Texas Instruments TINSPIRE Reference Guide - Page 40

depVar

Get Texas Instruments TINSPIRE PDF manuals and user guides View all Texas Instruments TINSPIRE manuals
Add to My Manuals
Save this manual to your list of manuals

Page 40 highlights

euler( ) Catalog > euler(Expr, Var, depVar, {Var0, VarMax}, depVar0, VarStep [, eulerStep]) ⇒ matrix euler(SystemOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, eulerStep]) ⇒ matrix euler(ListOfExpr, Var, ListOfDepVars, {Var0, VarMax}, ListOfDepVars0, VarStep [, eulerStep]) ⇒ matrix Differential equation: y'=0.001*y*(100-y) and y(0)=10 Uses the Euler method to solve the system -d----d---e---p----V----a--r= Expr(Var, depVar) d Var with depVar(Var0)=depVar0 on the interval [Var0,VarMax]. Returns a matrix whose first row defines the Var output values and whose second row defines the value of the first solution component at the corresponding Var values, and so on. £ ¡ ¢ To see the entire result, press and then use and to move the cursor. System of equations: Expr is the right-hand side that defines the ordinary differential equation (ODE). with y1(0)=2 and y2(0)=5 SystemOfExpr is the system of right-hand sides that define the system of ODEs (corresponds to order of dependent variables in ListOfDepVars). ListOfExpr is a list of right-hand sides that define the system of ODEs (corresponds to the order of dependent variables in ListOfDepVars). Var is the independent variable. ListOfDepVars is a list of dependent variables. {Var0, VarMax} is a two-element list that tells the function to integrate from Var0 to VarMax. ListOfDepVars0 is a list of initial values for dependent variables. VarStep is a nonzero number such that sign(VarStep) = sign(VarMax-Var0) and solutions are returned at Var0+i·VarStep for all i=0,1,2,... such that Var0+i·VarStep is in [var0,VarMax] (there may not be a solution value at VarMax). eulerStep is a positive integer (defaults to 1) that defines the number of euler steps between output values. The actual step size used by the euler method is VarStepàeulerStep. Exit Exit Exits the current For, While, or Loop block. Function listing: Exit is not allowed outside the three looping structures (For, While, or Loop). Note for entering the example: In the Calculator application @ on the handheld, you can enter multi-line definitions by pressing · instead of at the end of each line. On the computer keyboard, hold down Alt and press Enter. Catalog > 34 TI-Nspire™ Reference Guide

  • 1
  • 2
  • 3
  • 4
  • 5
  • 6
  • 7
  • 8
  • 9
  • 10
  • 11
  • 12
  • 13
  • 14
  • 15
  • 16
  • 17
  • 18
  • 19
  • 20
  • 21
  • 22
  • 23
  • 24
  • 25
  • 26
  • 27
  • 28
  • 29
  • 30
  • 31
  • 32
  • 33
  • 34
  • 35
  • 36
  • 37
  • 38
  • 39
  • 40
  • 41
  • 42
  • 43
  • 44
  • 45
  • 46
  • 47
  • 48
  • 49
  • 50
  • 51
  • 52
  • 53
  • 54
  • 55
  • 56
  • 57
  • 58
  • 59
  • 60
  • 61
  • 62
  • 63
  • 64
  • 65
  • 66
  • 67
  • 68
  • 69
  • 70
  • 71
  • 72
  • 73
  • 74
  • 75
  • 76
  • 77
  • 78
  • 79
  • 80
  • 81
  • 82
  • 83
  • 84
  • 85
  • 86
  • 87
  • 88
  • 89
  • 90
  • 91
  • 92
  • 93
  • 94
  • 95
  • 96
  • 97
  • 98
  • 99
  • 100
  • 101
  • 102
  • 103
  • 104
  • 105
  • 106
  • 107
  • 108
  • 109
  • 110
  • 111
  • 112
  • 113
  • 114
  • 115
  • 116
  • 117
  • 118
  • 119
  • 120
  • 121
  • 122
  • 123
  • 124
  • 125
  • 126
  • 127
  • 128
  • 129
  • 130
  • 131
  • 132
  • 133
  • 134
  • 135
  • 136
  • 137
  • 138
  • 139
  • 140
  • 141
  • 142
  • 143
  • 144
  • 145
  • 146
  • 147
  • 148
  • 149
  • 150
  • 151
  • 152
  • 153
  • 154
  • 155
  • 156
  • 157
  • 158
  • 159
  • 160
  • 161
  • 162
  • 163
  • 164
34
TI-Nspire™ Reference Guide
euler()
Catalog >
euler(
Expr
,
Var
,
depVar
,
{
Var0, VarMax
}
,
depVar0
,
VarStep
[
,
eulerStep
]
)
⇒
matrix
euler(
SystemOfExpr
,
Var
,
ListOfDepVars
,
{
Var0
,
VarMax
}
,
ListOfDepVars0
,
VarStep
[
,
eulerStep
]
)
⇒
matrix
euler(
ListOfExpr
,
Var
,
ListOfDepVars
,
{
Var0
,
VarMax
}
,
ListOfDepVars0
,
VarStep
[
,
eulerStep
]
)
⇒
matrix
Uses the Euler method to solve the system
=
Expr
(
Var
,
depVar
)
with
depVar
(
Var0
)=
depVar0
on the interval [
Var0
,
VarMax
]. Returns a
matrix whose first row defines the
Var
output values and whose
second row defines the value of the first solution component at the
corresponding
Var
values, and so on.
Expr
is the right-hand side that defines the ordinary differential
equation (ODE).
SystemOfExpr
is the system of right-hand sides that define the system
of ODEs (corresponds to order of dependent variables in
ListOfDepVars
).
ListOfExpr
is a list of right-hand sides that define the system of ODEs
(corresponds to the order of dependent variables in
ListOfDepVars
).
Var
is the independent variable.
ListOfDepVars
is a list of dependent variables.
{
Var0
,
VarMax
} is a two-element list that tells the function to
integrate from
Var0
to
VarMax
.
ListOfDepVars0
is a list of initial values for dependent variables.
VarStep
is a nonzero number such that
sign(
VarStep
)
=
sign(
VarMax
-
Var0
)
and solutions are returned at
Var0
+i·
VarStep
for
all i=0,1,2,… such that
Var0
+i·
VarStep
is in [
var0
,
VarMax
] (there may
not be a solution value at
VarMax
).
eulerStep
is a positive integer (defaults to 1) that defines the number
of euler steps between output values. The actual step size used by the
euler method is
VarStep
à
eulerStep
.
Differential equation:
y'=0.001*y*(100-y) and y(0)=10
To see the entire result, press
£
and then use
¡
and
¢
to
move the cursor.
System of equations:
with
y1
(0)=2 and
y2
(0)=5
Exit
Catalog >
Exit
Exits the current
For
,
While
,
or
Loop
block.
Exit
is not allowed outside the three looping structures (
For
,
While
,
or
Loop
).
Note for entering the example:
In the Calculator application
on the handheld, you can enter multi-line definitions by pressing
@
instead of
·
at the end of each line. On the computer keyboard,
hold down
Alt
and press
Enter
.
Function listing:
depVar
d
Var
d
---------------------