variable ''x'' and ''y''.  For equations may be in the form of equalities (=) or inequalities (>,<).  For inequalities, the equation may be bounded between lower and upper limits that are also functions of variables.
Added lines 15-19:
|| = ||Equality || x=y ||
|| < ||Less than || x<y ||
|| <= ||Less than or equal || x<=y ||
|| > ||Greater than || x>y ||
|| >= ||Greater than or equal || x>=y ||
Added lines 21-23:
|| - ||Unary minus || -(x-y) = 0 ||
|| - ||Unary minus || -(x-y) = 0 ||
|| - ||Unary minus || -(x-y) = 0 ||
Changed lines 47-48 from:
A couple differential and algebraic equations are shown below.  The steady-state solution is p=2, x=-1.0445, y=0.1238, and z=-1.0445.  For steady-state solutions the differential variables (''$x'') are set to zero.  Variables x, y, and z were not given initial values.  In the absence of an initial condition, variables are set to a default value of 1.0.
to:
A couple differential and algebraic equations are shown below.  For steady-state solutions the differential variables (''$x'') are set to zero.  Variables x, y, and z were not given initial values.  In the absence of an initial condition, variables are set to a default value of 1.0.
Changed line 51 from:
 ! Example model that demonstrates a few equations
to:
 ! Example with three equality equations
Added lines 69-92:

  The steady-state solution is:
  p=2
  x=-1.0445
  y=0.1238
  z=-1.0445. 

(:cellnr:)

 ! Example with an inequality
 Model example
  Variables
    x
    y
    z
  End Variables

  Equations
    x = 0.5 * y
    0 = z + 2*x
    x < y < z
  End Equations
 End Model

September 25, 2008, at 06:21 PM by 158.35.225.230 -
Changed lines 41-62 from:
(:table class='markup horiz' align='left':)
(:cellnr  class
='markup1':)
>>blue<<
[@!
Example model that demonstrates a few equations
Model example
  Parameters
    p = 2
  End Parameters

  Variables
    x
    y
    z
  End Variables

  Equations
    exp(x*p)=y
    z = p*$x + x
    (y+2/x)^(x*z) * (log(tanh(sqrt(y-x+x^2))+3))^2 = 2+sinh(y)+acos(x+y)+asin(x/y)
  End Equations
End Model@]
>><<
to:
(:table border=1 width=50% align=left bgcolor=#EEEEEE cellspacing=0:)
(:cellnr:)
 !
Example model that demonstrates a few equations
 Model example
   Parameters
     p = 2
   End Parameters

   Variables
     x
     y
     z
   End Variables

   Equations
     exp(x*p)=y
     z = p*$x + x
     (y+2/x)^(x*z) * (log(tanh(sqrt(y-x+x^2))+3))^2 = 2+sinh(y)+acos(x+y)+asin(x/y)
   End Equations
 End Model
September 25, 2008, at 04:08 PM by 158.35.225.230 -
Changed lines 9-10 from:
!!! Equation operands
to:
!!! Operations
Changed line 37 from:
!!! Equation Example
to:
!!! Example