Complex Analysis Made Easy for the TI89/Titanium/92+/Voyage200

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Version 2.0 released 2/2010

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F1: Basics F2: Analysis F3: Integrals F4: Transforms F5: More F6: Exit

1 Identities and Formulas Limit Properties Find Indefinite Integrals Laplace Transform: Definition and Examples Taylor and PowerSeries (Steps) Exit

2 Complex Numbers (Steps) Compute Limit of f(z) (Steps) Show Steps to find Indefinite Integral Solve DEQ using Laplace Transforms (Steps) Vector Calculus About

3 Solve any Complex Equations Compute Limit of f(x,y) (Steps) Definite Integral (Steps) Laplace Transform (Steps) Differential Geometry

4 f(z) Explorer (Steps) Continuity Definition Integration Rules Inverse Laplace Transform Partial Fractions (Steps)

5 Complex Roots of Unity Use Cauchy Riemann Equations (Steps) Compute Curve Integrals (along a path) (Steps) Inverse Laplace Transform (Steps) Complex Partial Fractions (Steps)

6 Complex n-th Roots Check if f(z) is analytic. (Steps) Compute Contour Integrals (Steps) Fourier Series (Steps)

7 f(z) Explorer (Steps) Find Derivative (1. , 2. , 3. ) and Evaluate it.

8 Find Pole & Residue (Steps) Show Steps to find Derivative

9 f(x,y) Explorer (Steps) Find f from u(x,y) (Steps)

A f(z) to f(x,y) Conversion (Steps) Theorems on Analytic Functions

B Complex Exponential Function w=e^z Find f from u(x,y)

C Complex Logarithm Harmonic Functions (Steps)

D Complex Powers Harmonic Conjugate (Steps)

E Complex TrigFunctions Conformal Mapping

F Compute √(a+bi) (Steps)

G Compute Complex DotProduct

H Compute Complex CrossProduct

I Compute Divergence (Steps)

J Compute Curl (Steps)

K Compute Gradient (Steps)

L Compute Potential (Steps)

M

Module: Complex Numbers

	F1: Edit / View	F2: Operations	F3: Steps	F4: Tutorial	F5: Exit
1	Edit	Solve any Complex Equation	Convert Polar to Cartesian Form	Tutorial	Exit
2	View	Compute/ Evaluate	Convert Cartesian to Polar Form
3	Graph Z1	Z1+Z2	Add Complex Numbers
4	Graph Z2	Z1-Z2	Subtract Complex Numbers
5	Graph Z1, Z2, Z1+Z2	Z2-Z1	Multiply Complex Numbers
6		Z1*Z2	Divide Complex Numbers
7		Z1/Z2	Exponentiate Complex Numbers
8		Z2/Z1	Perform DeMoivre Theorem
9		Conjugate(Z1)
A		Z1*Conjugate(Z1)
B		\|Z1\|
C		\|Z2\|
D		Z1^n
E		Z2^n
F		Write own equation
G		Arg(z)

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
1	Find terms of a Recursive Sequence:	Enter Equation of Series	Find Interval of Convergence of a Power Series using Ratio Test.	Graph f(z) and its power series representation about z=a using n Terms.	Alt Series
2	Find terms of an Explicit Sequence:	N-th Term Test for Convergence Does a_n --> 0 as n--> oo ?		Find Taylor Series Representation of f(z) about x=a using n Terms.	Alt Series: Find n.
3	Sequence Convergence Tester:	Geometric Series Test		Find Taylor Series about z=a using its definition. Use it to approx. f(z) near x=a. Also differentiate and integrate it.	Alt Taylor Series
4	Sequence Formula Finder:	Integral Test		Differentiate Taylor series of f(z)	Taylor Series for f(z)
5	Partial Sum: Sum Up the first n Terms	Alternating Series Test		Integrate Taylor series of f(z)	Taylor Series \|f^(n+1)(z)\|<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
		Root Test

Module: 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	Gradient	Line Integral
2	Dir Derivatives	Arc Length
3	Divergence	Surface Integral
4	Curl	Surface Area
5	Jacobian	Gauss Theorem
6	Hessian	Green's Theorem
7	LaPlacian	Stokes Theorem
8	Taylor's Theorem	Nth Integral

Module: Differential Geometry

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