﻿ ﻿ AI Fractional Calculus Computer Algebra System, Electrochemistry Software, chat GPT, AI math GPT
+ + + =

# Software Help

## Content

1. Introduction
2. Getting Help
3. Rules
4. How to use?
5. Computing
6. Document

## Introduction

The Math Handbook Calculator has the function of machine learning. It is unique in the world to solve the function of any order (such as 0.5 order) differential equations. Enter mathematical formulas on the Mathematics Handbook website, click continuously to calculate calculus, solve equations, give analytical solutions and numerical solutions and diagrams, interactively zoom in the drawing, and zoom in with the mouse wheel. You can use it on your mobile phone to learn computing and development anytime, anywhere.

## Getting Help

1. It has extensive built-in documentation, accessible by typing a math function or a function name or a keyword, followed by a question mark? e.g.
• or click the button. e.g.

2. AI chat GPT followed by double question mark?? e.g.
• or click the button. e.g.

3. Show usage by starting with help
4. Show source code by starting with code

## Rules

It uses := for assignment. It uses = for equation in MathHandbook and for assigment in JavaScript. It uses ==, <=, >=, < and >, for comparison, != in JavaScript and <> in MathHandbook.

put function arguments in parentheses: sin(x) -- correct, sin x -- incorrect; do not omit multiplication: x*sin(x) -- correct, x sin(x) -- incorrect. Usual keywords are lowercase, which are different from uppercase, e.g. sin is different from Sin. Its default variable is small letter x, but its default index variable in discrete math is k.

By default, the unknown function is y(x) and its initial value is y(0)=0.
For ordinary differential equation, an independent variable is x.
For a partial differential equation, the unknown function is y(1,x) and y(1,t) with its two independent variables x and t.
For a system of equations, two unknown functions are x(t) and y(t) with an independent variable t.

There are 6 way to input derivative of y: y(1,x), ds(y,x), d(y(x),x), ds(y), d(y(x)), y'
There are 3 way to input second order derivative of y: y(2,x), ds(y,x,2), d(y(x),x,2)
There are 3 way to input the 0.5 order derivativeof y: y(0.5,x), ds(y,x,0.5), d(y(x),x,0.5)
There are 4 way to input the 0.5 order integral of y: y(-0.5,x), ds(y,x,-0.5), d(y(x),x,-0.5), ints(y,x,0.5)

more are in Differential equation and example.

## How to use?

buttonto do
the ENTER Clear
the ENTER key in your keybord to calculate symbolly.
JavaScript numeric 数值计算
help 帮助查看
AI chat GPT

There are many ways :
1. Input or click sin(x) , click for integration, click button for derivative to check its result, click again for second derivative, click to inverse function, click for definition, click to simplify, click ......
2. Input the unkown y as seond argument,
then click the button to solve for unknown y.
3. Input command by use of the first function as command :
then hit the button or the ENTER key in your keybord.
4. Input function :
5. Input function by use of "," or ";" as separator for multistatements :
6. Input question mark ? to show index :
7. Input keyword and question mark ? to show its content :
8. Input function and question mark ? to show its function source :
9. Input function and the = mark to calculate numerically :
10. Input function, then hit the button to calculate numerically :
11. Input keyword and then click the question mark ? button to show its content :
12. Input function and then click the question mark ? button to show its function graph :
13. just click the question mark ? button to show index. i.e.
more is in example

## Computing

• by calculator
• Cloud computing 云计算 = Web Address calculator 网址计算器 = Web calculator = URL calculator
Input your formula x from URL in browser to compute x, and share your computation with URL. please replace the plus sign + with %2b, the power sign ^ with **, as URL did not know + ^.

### MathHandbook

- online Computer Algebra System for symbolic computation of any order of fractional derivative. It has three versions:
1. Java version: Java Applet run on phone and tablet and computer that support Java online and off-line. iPhone and iPad do not support Java so it cannot run. Do you want to run MathHandbook offline? please order java version.
2. Phone version: run on any phone online.
3. DOS version: run on PC. Its old name is SymbMath.

## Document

• Java for computation.
• JavaScript for plotting graphics.
• math handbook
• math word
• complex math for complex function and computation.

### MathHandbook

- Computer Algebra System symbolic computation.
1. brief
2. Function - complex function - Special Function
3. Internal Function - system function in the .class file.
4. External Function - user-defined function in text file, which is auto loaded. You can add your own new function.
5. manual - mathHandbook.doc
6. developer document
7. example
8. graphics

### SymbMath

- PC DOS version of symbolic computation Computer Algebra System.