﻿﻿﻿ Fractional Calculus Computer Algebra System, Electrochemistry Software, Massage
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PART 1    User's Guide

1.        Introduction
1.1       What is SymbMath
1.2       Capabilities
1.4       A List of Files in SymbMath

2.        SymbMath Environment: Windows and Menus

2.1.1     Open
2.1.2     New
2.1.3     Save Input
2.1.4     Save Output
2.1.5     DOS Shell
2.1.6     Exit

2.5.2     Input window
2.5.3     Input border
2.5.4     Output window
2.5.5     Output border
2.5.6     Status line

2.9       Editor and Edit Help Menu
2.9.1.1   Show help file
2.9.1.2   Cursor movement
2.9.1.3   Insert & Delete
2.9.1.4   Searching
2.9.1.5   Block functions
2.9.1.6   Special block functions
2.9.1.7   File functions
2.9.1.8   Application keys
2.9.1.9   Miscellaneous
2.9.1.10  Global functions
2.9.1.11  Hot keys
2.9.2     Edit commands
2.9.3     Copy and paste

PART 2    Programmer's Guide

3.        Programming in SymbMath

3.1.      Data Types
3.1.1     Numbers
3.1.2     Constants
3.1.3     Variables
3.1.4     Patterns

3.1.5     Functions, Procedures and Rules
3.1.5.1   Standard Mathematical Functions
3.1.5.2   Calculus Functions
3.1.5.3   Test Functions
3.1.5.4   Miscellaneous Functions
3.1.5.5   User-defined Functions
3.1.5.6   Procedures
3.1.5.7   Rules

3.1.6     Equations
3.1.7     Inequalities
3.1.8     Arrays and Array Index
3.1.9     Lists and List Index
3.1.10    Strings

3.2.      Expressions
3.2.1     Operators
3.2.1.1   Arithmetic Operators
3.2.1.1   Relational Operators
3.2.1.2   Logical Operators
3.2.2     Function Calls

3.3.      Statements
3.3.1     Comment Statements
3.3.2     Evaluation Statements
3.3.3     Assignment Statements
3.3.4     Conditional
3.3.5     Loop

3.3.6     Switch
3.3.6.1   Output Switch
3.3.6.2   Case Switch
3.3.6.3   Numeric Switch
3.3.6.4   Expand Switch
3.3.6.5   ExpandExp Switch

3.3.8     DOS Command Statements
3.3.9     Sequence Statements

3.4.      Libraries and Packages
3.4.1     Initial Package
3.4.2     Chemical Calculation Package

3.5.      Interface with Other Software

4.        Examples

4.1       Calculation
4.1.1     Discontinuity and one-sided value
4.1.2     Undefined and indeterminate forms

4.2       Simplification
4.2.1     Assuming domain
4.2.2     Comparing and testing numbers

4.3       Defining Your Own Functions, Procedures and Rules

4.3.1.1   Defining Conditional Functions
4.3.1.2   Defining Case Functions
4.3.1.3   Defining Piece-wise Functions
4.3.1.4   Defining Recursive Functions
4.3.1.5   Defining Multi-value Functions

4.4       Limits
4.4.1     One-sided Limits
4.4.2     Numeric Limits: NLim()

4.5       Differentiation
4.5.1     One-sided derivatives
4.5.2     Defining f'(x)

4.6       Integration
4.6.1     Indefinite Integration
4.6.2     Definite Integration
4.6.3     Numeric Integration: NInte()

4.7       Solving Equations
4.7.1     Solving Algebraic Equations
4.7.2     Equation Solver: Solve()
4.7.3     Polynomial Solver: PSolve()
4.7.4     Numeric Solver: NSolve()
4.7.5     Solving Differential Equations
4.7.6     Differential Solver: DSolve()

4.8       Sums, Products, Series and Polynomials
4.8.1     Partial Sum
4.8.2     Infinite Sum
4.8.3     Series
4.8.4     Polynomials

4.9       Arrays, Lists, Vectors and Matrices

4.9.1     Arrays
4.9.1.1   Entering Arrays
4.9.1.2   Accessing Arrays
4.9.1.3   Modifying Arrays
4.9.1.4   Operating Arrays

4.9.2     Lists
4.9.2.1   Entering Lists
4.9.2.2   Accessing Lists
4.9.2.3   Modifying Lists
4.9.2.4   Operating Lists

4.9.3     Vectors and Matrices

4.10      Statistics
4.11      Tables of Function Values

4.12      Conversion
4.12.1    Converting to Numbers
4.12.2    Converting to Lists
4.12.3    Converting to Strings
4.12.4    Converting to Table

4.13      Getting parts of expression
4.13.1    Getting type of data
4.13.2    Getting operators
4.13.3    Getting operand
4.13.4    Getting coefficients

4.14      Database
4.14.1    Phone No.
4.14.2    Atomic Weight
4.14.3    Chemical Reaction

4.15      Learning from User
4.15.1    Learning integrals from derivatives
4.15.2    Learning complicated integrals from a simple indefinite integral
4.15.3    Learning definite integral from indefinite integral
4.15.4    Learning integrals from algebra
4.15.5    Learning complicated derivatives from a simple derivative
4.15.6    Learning complicated algebra from simple algebra
4.15.7    Learning vs. programming

5.        Graphics
5.1       Drawing lines and arcs
5.2       Plotting y = f(x)
5.3       Plotting parametric functions x = x(t) and y = y(t)
5.4       Plotting r = f(t) in polar coordinates
5.5       Plotting data

PART 3    Reference Guide

6.        Inside SymbMath
6.1       Internal Structure
6.2       Internal Format

7.        System Limits

8.        Keywords
8.1       Keywords in Topic Order
8.2       Keywords in Alphabetical Order
8.3       Glossary

9.        References
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