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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. An independent variable is x for ordinary differential equation. 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)

Details are in Differential equation and example.

Cloud computing

    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 + ^.
  1. : differentiate x, and plot.
  2. : math programming x in the math calculator.
  3. : plot x in the graph.
  4. : plot x in the 2D graph.
  5. : plot x in the 3D graph.
  6. : plot x in the 3D graph by Microsoft Internet Brower IE.
  7. : plot x in the contour 3D graph.
  8. : plot x in the complex 3D graph.
  9. : plot x in the implicit 3D graph.
  10. : plot x in the parametric 3D graph.
  11. : plot x in the spin 3D graph.
  12. : plot x in the wireframe 3D graph.
  13. : show a htm page of the file name test.
  14. : code a htm page for the file name test.
    HTML + CSS + JavaScript + LaTeX + graph programing
  15. : python programing for the file name test.
  17. = : math hand in the math calculator.
    please read online manual part 2 programmer's guide.
  18. = math programing by hand in Chinese.

    数学手册计算器是三合一 = 数学手册+计算器+计算机代数系统 = 看书做题+计算画图+编程开发. 具有机器学习的功能,举一反三,解任意阶(0.5i 阶)微分方程的功能,世上独一无二。在数学手册网上输入数学公式,一步一步点击计算微积分,解方程,给出解析解和图解, 自动制图, 互动放大。在手机上看书做题, 计算制图,编程开发。不需要下载,转发链接就可以共享互动。

    请看用户手册第2部份 程序员指南.


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.

- online Computer Algebra System for symbolic computation of any order of fractional derivative. It has three versions:

  1. PC version: DOS version run on PC. Its old name is SymbMath, you can download it.
  2. Java version: Java Applet run on phone and tablet that support Java online and off-line. iPhone and iPad do not support Java so it cannot run.
  3. Phone version: run on any phone online. It does not requires to download anything.


  • Java for computation.
  • JavaScript for plotting graph.
  • complex math for complex function and computation.


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


    - PC DOS version of symbolic computation Computer Algebra System.
    1. table of content
    2. brief
    3. SymbMath.doc
    4. Lists of Review
    5. Review
    6. download


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