Texas Instruments TI-Nspire CAS User manual

TI-Nspire™ CAS
Reference Guide
This guidebook applies to TI-Nspire™ software version 4.3. To obtain the latest version
of the documentation, go to education.ti.com/guides.

2
Important Information
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License
Please see the complete license installed in C:\ProgramFiles\TIEducation\<TI-Nspire™
Product Name>\license.
© 2006 - 2016 Texas Instruments Incorporated

Contents
Important Information 2
Expression Templates 5
Alphabetical Listing 12
A12
B21
C24
D49
E60
F70
G79
I86
L93
M109
N117
O126
P128
Q137
R140
S153
T178
U193
V194
W195
X197
Z198
Symbols 206
Empty (Void) Elements 232
Shortcuts for Entering Math Expressions 234
EOS™ (Equation Operating System) Hierarchy 236
Error Codes and Messages 238
Warning Codes and Messages 246
Support and Service 249
Texas Instruments Support and Service 249
3

4
Service and Warranty Information 249
Index 251

Expression Templates
Expression templates give you an easy way to enter math expressions in standard
mathematical notation. When you insert a template, it appears on the entry line with
small blocks at positions where you can enter elements. A cursor shows which element
you can enter.
Position the cursor on each element, and type a value or expression for the element.
Fraction template /p keys
Note: See also / (divide), page 208.
Example:
Exponent template lkey
Note: Type the first value, press l, and
then type the exponent. To return the cursor
to the baseline, press right arrow (¢).
Note: See also ^ (power), page 209.
Example:
Square root template /q keys
Note: See also √() (square root), page
219.
Example:
Nth root template /l keys
Note: See also root(), page 150.
Example:
Expression Templates 5

6 Expression Templates
Nth root template /l keys
e exponent template ukeys
Natural exponential eraised to a power
Note: See also e^(), page 60.
Example:
Log template /s key
Calculates log to a specified base. For a
default of base 10, omit the base.
Note: See also log(), page 105.
Example:
Piecewise template (2-piece) Catalog >
Lets you create expressions and conditions
for a two-piece piecewise function. To add
a piece, click in the template and repeat the
template.
Note: See also piecewise(), page 130.
Example:

Piecewise template (N-piece) Catalog >
Lets you create expressions and conditions
for an N-piece piecewise function. Prompts
for N.
Note: See also piecewise(), page 130.
Example:
See the example for Piecewise template (2-
piece).
System of 2 equations template Catalog >
Creates a system of two equations. To add
a row to an existing system, click in the
template and repeat the template.
Note: See also system(), page 177.
Example:
System of N equations template Catalog >
Lets you create a system of Nequations.
Prompts for N.
Note: See also system(), page 177.
Example:
See the example for System of equations
template (2-equation).
Absolute value template Catalog >
Note: See also abs(), page 12. Example:
Expression Templates 7

8 Expression Templates
Absolute value template Catalog >
dd°mm’ss.ss’’ template Catalog >
Lets you enter angles in dd°mm’ss.ss’’
format, where dd is the number of decimal
degrees, mm is the number of minutes, and
ss.ss is the number of seconds.
Example:
Matrix template (2 x 2) Catalog >
Creates a 2 x 2 matrix.
Example:
Matrix template (1 x 2) Catalog >
.Example:
Matrix template (2 x 1) Catalog >
Example:
Matrix template (m x n) Catalog >
The template appears after you are
prompted to specify the number of rows
and columns.
Example:

Matrix template (m x n) Catalog >
Note: If you create a matrix with a large
number of rows and columns, it may take a
few moments to appear.
Sum template (Σ)Catalog >
Note: See also Σ() (sumSeq), page 220.
Example:
Product template (Π)Catalog >
Note: See also Π() (prodSeq), page 219.
Example:
First derivative template Catalog >
The first derivative template can also be
used to calculate first derivative at a point.
Note: See also d() (derivative), page 217.
Example:
Expression Templates 9

10 Expression Templates
Second derivative template Catalog >
The second derivative template can also be
used to calculate second derivative at a
point.
Note: See also d() (derivative), page 217.
Example:
Nth derivative template Catalog >
The nth derivative template can be used to
calculate the nth derivative.
Note: See also d() (derivative), page 217.
Example:
Definite integral template Catalog >
Note: See also∫() integral(), page 217.
Example:
Indefinite integral template Catalog >
Note: See also ∫() integral(), page 217.
Example:
Limit template Catalog >
Example:

Limit template Catalog >
Use −or (−) for left hand limit. Use + for
right hand limit.
Note: See also limit(), page 10.
Expression Templates 11

