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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. 

 

 

Table Of Contents   User testimony: 
A.C.:
"It is the best Calculus program in the world because it covers everything that is AP Calculus relevant."   
L.N.: "It cut down a lot of time on checking answers, it helped a great deal ."
R.R.: "I learned a lot Calculus by using the program."    
P.W.: "The program makes learning Calculus really easy. The animations help a great deal. This program was created with a lot of care."
M.S.: "I am not quite sure how I would have survived AP Calculus without the program."
0. Software Updates
Version 10.0
Version 9.2
Version 9.1
Version 9.0
Version 8.0
Version 7.0
Version 6.0 
Version 5.0 
1. Prerequisites and Installation of the Software Package
1.1 Exiting a module or quitting program 
2. Modules of the Software Package
2.1  Start here: AP Calculus (AB)
2.2  Differential Equations
2.3  Implicitly Defined Functions & Implicit Differentiation 
2.4  One Dimensional Motion
2.5  Integral Approximation
2.6  Volume of Solids 
2.7  Unit Circle
2.8  AP Calculus (BC) or Calculus 2 
2.9  Series and Convergence
2.10 Calculus III  (Multivariable Calculus)
2.11 Vector Calculus
2.12 Analytic Geometry
2.13 Differential Geometry
3 User Assistance
3.1 CME User Guide
3.2 TI89 - Basic Instructions    (pdf - By Carolyn Meitler Concordia University Wisconsin)

 

 

Improvements of version 10.0 (updated. 2/2013): (requirements: RAM: 160,000 ,  Flash ROM: 292,000 . )
- Sequences and Series
- Taylor Series - Step by Step
- Relative Rate of Change
- Directional Derivatives, Gradient, Lagrange Multiplier (multi-variable functions) - Step by Step
- Entire new Module on Analytic Geometry (Vector, Lines and Planes) 
  Ex: all Vector Functions, Lines in Plane/Space, their distances, intersections, parameter forms of lines and planes.
  Angles between lines or planes, normal vectors, and much more
  (this replaces the module on differential geometry which can be freely downloaded here

 
 

 
Improvements of version 9.2 (updated. 6/09): (requirements: RAM: 160,000 ,  Flash ROM: 289,000 . )
-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
-Weierstrass Substitution for Integration
-Improper Integrals - Step by Step

 
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. 

 
Improvements of version 9.0 (released. 3/07): (requirements: RAM: 160,000 ,  Flash ROM: 269,000 . )

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

Improvements of version 8.0 (released. 9/06): (requirements: RAM: 160,000 ,  Flash ROM: 233,000 . )  


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.

 

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.)  
 
Ex 2)  Step by Step Power Rule
   
 
Ex 3)  Step by Step Expand and Integrate
   
 
Ex 4)  Step by Step Differentiation using Chain Rule
 
 
Ex 5)  Step by Step Differentiation using Product Rule
   

 

 

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, ...
 
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. 
 

 

 

 


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: 

 

 

F1: Functions 
         f(x) 

F2: Limits

F3: Derivatives

F4: Integrals

F5: Trig+Tools

F6:  Calculus+

F7: Exit

1

All in 1 Explorer

Rules on Limits
incl: L'hopital, rational functions

Find Derivatives
incl. by Def., Secant-TangentLine
Animati
on , Relative Rate of Change, Evaluate f', Find and Evaluate f''

Find Antiderivatives
of f(x)
 

UnitCircle
Click here for details

Functions

Exit

2

Graph f(x)

Find 1-sided Limit

Show Steps for Chain-, Product-, Quotient- and Power Rule. Or using the Definition. 

 

View Sample

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.
Weierstrass Substitution,
 View Sample

List of Trig-Identities

 Calculus BC or Calculus II

About

3

Find f(g(x) in steps

 Find Limit
of f(x) as x-> a

Rules to Find f':
Product-, Quotient-, Chain-, Trig-deriv.

