Calculator User Manual

Appendix A: Functions and Instructions 809
the general solution.
initialCondition is an equation of the form:
dependentVar ( initialIndependentValue ) =
initialDependentValue
The
initialIndependentValue and initialDependentValu
e
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
øxøcos(3øx)
10
ì
e
p
6
øxøsin(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:
5Eë 14 ù max(dim( squareMatrix ))
ù rowNorm(
squareMatrix )
det([a,b;c,d]) ¸ aød ìbøc
det([1,2;3,4])
¸ ë2
det(identity(3)
ìxù[1,ë2,3;
ë2,4,1;ë6,ë2,7])
¸
ë(98øxòì55øxñ+
12øx ì1)
[1
E20,1;0,1]!mat1 [
1.E20 1
0 1
]
det(mat1) ¸ 0
det(mat1,.1) ¸ 1.
E20