12 Alphabetical Listing
Alphabetical Listing
Items whose names are not alphabetic (such as +, !, and >) are listed at the end of this
section, page 206. Unless otherwise specified, all examples in this section were
performed in the default reset mode, and all variables are assumed to be undefined.
A
abs() Catalog >
abs(Expr1)⇒expression
abs(List1)⇒list
abs(Matrix1)⇒matrix
Returns the absolute value of the
argument.
Note: See also Absolute value template,
page 7.
If the argument is a complex number,
returns the number’s modulus.
Note: All undefined variables are treated as
real variables.
amortTbl() Catalog >
amortTbl(NPmt,N,I,PV,[Pmt],[FV],
[PpY],[CpY],[PmtAt],[roundValue])⇒
matrix
Amortization function that returns a matrix
as an amortization table for a set of TVM
arguments.
NPmt is the number of payments to be
included in the table. The table starts with
the first payment.
N,I,PV,Pmt,FV,PpY,CpY, and PmtAt
are described in the table of TVM
arguments, page 191.
• If you omit Pmt, it defaults to
Pmt=tvmPmt
(N,I,PV,FV,PpY,CpY,PmtAt).
• If you omit FV, it defaults to FV=0.
• The defaults for PpY,CpY, and PmtAt
are the same as for the TVM functions.

amortTbl() Catalog >
roundValue specifies the number of
decimal places for rounding. Default=2.
The columns in the result matrix are in this
order: Payment number, amount paid to
interest, amount paid to principal, and
balance.
The balance displayed in row nis the
balance after payment n.
You can use the output matrix as input for
the other amortization functions ΣInt() and
ΣPrn(), page 221, and bal(), page 21.
and Catalog >
BooleanExpr1 and BooleanExpr2 ⇒
Boolean expression
BooleanList1 and BooleanList2 ⇒
Boolean list
BooleanMatrix1 and BooleanMatrix2 ⇒
Boolean matrix
Returns true or false or a simplified form of
the original entry.
Integer1 andInteger2 ⇒integer
Compares two real integers bit-by-bit using
an and operation. Internally, both integers
are converted to signed, 64-bit binary
numbers. When corresponding bits are
compared, the result is 1 if both bits are 1;
otherwise, the result is 0. The returned
value represents the bit results, and is
displayed according to the Base mode.
You can enter the integers in any number
base. For a binary or hexadecimal entry, you
must use the 0b or 0h prefix, respectively.
Without a prefix, integers are treated as
decimal (base10).
In Hex base mode:
Important: Zero, not the letter O.
In Bin base mode:
In Dec base mode:
Note: A binary entry can have up to 64 digits
(not counting the 0b prefix). A hexadecimal
entry can have up to 16 digits.
Alphabetical Listing 13

14 Alphabetical Listing
angle() Catalog >
angle(Expr1)⇒expression
Returns the angle of the argument,
interpreting the argument as a complex
number.
Note: All undefined variables are treated as
real variables.
In Degree angle mode:
In Gradian angle mode:
In Radian angle mode:
angle(List1)⇒list
angle(Matrix1)⇒matrix
Returns a list or matrix of angles of the
elements in List1 or Matrix1, interpreting
each element as a complex number that
represents a two-dimensional rectangular
coordinate point.
ANOVA Catalog >
ANOVA List1,List2[,List3,...,List20][,Flag]
Performs a one-way analysis of variance for
comparing the means of two to 20
populations. A summary of results is stored
in the stat.results variable. (page 172)
Flag=0 for Data, Flag=1 for Stats
Output variable Description
stat.FValue of the Fstatistic
stat.PVal Smallest level of significance at which the null hypothesis can be rejected
stat.df Degrees of freedom of the groups
stat.SS Sum of squares of the groups
stat.MS Mean squares for the groups

Output variable Description
stat.dfError Degrees of freedom of the errors
stat.SSError Sum of squares of the errors
stat.MSError Mean square for the errors
stat.sp Pooled standard deviation
stat.xbarlist Mean of the inputof the lists
stat.CLowerList 95% confidence intervals for the mean of each input list
stat.CUpperList 95% confidence intervals for the mean of each input list
ANOVA2way Catalog >
ANOVA2way List1,List2[,List3,…,List10]
[,levRow]
Computes a two-way analysis of variance for
comparing the means of two to 10
populations. A summary of results is stored
in the stat.results variable. (See page 172.)
LevRow=0 for Block
LevRow=2,3,...,Len-1, for Two Factor,
where Len=length(List1)=length(List2) = …
= length(List10) and Len/LevRow Î
{2,3,…}
Outputs: Block Design
Output variable Description
stat.F F statistic of the column factor
stat.PVal Smallest level of significance at which the null hypothesis can be rejected
stat.df Degrees of freedom of the column factor
stat.SS Sum of squares of the column factor
stat.MS Mean squares for column factor
stat.FBlock Fstatistic for factor
stat.PValBlock Least probability at which the null hypothesis can be rejected
stat.dfBlock Degrees of freedom for factor
stat.SSBlock Sum of squares for factor
Alphabetical Listing 15

