Texas Instruments TITANIUM TI-89 - Manual (Page 809)

Appendix A: Functions and Instructions 809
the general solution.
initialCondition is an equation of the form:
dependentVar ( initialIndependentValue ) =
initialDependentValue
The initialIndependentValue and initialDependentValue
can be variables such as x0 and y0 that have no
stored values. Implicit differentiation can help
verify implicit solutions.
soln|x=0 and y=0 ¸ true
d (right(eq)ìleft(eq),x)/
( d (left(eq)ìright(eq),y))
! impdif(eq,x,y) ¸
Done
ode|y'=impdif(soln,x,y) ¸
true
DelVar ode,soln ¸ Done
deSolve( 2ndOrderOde and initialCondition1 and
initialCondition2 , independentVar ,
dependentVar ) ⇒ ⇒ ⇒ ⇒ a particular solution
Returns a particular solution that satisfies
2ndOrderOde and has a specified value of the
dependent variable and its first derivative at one
point.
deSolve(y''=y^(ë1/2) and y(0)=0 and
y'(0)=0,t,y) ¸
2øy 3/4
3
=t
solve(ans(1),y) ¸
y=
2 2/3 ø (3øt) 4/3
4
and t‚0
For initialCondition1 , use the form:
dependentVar ( initialIndependentValue ) =
initialDependentValue
For initialCondition2 , use the form:
dependentVar ' ( initialIndependentValue ) =
initial1stDerivativeValue
deSolve( 2ndOrderOde and boundaryCondition1 and
boundaryCondition2 , independentVar ,
dependentVar ) ⇒ ⇒ ⇒ ⇒ a particular solution
Returns a particular solution that satisfies
2ndOrderOde and has specified values at two
different points.
deSolve(w''ì2w'/x+(9+2/x^2)w=
xù
e ^(x) and w(p/6)=0 and
w(p/3)=0,x,w) ¸
w=
e
p
3
ø xøcos(3шx)
10
м
e
p
6
ø xøsin(3øx)
10
+
x ⋅ e x
10
det() MATH/Matrix menu
det( squareMatrix [, tol ]) ⇒ ⇒ ⇒ ⇒ expression
Returns the determinant of squareMatrix .
Optionally, any matrix element is treated as zero
if its absolute value is less than
tol . This tolerance
is used only if the matrix has floating-point
entries and does not contain any symbolic
variables that have not been assigned a value.
Otherwise,
tol is ignored.
• If you use ¥ ¸ or set the mode to
Exact/Approx=APPROXIMATE , computations
are done using floating-point arithmetic.
• If
tol is omitted or not used, the default
tolerance is calculated as:
5 E
л 14 щ max(dim( squareMatrix ))
ù rowNorm( squareMatrix )
det([a,b;c,d]) ¸ aшd м bшc
det([1,2;3,4]) ¸ ë 2
det(identity(3) ì xщ[1,л2,3;
л 2,4,1;л6,л2,7]) ¸
л (98øxòì55øxñ+ 12шx м 1)
[1
E
20,1;0,1]!mat1 [
1.
E
20 1
0 1]
det(mat1) ¸ 0
det(mat1,.1) ¸ 1.
E
20