eFunda: Symbolical & Numerical Calculator Input Help

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The input formats of constants, elementary functions, special functions, Greek letters, and other special characters are based on Mathematica^® of Wolfram Research. Please refer to The Mathematica Book by Stephen Wolfram for the complete lists or click the individual link for a quick look-up. Some general principles are summarized as follows:

1.
All entries including constants, functions, variables, characters, etc. are CASE SENSITIVE.

2.
Numerical values such as 1.23e6 and 4.37E-12 should always be entered as 1.23*10^6 and 4.37*10^-12 respectively, since "E" is used for the exponential while "e" is considered a variable.

3.
"1/2" is a fraction while "0.5" is a floating point number. For example, Pi^(1/2) = Sqrt[Pi] versus Pi^0.5 = 1.7724538509055159. Fractions will be preserved as long as possible, until users choose "Expand constants and fractions to numerical values" in "Evaluation".

4.
All built-in functions, constants, and special characters begin with a Capital Letter to differentiate from variables. For instance,

  · Trigonometric (circular) sine x square, sin²x, should be input as .

· Inverse hyperbolic cosine x, cosh^-1x, should be input as .

· Natural logarithmic function of x, ln(x), should be input as Log[x]. Common log of x (base 10), i.e., log₁₀(x) should be Log[10,x].

· Functions with more than one kind/order should be spelled out explicitly. For example, Bessel function of the first kind of order 0, J0(x) , should be input as BesselJ[0,x].

Please note that square brackets, "[...]", are used in functions whereas parentheses, "(...)", are used to group algebraic operations.

5.
Values of common constants can be entered symbolically. For example,

  · E (capital E) for the exponential e = 2.71828...,

· Pi (capital P and small i) for the ratio of the circumference and the diameter of a circle = 3.14159...,

· I (capital I) for the imaginary unit ,

· Infinity (begins with capital I) for infinity ().

6.
Greek letters and special characters can be used in Standard Display, Hand Write, and TeX formats but will NOT display properly in other formats. They can be entered in the format of "\[Name]". For instance,

  · \[Delta] for Delta and \[CapitalDelta] for Capital Delta ,

  · \[AHat] for A-Hat and \[CapitalAHat] for Capital A-Hat .

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