  Rules to Integrate
incl Integration by Subst., by parts, power rule, Trig, FTC
 

List of Derivatives and Integrals of Trig Functions

Multivar. calculus  

4

Find Inverse L'Hopital Rule - Step by Step Make SignChart of  f(x), f'(x) and f''(x)

Net Area 
f(x)dx

Ln(x) - Rules

Area Approximation  

5

Find Asymptotes 
vertical and horizontal

 Continuity

Find Rel Min/Max
when is f'(x)=0
f(a)=f(x0)+∫f'(x)dx  Find Intersection    Differential Equations  

6

Slant Asymptotes 

 Continuity Solver

Find Tangent Line
of f(x) at x=a

Total Area
|f(x)|dx

Solver Analytic Geometry  

7

Find Domain

Continuity/ Differentiability Checker

Find Point of Tangency
of f(x) and a linear function

Enclosed Area

Factor Implicit Differentiation  

8

Find Discontinuity

Intermediate Value Theorem 

Parallel Tangents 2 Equal Areas
Find k on (a,b) so that Area1=Area2
 
Expand 1- dim Motion

 

9

Find Range

 

Find Normal Line
of f(x) at x=a

Average Value Theorem
of f(x) on [a,b]

Synthetic Division in steps Param, Vector, Polar

 

A

Find Symmetry
even, odd, neither

 

Differential Equations
Click here for details

Area Approximation
Click here for details

Partial Fractions in steps. Related Rates  

B

Find Zeros

 

Implicit Differentiation
Click here for details

Find Volume
Click here for details

Common Denominator Sequences and Series  

C

Find Rel Min/Max
when f'(x)=0

  Average Rate of Change   Simplify Fractions Volume of Solids  

D

Find Absolute Minimum and  Maximum
of f(x) on [a,b]

  Find Secant Line   Newton Method 
to estimate zeros
Vector Calculus  

E

Find Inflection Points
of f(x) on [a,b]

  Mean Value Theorem
Find c on [a,b], so that f'(c)=[f(b)-f(a)]/(b-a)
  Bisection Method 
to estimate zeros
Rate Problems (Water or Oil leaking, Cars, Amusement Park, etc)  

F

    Find Inverse Slope
Compute d/dx[f-1(c)]
  Rad->Deg    

G

    1-dim. Motion
Click here for details
  Deg -> Rad    

H

    Related Rates
Intro, Examples and Animations (Pond Surface expands, Moving Ladder) 
       

I

    Piecewise defined Functions
Compute a and b so that f(x) is continuous and differentiable
       
      Logarithmic Differentiation        
      Differentials        

 


2.2  The Differential Equations Module

The following gives an overview of all functions in the Differential Equations module: 

 

         DIFFERENTIAL EQUATIONS       

Option# in head menu

F1: Enter DEQ

F2: Solve DEQ

F3: Steps

F4: Compute

F5: Graph

F6: Euler

F6: Exit

Return to main screen)

1

dy/dx = f(x,y)  
Any separable Diff Eqn.

Solve dy/dx = f(x,y)

Show Steps

Compute y(a)

Graph Slope Field

Approximate analyt. solution to Diff Eqn.  upon entering (x0,y0), step size and #points.

2

y'(t) = k*y(t)
Exponential Growth

Solve  y'(t) = k*y(t)
Exponential Growth

 

Solve y(x)=C

Graph Particular Solution

 

 

3

y'(t) = k*(y(t)-A)
Ex: Newton's Law of Cooling

Solve
y'(t) = k*(y(t)-A)
Ex: Newton's Law of Cooling

 

Tangent at x=a

Clear Graph

 

 

4

y'(t) = k*(A-y(t))
Ex: Wolves problem

Solve
y'(t) = k*(A-y(t))
Ex: Wolves problem

 

Find d2y/dx2

Select Window Size
define xmin, xmax, ymin, ymax, # vertical and horiz. lines

 

 

5

y'(t) = k*y*(A-y)
Logistic Growth

Solve
y'(t) = k*y*(A-y)
Logistic Growth

 

Limit x-> infinity  

 

 

 

 


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

Option# in head menu

F1: Enter Equation

F2: Graph Equation

F3:  (x,y)

F4:  dy/dx

F5: d2y/dx2

F6: Tangents

F7: Exit

Return to main screen

1

Ex1) x2+y2=4 or 
Ex2) y3 + 3x2y + 13 = 0

  

Find y given x.

