 -- CALCULUS MADE EASY -- Step by Step Integration Step by Step Differentiation Step by Step Limits (L'Hopital Rule) Step by Step Differential Equations Step by Step Interval of Convergence Step by Step Implicit Differentiation Step by Step Implicit Diff. (2. Derivative) Step by Step Area Approximation Step by Step Partial Fractions Step by Step Logarithmic Differentiation Step by Step Inverse Slope Step by Step Trig Substitution Step by Step Synthetic Division Step by Step Volume (by Revolution) Step by Step Composition of Functions Step by Step Parametric Equations Step by Step Parametric Equations (2) Step by Step Polar Equations Signcharts for f, f' and f" All-in-one Function Explorer Auto Domain Finder Auto Series Convergence Tester Auto Sequence Convergence Tester Rate Analysis Continuity & Differentiability Checker Graph 3D - Solid of Revolution Analytic Geometry - Parameter to Normalform Analytic Geometry - Find Parameterform Analytic Geometry - Tangent&Normalvector -- MATRIX MADE EASY -- Step by Step - Find Inverse Step by Step - Find Determinant Step by Step - Row-Echelon Step by Step - Reverse Row-Echelon Step by Step - Cramers Rule Step by Step - Solve 2x2 (nxn) System Step by Step - Simplex Algorithm Step by Step - EigenValue&EigenVector Step by Step - Determine Nullity DIFFERENTIAL EQUATIONS MADE EASY Step by Step - Solve Separable DEQ. Step by Step - Solve 2. Order DEQ. Step by Step - Variation of Parameter Step by Step - Undetermined Coefficients Draw Phase Line + Analyze Solve M(x,y)dy+N(x,y)dx=0 Step by Step - System of Equations Step by Step - Solve DEQ using Laplace Laplace&Inverse Transform --TRIGONOMETRY MADE EASY-- Step by Step - Auto Triangle Solver(SAS) Step by Step - Auto Triangle Solver (SAA) Step by Step - Triangle Solver (SSS) View Trig Identities and Formulas View the UnitCircle Coordinates. Convert Degrees to Radian. Graph Trig Functions. Evaluate Trig Functions. -- PRECALCULUS MADE EASY -- Equation(s) Solver Find Domain Step by Step - Synthetic Division Solve any Triangle Compute Matrices Find Tangent Lines Exponential Functions Solver Find Numbers in Sequences --ACCOUNTING BUSINESS MADE EASY-- Statistics & Forecasting Compute Ratios QuickAcid Test Compute Percentages Create Amortization Schedule Compute Loans Loan Solver -- CONICS MADE EASY -- Step by Step - Conic Analysis Step by Step - Conic Analysis(2) Step by Step - Complete the Square View Conics Information Rotation of Axis View Rotation Equations Conic Analysis - Polar Eqn -- NUMBER THEORY MADE EASY -- Find Primes or Coprimes Step by Step Euclidean Algorithm Create Mod Tables Perform RSA Encryption Perform Chinese Remainder Theorem Find Primitive Roots Solve Congruences Solve Quadratic Congruences Perform Fermat's Little Theorem Perform Goldbach Conjecture -- ALGEBRA MADE EASY -- Step by Step - Find GCD Step by Step - Compute Powers Step by Step - Complex Numbers View Fundamental Laws All-in-1 Function Explorer Distance, Midpoint, Slope of 2 Points Find Domain of any Function Exponential, Log Functions Factoring and Distributing Geometry: Circles, etc Matrix and Vector Computations Combinations, Permutations, Pascal Triangle Step by Step - Partial Fractions Probabilities Sequences: Arithmetic, Geometric .. Simplify Algebraic Expressions Solve Equalities, Inequalities Solve System of Equations Trig: Solve any Triangle View Trig Identities Trig: View UnitCircle Scroll down to select APP and observe the provided Step by Step solutions to the right. It is worldwide the only Math software that can do this!!! Click to view the Differentiation and Integration slides at your speed.   # 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 7.0 1.1 Exiting a module or quitting program 2.1  Start here: AP Calculus (AB) 2.7  Unit Circle 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 (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

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 Animation , 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 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 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 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 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 8 Find Discontinuity Intermediate Value Theorem Parallel Tangents 2 Equal Areas Find k on (a,b) so that Area1=Area2 Expand 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 A Find Symmetry even, odd, neither Partial Fractions in steps. Related Rates B Find Zeros Common Denominator C Find Rel Min/Max when f'(x)=0 Average Rate of Change Simplify Fractions D Find Absolute Minimum and  Maximum of f(x) on [a,b] Find Secant Line Newton Method  to estimate zeros 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

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)|

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

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  