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Calculus
Made Easy©
for
TI-89, TI-89 Titanium, TI-92+ and Voyage200
 
Use
in High School for AP Calculus AB & BC,
in College for Calculus I,II and III.
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| Improvements of
version 9.2 (released. 4/08): (requirements:
RAM: 160,000 , Flash ROM: 283,000 . ) |
| -Rate problems Analysis (Ex Water enters a
tank at a rate of ...)
-Area Approximation now shows errors
-Improved function graphing capabilities
-Improved Sums of Series
-Improved Rel Min/Max of Multi-Variable Calculus |
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| Improvements of
version 9.1 (released. 11/07): (requirements:
RAM: 160,000 , Flash ROM: 281,000 . ) |
| -Step by step differentiation using limit
definition - Differentiate sinh(x) and cosh(x) step by
step
- Integrate more functions step by step : ex arccos(x)
- Optimized display in Limits with L'hopital step by
step. |
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| Improvements of
version 9.0 (released. 3/07): (requirements:
RAM: 160,000 , Flash ROM: 269,000 . ) |
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Calculus Made Easy v9.0 now beats Mathematica, Maple ,
etc in terms of showing step by step solutions for all
aspects of Calculus:
Step by step solutions for DIFFERENTIATION, INTEGRATION,
LIMITS, DIFFERENTIAL EQUATIONS, IMPLICIT DIFFERENTIATION,
LOGARITHMIC DIFFERENTIATION, DIFFERENTIALS, PARTIAL
FRACTIONS, TRIG SUBSTITUTION, SOME PRECALCULUS TOPICS SUCH SYNTHETIC DIVISION, PARTIAL
FRACTIONS, COMPOSITION
OF FUNCTIONS, All in one SERIES tester, All in one FUNCTION
Explorer, and much more...
No other software covers
Calculus I (Calc AB) , II (Calc BC) , III (multivariable),
Differential Equations, Vector Calculus and Differential
Geometry!!
What is new:
-Step by step solutions to the above topics (A major
breakthrough in math software design: no other software is
able to show stepwise solutions. Try Mathematica, Maple,
Derive, etc)
-Gamma Function, LaPlace Transform, Fourier Series,
Lagrange Multiplier , Bessel Function
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| Improvements of
version 8.0 (released. 9/06): (requirements:
RAM: 160,000 , Flash ROM: 233,000 . ) |
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Calculus Made Easy v8.0 has become the ultimate educational
tool to study Calculus.
No other software provides detailed Step by Step Solutions
to Integration (using U-Substitution (choose u yourself or
let CME do it for you!),
Integration by Parts, by Partial Fractions, Power Rule,
Expand/Rewrite, Arctan(x) and Arcsin(x) Integrals, etc) and
Differentiation (Chain-, Power- , Product- and Quotient
Rule) problems.
No other software covers
Calculus I (Calc AB) , II (Calc BC) , III (multivariable),
Differential Equations, Vector Calculus and Differential
Geometry!!
What is new in version 8.0 ?
1) Auto-Differentiation and Integration. View
sample.
2) Vector Calculus (new Module) : Find Gradient, Dir
Derivatives, Divergence, Curl, Jacobian, Hessian, LaPlacian,
Line Integrals, Arc Length, Surface Integrals+ Area, Gauss,
Stokes, and Green's Theorem, etc 3) Differential Geometry:
Frenet Frame, Curvature, Torsion, Involute, Plane Evolute,
ArcLength, Unit Normal, Shape Operator, Gaussian Operator,
Mean Curvature, 1. + 2. Fundamental, Christoffel Symbol, etc
4) Simplified Navigation: Access each module from the main
module under F6. 5) User settings (i.e. Number Digits, Angle, etc) are retained
after CME exits.
6) Continuity /Differentiability Checker for piecewise
defined functions. 7) Bisection Method to find zeros.
Select by # Iterations or by Error.
8) Newton Method: Select by # Iterations or by Error.
