Texas Instruments TI-85 User Manual

Program DFIELD
Output: A direction field for
dy
dx
= f(x, y) or for the
system
dx
dt
= g(x, y),
dy
dt
= h(x, y). In the later case, we take
f(x, y) = h(x, y)/g(x, y).
Input: f(X, Y ) as the Y
1
variable.
:ClrDraw
:FnOff
:(Xmax−Xmin)/10 → S
:Xmin+S → X
:Ymin+S → Y
:Lbl 1
:X − S/5 → A
:Y − SY
1
/5 → B
:X + S/5 → C
:Y + SY
1
/5 → D
:Line(A,B,C,D)
:Y + S → Y
:If Y <Ymax
:Goto 1
:X + S → X
:Ymin→ Y
:If X ≥ Xmax
:Stop
:Goto 1
Program EULER
Output: An approximate solution using Euler’s method
to
dy
dx
= f(x, y), y
0
= y(x
0
) on the interval [x
0
, b].
Input: f(X, Y ) as the Y
1
variable, X0 as x
0
, Y0 as
y
0
= y(x
0
), H and B as h and b in Euler’s method
:FnOff
:Disp “X0”
:Input X
:Disp “Y0”
:Input Y
:Disp “H”
:Input H
:Disp “B”
:Input B
:Lbl 1
:Disp “X=”
:Disp X
:Disp “Y=”
:Disp Y
:Pause
:Y + HY
1
→ Y
:X + H → X
:If X ≤ B + H
Goto 1
Stop
Program EULERG
Output: The graph of an approximate solution to y
0
=
f(x, y), y(0) = x
0
on the interval [x
0
, B] using Euler’s
method.
Input: f(X, Y ) as the Y
1
variable, X0 as x
0
, Y0 as
y
0
= y(x
0
), H as h in Euler’s method. Set the RANGE
variables so that x
min
= x
0
and x
max
= B.
:ClrDraw
:FnOff
:Disp “X0”
:Input X
:Disp “Y0”
:Input Y
:Disp “B”
:Input B
:Disp “H”
:Input H
:Lbl 1
:X → P
:Y → Q
:Pt-On(X,Y)
:P → X
:Q → Y
:Y + HY
1
→ Y
:X + H → X
:If X < B + H
:Goto 1
:Stop
Program EULERS
Output: A graph of an approximate solution to the sys-
tem of differential equations
dX
dt
= P (x, y, t),
dY
dt
=
P (x, y, t), X(t
0
) = X
0
, Y (t
0
) = Y
0
using Euler’s
method.
Input: P (X, Y, T ) as the Y
1
variable, Q(X, Y, T ) as the
Y
2
variable, H as h in Euler’s method. Set the range
variables as desired.
:FnOff
:ClrDraw
:(Xmax−Xmin)/H → N
:Disp “X0”
:Input X
:Disp “Y0”
:Input Y
:Disp “H”
53

Texas Instruments TI-85 Specifications

General

Brand	Texas Instruments
Model	TI-85
Category	Calculator
Language	English

Summary

Section 1.0 in Text: Graphing Basics

The Viewing Window Explained

Defines and illustrates the calculator's viewing screen boundaries (Xmin, Xmax, Ymin, Ymax).

Graphing in Standard Viewing Window

Instructions for graphing a function in the default viewing window settings.

Adjusting Viewing Window and Trace

Change Viewing Window Dimensions

Steps to adjust the viewing window parameters for graphing.

Using the TRACE Feature

How to use the TRACE feature to find points on a graph.

Section 1.1 in Text: Advanced Graphing

Piecewise Functions and Dot Mode

Graphing piecewise functions and using DOT mode for better display.

Section 1.2 in Text: Function Operations

The Root Operation for Zeros

Finding the x-intercept (zero) of a function using the calculator.

Finding Function Intersections

The Intersect Operation

Finding the point where two functions intersect.

Section 2.1 in Text: Statistics and Regression

STAT and LinReg for Data Analysis

Performing linear regression to find the best-fit line for data points.

Advanced Statistics and Table Generation

The TABLE Operation

Creating tables of function values by setting input parameters.

Function Evaluation and Program Execution

The Value Operation for Accuracy

Evaluating a function at specific x-values for high accuracy.

Executing Calculator Programs

Running user-defined or pre-loaded programs on the calculator.

Section 3.2 in Text: Tangents and Secants

Drawing Tangent Lines with DRAW

Using the DRAW menu to graph a tangent line to a function.

Section 5.2 in Text: Numerical Derivatives

nDeriv for First Derivatives

Calculating the numerical derivative of a function.

Chapter 12 Project: Predator and Prey Dynamics

The Program EULERS for System Dynamics

Troubleshooting Calculator Issues