Find dy/dx
Ex1) y'=-x/y
Ex2) y'=(-2xy)/(x2+y2)
 

Find d2y/dx2
Ex1) y"=-(x2+y2)/y3

Find Tangent at x=a 

2

 

 

Find x given y.

Compute 
Slope at (x,y)

Compute 
Concavity at (x,y)

Find Tangent at y=c

 

3

 

 

 

  Show Steps

  Show Steps

Find Horizontal Tangents (dy/dx = 0)

 

4

 

 

 

 

 

Find Vertical Tangents (dx/dy = 0)

 

 


2.4  The 1-Dimensional Motion Module

The following gives an overview of all functions in the 1-Dimensional Motion Module:


1-DIMENSIONAL MOTION

Option# in head menu

F1: Rules

F2: Velocity

F3: Acceleration

F4: Exit

 

Return to main screen

1

Ex1) v(t)=s'(t)
Ex2) speed increases if v(t) and a(t) are both pos. or neg.
Ex3) Object reverses when v(t) changes sign.
And more
.

Animation: Vertical Ball Throw - 
displays throw, s(t), v(t) and a(t)

Find Velocity Function

2

 

Speed Definition

Find Position Function

 

3

 

Find Average Velocity 
between t1 and t2

 

 

4

 

Reverse Direction  
between t1 and t2

 

 

5

 

Total Distance covered
between t1 and t2

 

 

6

 

Find Position Function

 

 

7

 

Find Acceleration Function

 

 

 


2.5  The Integral Approximation Module

The following gives an overview of all functions in the Integral Approximation Module:

                                                  INTEGRAL APPROXIMATION

Option# in head menu

F1: Enter Equation

F2: Approximate
Each Method below involves numerical answers and graphical explanations. 

F3: Exact Answer for comparison

F4: Exit

Return to main screen

1

  Enter f(x), a, b, and #subintervals

LRAM

 

2

 

MRAM

 

 

3

 

RRAM

 

 

4

 

Trapezoids

 

 

5

 

Area Approximation
using data from table.

 

 

6

  Approximation Rules    

7

  Simpson Rule    

 


2.6  The Volume Module

The following gives an overview of all functions in the Volume Module:
   

VOLUME

Option# in head menu

F1: Disk Method 
about x-axis

F2: Washer Method
about x-axis

F3: Cross Sections

Displays the formulas and computes  volumes of solids having various cross sections. 

F4:  Shell Method
about y-axis

F5: Washer Method
about y-axis

Enter R(y), r(y) and [c,d]
to compute Volume of enclosed rotated area about y-axis 

F6: Exit

1

Enter R(x) and [a,b] 
to compute Volume of rotated area about x-axis  

Enter R(x), r(x) and [a,b]
to compute Volume of enclosed rotated area about x-axis 

Enter H(x), h(x) and [a,b] 
to compute Volume of enclosed rotated area about y-axis 

 

2

2 Equal Volumes
Find k on (a,b) so that Volume1=Volume2

2 Equal Volumes
Find k on (a,b) so that Volume1=Volume2

 

2 Equal Volumes
Find k on (a,b) so that Volume1=Volume2

 

 

3

 

Rotate about the horizontal line y=h

 

Rotate about the vertical line x=a

 

 

4

 

 

 

 

 

 

 

 


2.7  The Unit Circle Module

The following gives an overview of all functions in the Unit Circle Module:
 

UNIT CIRCLE

F1: Quadrant I

Display of Unit Circle Coordinates for 0, 30, 45, 60 degrees. 

F2: Quadrant II

Display of Unit Circle Coordinates for p0, 120, 135, 150 degrees.

F3: Quadrant III

Display of Unit Circle Coordinates for 180, 210, 225, 240 degrees.

F4: Quadrant IV

Display of Unit Circle Coordinates for 270, 300, 315, 330 degrees.

F5: Rules

Incl: Circle Equation, sin(x), cos(x) , tan(x).

F6: Exit

 

Return to main screen

 


2.8  The AP Calculus (BC) Module

The following gives an overview of all functions in the AP Calculus (BC) Module:


  AP CALCULUS (BC)

Option# in head menu

F1: Integrals

F2: Parametrics 

F3: Vectors

F4: Polar

F5: Series

Click here for details

 

F6: Exit

 

Return to main screen

1

Improper Integrals

Evaluate (x(t),y(t)) at  t=a

Vector rules such as addition, multiplication, etc. 

