Common Mathematica Code

Author: John J Weber III, PhD

Grouping Symbols

There are at least three different grouping symbols:

• [ ], used for arguments of built-in Mathematica functions only.

• { }, used for grouping related mathematical items, for example:

  • domain; $\{x,−10, 10\}$
  • multiple functions; $\{x, x^2, \sqrt{x}\}$
  • $(x, y)$ points; $\{3,−2\}$
  • lists; $\{2, 4, 6, 8, 10\}$
  • etc.

• ( ), used for grouping expressions, for example

  • $\text{E}ˆ(2x)$
  • $x^2(x + 3)$
  • $1∕(x^2 − x − 1)$
  • etc.

Trigonometric Functions

• $\sin{(x)}$ where $x$ is in radians: Sin[x]
• $\sin{(x)}$ where $x$ is in degrees: Sin[x Degree]
• $\cos{(x)}$ where $x$ is in radians: Cos[x]
• $\cos{(x)}$ where $x$ is in degrees: Cos[x Degree]
• $\tan{(x)}$ where $x$ is in radians: Tan[x]
• $\tan{(x)}$ where $x$ is in degrees: Tan[x Degree]
• $\csc{(x)}$ where $x$ is in radians: Csc[x]
• $\csc{(x)}$ where $x$ is in degrees: Csc[x Degree]
• $\sec{(x)}$ where $x$ is in radians: Sec[x]
• $\sec{(x)}$ where $x$ is in degrees: Sec[x Degree]
• $\cot{(x)}$ where $x$ is in radians: Cot[x]
• $\cot{(x)}$ where $x$ is in degrees: Cot[x Degree]

NOTE: To raise a trig function to a power, e.g., $\sin^2{(x)}$: Sin[x]^2

Inverse Trigonometric Functions

• $\sin^{−1}{(x)}$ in radians: ArcSin[x]
• $\sin^{−1}{(x)}$ in degrees: N[ArcSin[x]/Degree]
• $\cos^{−1}{(x)}$ in radians: ArcCos[x]
• $\cos^{−1}{(x)}$ in degrees: N[ArcCos[x]/Degree]
• $\tan^{−1}{(x)}$ in radians: ArcTan[x]
• $\tan^{−1}{(x)}$ in degrees: N[ArcTan[x]/Degree]

Hyperbolic Functions

• $\sinh{(x)}$: Sinh[x]
• $\cosh{(x)}$: Cosh[x]
• $\tanh{(x)}$: Tanh[x]
• $\text{csch}{(x)}$: Csch[x]
• $\text{sech}{(x)}$: Sech[x]
• $\coth{(x)}$: Coth[x]

Inverse Hyperbolic Functions

• $\sinh^{−1}{(x)}$: ArcSinh[x]
• $\cosh^{−1}{(x)}$: ArcCosh[x]
• $\tanh^{−1}{(x)}$: ArcTanh[x]

Logarithmic Functions

• $\ln{(x)}$: Log[x]
• $\log_{b}{(x)}$: Log[b,x], where $b > 0$, $b\ne 1$

Exponential Function

• $e^x$: $\text{E}\text{^}x$

Radical Functions

• $\sqrt{x}$: Sqrt[x]
• $\sqrt[n]{x}$: Surd[x,n]

Absolute Value Functions

• $|x|$: Abs[x]

Implicit Multiplication

NOTE: Implicit multiplication is understood between a number and a variable.

• $xy$: $x*y$

Exponents

• $x^2$: $x\text{^}2$
• $2^{x+y}$: $2\text{^}(x+y)$

Constants

• $\pi$: Pi
• $e$: E

CC BY-NC-SA 4.0

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License [http://creativecommons.org/licenses/by-nc-sa/4.0/].

Last Modified: Monday, 23 November 2020 6:16 EDT