9) Solver was expanded: Solve on given Interval, Solve
for any variable. 10) All-in-one f(x)-Explorer: Find coord.
for min/max, point of inflections, intervals for
in/decreasing, concave up/down in 1 step. Very helpful.
11) Find Equation for given Sequence (arithmetic, geometric,
quadratic, fibonacci, etc.)
12) Enclosed Area: Intersection Points of 2 functions are
found and used automatically.
13) Volume of Revolution: Washer, Shell Methods:
Intersection are found and used automatically.
14) Antiderivatives Option: Find the constant C given x and
y.
15) Related Rates: Differentiate with respect t 16) Related
Rates: Solver
17) Examples for nearly all Dialog Boxes.
18) Yahtzee removed.
19) Inverses: Find slope of each point (if more than one.)
20) Find n-th Derivative and evaluate.
21) Find Center of Mass.
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| Improvements of
version 7.0
(released. 3/06): |
1) Better than Mathematica, Maple: View
Step by Step Solutions for integration methods such as
u-substitution (choose u yourself or let CME do it for
you!), integration by parts, partial fractions, power rule,
expand/rewrite first, arctan(x) and arcsin(x) integrals.
2) View Step by Step Solutions for differentiation methods
such as chain rule, product rule, quotient rule, power
rule.
3) Find Domain and Discontinuities of a function. Draw the
Sign Charts (as needed for number line tests) for f(x),
f'(x), f"(x) .
4) Jacobian and Hessian, - Differentials for f(x,y) and
f(x,y,z) for Multivariable Calculus.
5) Enter recursive and explicit formulas for sequences
and display them. Automatic Sequence Convergence
Tester.
6) Perform the Limit Convergence Test to determine
convergence of a series.
7) Unit Circle shows angles in radian as well.
8) Ultimate Solver: Solve any equation for any variable.
9) Algebra: Simplify fractions, Expand polynomials, Find
proper Fractions
| Ex 1) Step by Step
U-Substitution (Steps that Mathematica,
Maple, etc don't show.) |
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| Ex 2) Step by Step Power
Rule |
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| Ex 3) Step by Step Expand
and Integrate |
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| Ex 4) Step by Step
Differentiation using Chain Rule |
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| Ex 5) Step by Step
Differentiation using Product Rule |
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Improvements of
version 6.0
(released. 4/05): |
1) Perform Logarithmic Differentiation.
Find Average Rate of Change. Simpson Rule for area
approximation.
2) Do both Fundamental Theorems of Calculus.
3) Graph ...functions, ...Average Value, ...Area between
Functions, Under Curves, two Areas of Equal Size, Net and
Total Area.
4) Display setup of Integrals before actual Integration.
More Information on Differential Equations:
Logistic Growth, Exponential Growth, etc.
5) Module to find Extrema of 2-dim. functions significantly
improved.
6) Take a break from Calculus and play a game of Yahtzee.
7) And much more...i.e. scroll answers too wide for screen,
... |
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| Improvements of version 5.0
(4/04): |
1) The annoying Alpha Lock for TI89 users
is eliminated:
Simply enter your expressions into the dialog boxes without
having to press the alpha button. |
2) Multivariable Calculus (Calc III) was
added to Calculus I and II:
Compute Partial Derivatives, Multiple Integrals, Implicit
Differentiation (also useful for 1-dimensional Calculus),
Extrema, Tangent planes, 3D-Plots and more. |
3) Compute Errors of Alternating and Taylor
Series:
Find errors. Find n so that error below a given bound, and
more. |
4) For Engineers and Engineering Students:
Compute Curl, Gradient, Directional Derivative and
Divergence. |
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1
Prerequisites and Installation of the Software Package
a)
Prerequisites:
- Use the TI-Connect software to transfer Calculus Made Easy to the
calculator. Download TI-Connect from the Texas Instruments web site
at http://education.ti.com/us/product/accessory/connectivity/down/download.html
.