Conversion: Rectangular <-> Polar Coordinates

2

Integration by Trig Substitution (I)

Graph Curve (x(t),y(t)) on [t1,t2]

Example: computation of new plane speed and direction.     Intersection    

3

Integration by Trig Substitution (II) 

Find dy/dx

Graph Curve (x(t),y(t)) on [t1,t2]  

Graph Polar Curve

   

4

Curve Length of f(x) on [a,b]

Find Tangent Line at t=a

When entering Position function s(t), 
compute of v(t), a(t), evaluate them , speed and magnitude of a(t)

Find x-axis, y-axis or origin Symmetry

   

5

Center of Mass

Find Horizontal Tangents

When entering Velocity function v(t), 
compute of s(t), a(t), evaluate them, speed and magnitude of a(t)

Find dy/dx

   

6

  Surface Area(x)

Find Vertical Tangents

When entering Acceleration function a(t), compute of s(t), v(t), evaluate them, speed and magnitude of a(t)

Find Tangents 

   

7

  Surface Area(y)

Find d2y/dx2

Gradient (2-dim)

Compute Area between origin and curve

   

8

 

Find Curve Length of (x(t),y(t)) on [t1,t2]

Direct. Derivative (2-dim)

Compute Enclosed Area between R(phi) and r(phi).

   

9

 

Find Enclosed Area  of loops on [t1,t2]   

Curl (3-dim)

Find Angle theta given x and r(theta)

   

A

 

Find Surface Area  of (x(t),y(t)) on [t1,t2]   

Divergence (3-dim) Find Angle theta given y and r(theta)    

B

 

Find Volume of Solid of Revolution  on [t1,t2]   

  Compute Curve Length of r(phi) on [phi1,phi2]    

 


2.9  The Series and Convergence Module

The following gives an overview of all functions in the Series and Convergence Module:  

SERIES & CONVERGENCE 

Option# in head menu

F1: Enter Series

F2: Tests for Convergence

F3: Power Series

F4: Taylor Series


F5: Error

F6: Exit


Return to Calculus (BC)

1

Find terms of a Recursive  Sequence:
Enter Equation of Series

Find Interval of Convergence of a Power Series using Ratio Test.

Graph f(x) and its power series representation about x=a using n Terms.

 

Alt Series

2

Find terms of an Explicit  Sequence:

N-th Term Test for Convergence
Does an --> 0 as n--> oo ?   

 

Find Taylor Series Representation of f(x) about x=a using n Terms.

Alt Series: Find n.   

3

Sequence Convergence Tester:

Geometric Series Test

 

Find Taylor Series about x=a using its definition. Use it to approx. f(x) near x=a. Also differentiate and integrate it. 

Alt Taylor Series  

4

 Sequence Formula Finder:

Integral Test  

 

Differentiate Taylor series of f(x) 

Taylor Series for f(x)   

5

Partial Sum:
Sum Up the first n Terms

Alternating Series Test  

 

Integrate Taylor series of f(x)

Taylor Series |f^(n+1)(x)|<M  

6

Graph  the first n Terms of Series

Ratio Test  

 

 

Taylor Series: Find n.   

7

 

All-in-One-Tester

       

8

  Comparison Test          

9

  Limit Convergence Test        

A

  p-Series Test         

B

  Root Test        

C

  Find Sum        

 

 

 

2.10  Calculus III

The following gives an overview of all functions in the Calculus III Module:  

CALCULUS III

 

 

F1: Plot f(x,y) 
         

F2: Limits

F3: Differentiate

F4: Integrate

F5: More

F6: Exit

1

  f(x,y): Limit
when x-> x0, y-> y0  

f(x,y) 
Find and Evaluate 
fx, fy, fxx, fxy, fyx, fyy

int(int( f(x,y) ))
Indefinite, double Integral
Convert Rectangular , Cylinder and Spherical coordinates  

