# Mathematics

Origin’s powerful mathematics tools can be categorized in the following groups:

## Data Transformation

### Set Column Values by Formula

**F(x) Column Formula row**

The F(x) Column Formula row in Origin worksheet lets you directly type expressions to calculate column values based on data in other columns and metadata elements

**Set Column Values Dialog**

Besides F(x)= column label row in worksheet to directly enter formula, Set Column Values dialog offers more useful features:

- Calculations can involve columns from other worksheets
- Over 500 functions in categories such as math, engineering, statistics, date-and-time, and string processing
- Before Formula Script to pre-process data prior to calculating results

### Normalization

Origin provides a tool for performing normalization of data either from a worksheet or a graph. The tool provides various methods for normalizing data.

- Divided by a Specified Value
- Normalize to [0, 1]
- Normalize to [0, 100]
- Z Scores (standardize to N(0, 1))
- Divided by Max

- Divided by Min
- Divided by Mean
- Divided by Median
- Divided by SD
- Divided by Norm

- Divided by Mode
- Divided by Sum
- Use Reference Plot\Use Reference Column
- Divided by Reference Cell
- Normalize to Point Picked from Graph

## Interpolation and Extrapolation

### 1D Interpolation/Extrapolation

**Interpolation/extrapolation**

Generate data with uniformly-spaced X values

**Interpolate/Extrapolate Y From X**

Generate data with a set of given X values

**Trace Interpolation**

Appropriate for cyclic or periodic curve

### 2D Interpolation/Extrapolation

**2D Interpolation/Extrapolation**

Generate data with uniformly-spaced XY datasets

**Interpolate Z From XY**

Generate Z values for a set of given XY values

**XYZ Trace Interpolation**

Perform interpolation of XYZ data by following the data trace in 3D.

### 3D Interpolation

Perform interpolation on (X, Y, Z, F) data points, and generate data with uniformly-spaced datasets

## Differentiation and Integration

### Differentiation

The differentiation tool in Origin can calculate derivative up to 9th order. Option for smoothing is also available for handling noisy data.The Differentiate Gadget also enables you to view the results interactively in a separate graph.

### Integration

- Numerical Integration on Columns
- Integrate Gadget
- 2D Integration Gadget and Volume Integration PRO

### Area Calculation

- Polygon Area
- Surface Area Calculation PRO

## Matrix-Based Operations

For mathematical operation on matrix data, the Set Matrix Values dialog also allows Before Formula Script to pre-process data prior to calculating the formula. Origin also provides tools for calculating the inverse of a matrix, shrink or expand a matrix, or filter a matrix using built-in or custom filters.