Use the latest operating system on your calculator.
Check/Upgrade using TI-Connect.
b)
Installation:
1.
Connect the Calculator to the Computer. Start TI Device Explorer of
the TI Connect software. Assure proper connection between calculator
and TI Connect by i.e. pressing the refresh button.
2. Save the downloaded Calculus Made Easy APP in a known folder on
your computer (easiest on the Desktop). Drag this APP file onto the
TI Device Explorer window. The transfer may take a little while, be
patient.
3. Start software by hitting the APPS button and
selecting "Calculus Made Easy".
1.1 Exiting a
module or quitting program
Simply press the ESC button to exit any module or quitting Calculus
Made Easy.
2
Calculus Made Easy - The Modules
2.1 Starting Screen
After
selecting "Calculus Made Easy" under APPS, the following
screen appears:
Access the
head menu by hitting the F1 or F2 or … key on the Calculator. To
access an item, simply scroll down from the head menu using the
cursor buttons.
The following
gives an overview of all functions in the main module:
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F1:
Functions
f(x)
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F2:
Limits
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F3:
Derivatives
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F4:
Integrals
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F5:
Trig+Tools
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F6: Calculus+
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F7:
Exit
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1
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All in
1 Explorer |
Rules
on Limits
incl: L'hopital, rational
functions
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Find
Derivatives
incl. by Def., Secant-TangentLine
Animation
, Evaluate f'
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Find
Antiderivatives
of f(x)
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UnitCircle
Click
here for details
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Functions |
Exit
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2
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Graph f(x)
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Find
1-sided Limit
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Show
Steps for Chain-, Product-, Quotient- and Power Rule. Or
using the Definition.
View
Sample
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Show
Steps for Definite Integrals, Integration
by U-Substitution, by Parts,
by Partial Fractions, Expand&Integrate,
Rewrite&Integrate,
ArcTan(x) Integrals,
ArcSin(x) Integrals,
Power Rule. View
Sample |
List
of
Trig-Identities
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Calculus
BC
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About
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3
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Find f(g(x)
in steps
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Find
Limit
of f(x) as x-> a
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Rules
to Find f':
Product-, Quotient-, Chain-, Trig-deriv.
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Rules
to Integrate
incl Integration by Subst., by
parts, power rule, Trig, FTC
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List
of
Derivatives and Integrals of Trig Functions
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Multivar. calculus
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4
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Find
Inverse
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Continuity
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Make
SignChart of f(x), f'(x) and f''(x)
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Net
Area
Integral f(x)dx
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Ln(x)
- Rules
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Vector
Calculus
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5
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Find
Asymptotes
vertical and horizontal
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Continuity
Solver
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Find
Rel Min/Max
when is f'(x)=0
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f(a)=f(x0)+int(f'(x)dx |
Find
Intersection
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Differential
Geometry
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6
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Slant
Asymptotes
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Continuity/ Differentiability Checker
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Find
Tangent Line
of f(x) at x=a
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Total
Area
Integral |f(x)|dx
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Solver |
Area Approximation
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7
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Find Domain |
Intermediate
Value Theorem
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Find
Point of Tangency
of f(x) and a linear function
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Enclosed
Area
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Factor |
Differential Equations
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8
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Find
Discontinuity
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Parallel
Tangents |
2
Equal Areas
Find k on (a,b) so that
Area1=Area2
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Expand |
Implicit Differentiation
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9
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Find Range
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Find
Normal Line
of f(x) at x=a
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Average
Value Theorem
of f(x) on [a,b]
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Synthetic Division in steps |
1- dim Motion |
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A
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Find Symmetry
even, odd, neither
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Differential
Equations
Click here for details
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Area
Approximation
Click here for details
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Partial
Fractions in steps. |
Param, Vector, Polar |
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B
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Find Zeros
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Implicit
Differentiation
Click here for details
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Find
Volume
Click here for details
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Common
Denominator |
Related
Rates |
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C
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Find Rel Min/Max
when f'(x)=0
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Average
Rate of Change |
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Simplify Fractions |
Sequences and Series |
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D
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Find Absolute Maximum
of f(x) on [a,b]
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Mean
Value Theorem
Find c on [a,b], so that f'(c)=[f(b)-f(a)]/(b-a)
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Newton
Method
to
estimate zeros |
Volume of Solids |
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E
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Find Absolute Minimum
of f(x) on [a,b]
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Find
Inverse Slope
Compute d/dx[f-1(c)]
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Bisection Method
to
estimate zeros |
Rate
Problems (Water or Oil leaking, Cars, Amusement Park, etc) |
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| F |
Find Inflection Points
of f(x) on [a,b]
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1-dim.
