CAS Calculators

Sean Surratt

TECM 2700 July 3, 2013

Table of Contents 3

Table of Contents Table of Contents ............................................................................ 3

Introduction .................................................................................... 5

Basics ...............................................................................................7

Exact and Approximate Results .................................................. 9

Trig Functions ............................................................................. 9

Shortcut Keys .............................................................................10

Syntax .........................................................................................10

Understanding Variables ........................................................... 11

Storing Variables .................................................................... 11

Deleting Variables .................................................................. 11

Variable Naming Conventions................................................ 11

Symbolic Math ............................................................................... 13

Symbolic Algebra ....................................................................... 15

Solving Equations ................................................................... 15

Factoring Expressions ............................................................ 15

Understanding Units .................................................................. 16

Unit Conventions .................................................................... 16

Unit Operations ...................................................................... 16

Symbolic Calculus ...................................................................... 17

Matrix/Vector/List ........................................................................ 19

Matrix ......................................................................................... 21

Creating a Matrix .................................................................... 21

Manipulating a Matrix ............................................................ 21

Matrix Operations .................................................................. 21

Vector ........................................................................................ 22

Vector Operations .................................................................. 22

4 CAS Calculators

Lists ........................................................................................... 22

Creating Lists ......................................................................... 22

Manipulating Lists ................................................................. 23

List Operations ...................................................................... 23

Introduction to Programming ...................................................... 25

Programs Make Life Easier ....................................................... 27

Make a Simple Program ............................................................ 27

Index ............................................................................................. 29

Introduction 5

Introduction This document will focus on the Texas Instruments nspire cx CAS

calculator. The ability to use a Calculator with a Computer Algebra

System is fundamental to be a successful engineering student

today. CAS calculators can solve long equations just by typing

them in and hitting solve. Students unskilled with this tool are at a

significant disadvantage. The best resource to learn about the TI

CAS is the TI nspire guidebook. For some the guidebook has a

steep learning curve. Reading this quick reference manual will

help lower the curve.

To download the guidebook visit the TI website at:

education.ti.com/en/us/guidebook/search/ti-nspire-cas

Basics

TI-nspire CX CAS 1

Basics 9

Exact and Approximate Results Results that are not whole numbers will automatically be shown in

a fractional or symbolic form. An exact result is a fraction and an

approximate result is a decimal.

Nspire Example I

Trig Functions

Press µ to find all the trig functions.

TI-nspire CX CAS 2

10 CAS Calculators

Shortcut Keys There are hidden shortcuts on the keypad that are listed in the

user manual. There are a few shortcuts you should memorize: Add a column g@

Add a row @

Integration template g+

Derivative template g-

Fraction template /p

Underscore /_ Shortcuts 1

Syntax Syntax is very important in computational math. Syntax is

basically the set of rules the system uses to communicate. Access

the list of commands from the catalog.

TI-nspire CX CAS 3

Syntax examples appear at the bottom of the screen when scrolling

through the list. Press e · to see more examples of syntax. Use

the expressions template to avoid syntax errors.

TI-nspire CX CAS 4

Basics 11

Understanding Variables

Storing Variables Variables are stored using the define or store commands.

Nspire Example II

Deleting Variables Delete variables using the Del Var command.

Nspire Example III

Variable Naming Conventions There are a few ways to name a variable.

single letter (x, y, z)

letter and number (x1,y1,z1)

name (observed, list, expected)

Symbolic Math

Symbolic Math 15

Symbolic Algebra

Solving Equations Use the Solve command to save time working out algebra

problems. Use this command to solve one equation for one

variable or multiple equations for multiple variables

simultaneously

Nspire Example IV

Factoring Expressions Use the Factor command to return an expression factored with

respect to a variable.

Nspire Example V

Expand expressions by following the same syntax as factoring.

Nspire Example VI

16 CAS Calculators

Understanding Units Units are very similar to variables. A list of measurement units and

constants are built into the catalog. If you don’t see a unit you

want to work with you can create your own. You just follow the

same steps as you would when defining a variable, but with an

underscore in front of the “variable”.