2

  f(x,y,z): Limit 
when x-> x0, y-> y0 , z-> z0 

f(x,y) 
Find Rel. Extrema 

int(int( f(x,y) ))
with xmin, xmax, ymin and ymax  as integration bounds

LaPlace Transform  

3

    Directional Derivative - multidimensional int(int( f(x,y) ))
with xmin, xmax, g1(x) and g2(x) or  ymin, ymax, h1(y) and h2(y)
as integration bounds
Fourier Series  

4

    Find Differential (2-variables) int(int(int( 1dzdydx )))
Gamma Function  

5

    f(x(t),y(t)) 
Find and Evaluate  f'(x(t),y(t)) 
int(int(int( f(x,y,z) dzdydx ))) Bessel Function  

6

   

f(x,y,z) - Gradient  
Find and Evaluate  fx, fy, fz.

     

7

    Find Differential (3-variables)      

8

   

f(x(t),y(t),z(t))
Find and Evaluate  f'(x(t),y(t),z(t))  

     

9

    Implicit Differentiation: F(x,y) = 0
Find dy/dx
     

A

   

Implicit Differentiation: F(x,y,z)=0 
Find dz/dx, Find dz/dy

     

B

   

Find Tangent plane  
at (x0,y0,z0) when F(x,y,z)=0.  

     

C

    Jacobian Matrix- multidimensional      

D

    Hesse Matrix- multidimensional      

E

    Lagrange Multiplier- multidimensional      

F

    Taylor Series - multidimensional      

 

 

 

 

 

 

2.11  Vector Calculus 

The following gives an overview of all functions in the Vector Calculus  Module:  

VECTOR CALCULUS

 

 

F1: Derivatives

F2: Integrate

F3: Evaluate

F4: Exit

1

Vector Derivatives Vector Integral    

2

Tangent and Normal Vector Line Integral    

3

Gradient Arc Length    

4

Divergence Surface Integral    

5

Curl Surface Area    

6

LaPlacian Gauss Theorem    

7

  Divergence Theorem    

8

  Green's Theorem    

9

  Stokes Theorem    

10

  Nth Integral    

 

 

2.12  Analytic Geometry 

The following gives an overview of all functions in the Analytic Geometry Module:  

ANALYTIC GEOMETRY

 

 

F1: Vectors

F2: Lines

F3: Planes

F4: Exit

1

About Vectors Find X=A+r*V Find X=A+r*V1+s*V2 Exit

2

Vector Arithmetic Check if Point P is on Line Check if Point P is on Plane  

3

Length(A)=|A| Convert A+r*V to
N0*(X-A)
Find Plane from Normal Vector N and Point P  

4

Unitvector Normal Vector Convert A+r*V1+s*V2 to
N0*(X-A)
 

5

Angle between Vector A and x-axis 2 Lines in Plane Analysis 2 Plane Intersection Analysis  

6

A in Polar Coordinates Are 2 Lines Parallel Distance from Pt. to Plane

7

Graph A or A+B Are 2 Lines in Space Distance from Pt. to Plane (alternative computation)

8

Dot Product of (A,B) Angle between 2 Lines Line and Plane in 3d Analysis  

9

Test Orthogonality Distance from Pt. to Line Angle between 2 Planes  

A

Angle between Vector A and B      

B

Cross-Product(A,B)      

C

Find Orthog. Vector      

D

Distance from A to B      

E

Projection A onto B      

F

Test of Independence      

G

Convert Polar Coord. (|v|,theta) to (v1,v2) rectangular Coord.      

H

Vector Differentiation      

I

Vector Integration      

J

Find Tangent and Normal Vectors      

K

Circle/Sphere Equation      

 

       

 

 

 

  

2.13  Differential Geometry  (download: diffgeo.zip)

The following gives an overview of all functions in the Differential Geometry Module:  

DIFFERENTIAL GEOMETRY

 

 

F1: Curve

F2: Surface

F3: Evaluate

F4: Exit

1

Frenet Frame Unit Normal    

2

Curvature Shape Operator    

3

Torsion Gaussian Curvature    

4

Involute Mean Curvature    

5

Plane Evolute First Fundamental    

6

ArcLength Function Second Fundamental    

7

  Christoffel Symbol    

8