Motion
Click here for details
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Rad->Deg |
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G |
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Related
Rates
Intro, Examples and Animations
(Pond Surface expands, Moving Ladder) |
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Deg ->
Rad |
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H |
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Piecewise
defined Functions
Compute a and b so that f(x) is
continuous and differentiable
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I |
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Logarithmic
Differentiation |
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Differentials |
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2.2
The Differential Equations Module
The following
gives an overview of all functions in the Differential Equations
module:
DIFFERENTIAL
EQUATIONS
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Option#
in head menu
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F1:
Enter DEQ
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F2:
Solve DEQ
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F3:
Steps |
F4:
Compute
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F5:
Graph
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F6:
Euler
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F6:
Exit
Return
to main screen)
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1
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dy/dx
= f(x,y)
Any
separable Diff Eqn.
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Solve
dy/dx
= f(x,y)
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Show
Steps |
Compute
y(a)
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Graph
Slope Field
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Approximate
analyt. solution to Diff Eqn. upon entering (x0,y0),
step size and #points.
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2
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y'(t)
= k*y(t)
Exponential Growth
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Solve
y'(t)
= k*y(t)
Exponential Growth
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Solve
y(x)=C
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Graph
Particular Solution
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3
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y'(t)
= k*(y(t)-A)
Ex: Newton's Law of Cooling
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Solve
y'(t)
= k*(y(t)-A)
Ex: Newton's Law of Cooling
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Tangent
at x=a
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Clear
Graph
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4
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y'(t)
= k*(A-y(t))
Ex: Wolves problem
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Solve
y'(t)
= k*(A-y(t))
Ex: Wolves problem
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Find d2y/dx2
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Select
Window Size
define xmin, xmax, ymin, ymax, #
vertical and horiz. lines
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5
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y'(t)
= k*y*(A-y)
Logistic Growth
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Solve
y'(t)
= k*y*(A-y)
Logistic Growth
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Limit
x-> infinity
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2.3
The Implicitly Defined Functions & Implicit
Differentiation Module
The
following gives an overview of all functions in the Implicitly
Defined Functions & Implicit Differentiation Module:
IMPLICITLY
DEFINED FUNCTIONS & IMPLICIT DIFFERENTIATION
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Option#
in head menu
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F1:
Enter Equation
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F2:
Graph Equation
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F3:
(x,y) |
F4:
dy/dx
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F5:
d2y/dx2
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F6:
Tangents
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F7:
Exit
Return
to main screen
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1
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Ex1)
x2+y2=4 or
Ex2) y3 + 3x2y + 13 = 0
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Find
y given x. |
Find
dy/dx
Ex1) y'=-x/y
Ex2) y'=(-2xy)/(x2+y2)
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Find
d2y/dx2
Ex1) y"=-(x2+y2)/y3
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Find
Tangent at x=a
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2
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Find
x given y. |
Compute
Slope at (x,y)
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Compute
Concavity
at (x,y)
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Find
Tangent at y=c
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3
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Show Steps
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Show Steps
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Find
Horizontal Tangents (dy/dx = 0)
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4
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Find
Vertical Tangents (dx/dy = 0)
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