Unit Conventions When working with units in equations use parentheses to avoid

syntax and order of operations errors.

Unit Operations To convert units use the Conversion Operator (¢).

Nspire Example VII

CAUTION: Temperature units must be converted using the

Temp Convert command.

TI-nspire CX CAS 5

Symbolic Math 17

Symbolic Calculus The CAS automatically evaluates L’Hopital’s rule, integration by

parts, and countless other methods.

Use the limit, derivative, and integral, templates under the

expressions template button enter values in just as you would on

paper.

Nspire Example VIII

TI-nspire CX CAS 6

Matrix/Vector/List

Nspire Example IX

Matrix/Vector/List 21

Matrix

Creating a Matrix

Select the expression template button

Input the dimensions of your matrix and press enter

Fill in the first element and press tab to move to the next.

Manipulating a Matrix If you need to add more elements to your matrix:

Add a column g@

Add a row @

Matrix Operations Matrix operations are straight forward. Just make sure you use

the rules for matrix multiplication, addition, etc.

Element Operations are less straight forward.

You must use the “dot multiply” commands.

Nspire Example X

22 CAS Calculators

Vector A vector is a matrix. Create and manipulate vectors as you would a

matrix.

Vector Operations The built in vector operations include Unit Vector, Cross Product,

Dot Product, and converting to different coordinate systems.

Nspire Example XI

NOTE: The order of the elements of in the Cross Product function

matter! (M=R x F)

Lists

Creating Lists To create a list you must use the curved brackets. After you create

a list store it as list1 or an appropriate name. Some list operations

require your list to be stored.

Nspire Example XII

Matrix/Vector/List 23

Manipulating Lists You can find everything you need to manipulate a list under the list operations tab. Manipulating the list is much faster than retyping the augmented list.

Nspire Example XIII

List Operations Select the list operations from the list math tab. These commands are very useful when working in statistics.

TI-nspire CX CAS 7

Introduction to Programming

Lua Programming Logo 1

Introduction to Programming 27

Programs Make Life Easier Find a group of problems in a course that use the same equations.

Make a flow chart of what to do when you encounter different

parameters in this group of problems. Write down the formulas

you would need for each step. That is basically what a program is.

Make a Simple Program Mohr’s circle is another problem that is simple but takes longer

than needed to work out. Write a program that solves Mohr’s

circle:

Nspire Example XIV

To make a new program open up the program editor and select

new program and name it Mohr.

28 CAS Calculators

Copy the code and test it out. Then try writing a program for a

problem in your class.

Define LibPub mohr(x,y,τ,β)=

Prgm

setMode(2,2)

setMode(5,2)

a:=((y+x)/(2))

r:=√((x-a)^(2)+τ^(2))

setMode(1,6)

-y))))/(2))

m:=a+r

n:=a-r

If α=±45 Then

θ:=45

Else

θ:=α

EndIf

φ:=θ+45

t:=r*sin(2*β-2*θ)

If x<y Then

-r*cos(2*β-2*θ)

-2*θ)

Else

-2*θ)

-r*cos(2*β-2*θ)

EndIf

Disp "σ max =",m," σ min =",n

Disp "σ ave =",a," τ max =",r

Disp "θp =",θ,"°"," θs =",φ,"°"

EndPrgm

Index 29

Indexapproximate, 9 command, 11, 15, 16 commands, 10, 21, 23 constants, 16 convert, 16 curved brackets, 22 Define, 11 Delete, 11 derivative, 16 Element, 21 exact, 9 Expand, 15 expression, 15, 21 Factor, 15 fractional, 9 guidebook, 5 integral, 16

limit, 16 Lists, 4, 22, 23 manipulate, 22, 23 Matrix, 3, 19, 21 operations, 16, 21, 22, 23 program, 4, 27, 28 Shortcut, 3, 10 Solve, 15 symbolic, 9 Syntax, 3, 10 template, 10, 16, 21 trig, 9 Unit, 3, 16, 22 units, 16 Variables, 3, 11 Vector, 3, 4, 19, 22