16 Alphabetical Listing
Output variable Description
stat.MSBlock Mean squares for factor
stat.dfError Degrees of freedom of the errors
stat.SSError Sum of squares of the errors
stat.MSError Mean squares for the errors
stat.s Standard deviation of the error
COLUMN FACTOR Outputs
Output variable Description
stat.Fcol Fstatistic of the column factor
stat.PValCol Probability value of the column factor
stat.dfCol Degrees of freedom of the column factor
stat.SSCol Sum of squares of the column factor
stat.MSCol Mean squares for column factor
ROW FACTOR Outputs
Output variable Description
stat.FRow Fstatistic of the row factor
stat.PValRow Probability value of the row factor
stat.dfRow Degrees of freedom of the row factor
stat.SSRow Sum of squares of the row factor
stat.MSRow Mean squares for row factor
INTERACTION Outputs
Output variable Description
stat.FInteract Fstatistic of the interaction
stat.PValInteract Probability value of the interaction
stat.dfInteract Degrees of freedom of the interaction
stat.SSInteract Sum of squares of the interaction
stat.MSInteract Mean squares for interaction
ERROR Outputs

Output variable Description
stat.dfError Degrees of freedom of the errors
stat.SSError Sum of squares of the errors
stat.MSError Mean squares for the errors
s Standard deviation of the error
Ans /v keys
Ans ⇒value
Returns the result of the most recently
evaluated expression.
approx() Catalog >
approx(Expr1)⇒expression
Returns the evaluation of the argument as
an expression containing decimal values,
when possible, regardless of the current
Auto or Approximate mode.
This is equivalent to entering the argument
and pressing /·.
approx(List1)⇒list
approx(Matrix1)⇒matrix
Returns a list or matrix where each
element has been evaluated to a decimal
value, when possible.
►approxFraction() Catalog >
Expr►approxFraction([Tol])⇒
expression
List►approxFraction([Tol])⇒list
Matrix►approxFraction([Tol])⇒matrix
Returns the input as a fraction, using a
tolerance of Tol. If Tol is omitted, a
tolerance of 5.E-14 is used.
Alphabetical Listing 17

18 Alphabetical Listing
►approxFraction() Catalog >
Note: You can insert this function from the
computer keyboard by typing
@>approxFraction(...).
approxRational() Catalog >
approxRational(Expr[,Tol])⇒expression
approxRational(List[,Tol])⇒list
approxRational(Matrix[,Tol])⇒matrix
Returns the argument as a fraction using a
tolerance of Tol. If Tol is omitted, a
tolerance of 5.E-14 is used.
arccos() See cos⁻¹(), page 35.
arccosh() See cosh⁻¹(), page 36.
arccot() See cot⁻¹(), page 37.
arccoth() See coth⁻¹(), page 38.
arccsc() See csc⁻¹(), page 41.
arccsch() See csch⁻¹(), page 41.

arcLen() Catalog >
arcLen(Expr1,Var,Start,End)⇒
expression
Returns the arc length of Expr1 from
Start to End with respect to variable Var.
Arc length is calculated as an integral
assuming a function mode definition.
arcLen(List1,Var,Start,End)⇒list
Returns a list of the arc lengths of each
element of List1 from Start to End with
respect to Var.
arcsec() See sec⁻¹(), page 154.
arcsech() See sech⁻¹(), page 154.
arcsin() See sin⁻¹(), page 164.
arcsinh() See sinh⁻¹(), page 165.
arctan() See tan⁻¹(), page 179.
arctanh() See tanh⁻¹(), page 180.
augment() Catalog >
augment(List1, List2)⇒list
Alphabetical Listing 19

20 Alphabetical Listing
augment() Catalog >
Returns a new list that is List2 appended to
the end of List1.
augment(Matrix1,Matrix2)⇒matrix
Returns a new matrix that is Matrix2
appended to Matrix1. When the “,”
character is used, the matrices must have
equal row dimensions, and Matrix2 is
appended to Matrix1 as new columns.
Does not alter Matrix1 or Matrix2.
avgRC() Catalog >
avgRC(Expr1,Var [=Value] [,Step])⇒
expression
avgRC(Expr1,Var [=Value] [,List1])⇒
list
avgRC(List1,Var [=Value] [,Step])⇒
list
avgRC(Matrix1,Var [=Value] [,Step])⇒
matrix
Returns the forward-difference quotient
(average rate of change).
Expr1 can be a user-defined function name
(see Func).
When Value is specified, it overrides any
prior variable assignment or any current “|”
substitution for the variable.
Step is the step value. If Step is omitted, it
defaults to 0.001.
Note that the similar function centralDiff()
uses the central-difference quotient.