# Class Calculus

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java.lang.Object

public final class Calculus extends Object
Calculus - numerical integration, differentiation, etc...
Version:
5.2.0
Author:
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• ## Field Summary

Fields
Modifier and Type
Field
Description
`static final int`
`GENERAL_DERIVATIVE`

`static final int`
`LEFT_DERIVATIVE`
Derivative type specification
`static final int`
`RIGHT_DERIVATIVE`

• ## Constructor Summary

Constructors
Constructor
Description
`Calculus()`

• ## Method Summary

Modifier and Type
Method
Description
`static double`
```backwardDifference(Expression f, double h, Argument x)```
Backward difference(h) operator (at the current value of the argument x)
`static double`
```backwardDifference(Expression f, double h, Argument x, double x0)```
Backward difference(h) operator (at x = x0)
`static double`
```backwardDifference(Expression f, Argument x)```
Backward difference(1) operator (at current value of argument x)
`static double`
```backwardDifference(Expression f, Argument x, double x0)```
Backward difference(1) operator (at x = x0).
`static double`
```derivative(Expression f, Argument x, double x0, int derType, double eps, int maxSteps)```
Numerical derivative at x = x0
`static double`
```derivativeNth(Expression f, double n, Argument x, double x0, int derType, double eps, int maxSteps)```
Numerical n-th derivative at x = x0 (you should avoid calculation of derivatives with order higher than 2).
`static double`
```forwardDifference(Expression f, double h, Argument x)```
Forward difference(h) operator (at the current value of the argument x)
`static double`
```forwardDifference(Expression f, double h, Argument x, double x0)```
Forward difference(h) operator (at x = x0)
`static double`
```forwardDifference(Expression f, Argument x)```
Forward difference(1) operator (at current value of argument x)
`static double`
```forwardDifference(Expression f, Argument x, double x0)```
Forward difference(1) operator (at x = x0)
`static double`
```integralTrapezoid(Expression f, Argument x, double a, double b, double eps, int maxSteps)```
Trapezoid numerical integration
`static double`
```solveBrent(Expression f, Argument x, double a, double b, double eps, double maxSteps)```
Brent solver (Brent root finder)

### Methods inherited from class java.lang.Object

`clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait`
• ## Field Details

• ### LEFT_DERIVATIVE

public static final int LEFT_DERIVATIVE
Derivative type specification
• ### RIGHT_DERIVATIVE

public static final int RIGHT_DERIVATIVE
• ### GENERAL_DERIVATIVE

public static final int GENERAL_DERIVATIVE
• ## Constructor Details

• ### Calculus

public Calculus()
• ## Method Details

• ### integralTrapezoid

public static double integralTrapezoid(Expression f, Argument x, double a, double b, double eps, int maxSteps)
Trapezoid numerical integration
Parameters:
`f` - the expression
`x` - the argument
`a` - form a ...
`b` - ... to b
`eps` - the epsilon (error)
`maxSteps` - the maximum number of steps
Returns:
Integral value as double.
• ### derivative

public static double derivative(Expression f, Argument x, double x0, int derType, double eps, int maxSteps)
Numerical derivative at x = x0
Parameters:
`f` - the expression
`x` - the argument
`x0` - at point x = x0
`derType` - derivative type (LEFT_DERIVATIVE, RIGHT_DERIVATIVE, GENERAL_DERIVATIVE
`eps` - the epsilon (error)
`maxSteps` - the maximum number of steps
Returns:
Derivative value as double.
• ### derivativeNth

public static double derivativeNth(Expression f, double n, Argument x, double x0, int derType, double eps, int maxSteps)
Numerical n-th derivative at x = x0 (you should avoid calculation of derivatives with order higher than 2).
Parameters:
`f` - the expression
`n` - the deriviative order
`x` - the argument
`x0` - at point x = x0
`derType` - derivative type (LEFT_DERIVATIVE, RIGHT_DERIVATIVE, GENERAL_DERIVATIVE
`eps` - the epsilon (error)
`maxSteps` - the maximum number of steps
Returns:
Derivative value as double.
• ### forwardDifference

public static double forwardDifference(Expression f, Argument x, double x0)
Forward difference(1) operator (at x = x0)
Parameters:
`f` - the expression
`x` - the argument name
`x0` - x = x0
Returns:
Forward difference(1) value calculated at x0.
• ### forwardDifference

public static double forwardDifference(Expression f, Argument x)
Forward difference(1) operator (at current value of argument x)
Parameters:
`f` - the expression
`x` - the argument name
Returns:
Forward difference(1) value calculated at the current value of argument x.
• ### backwardDifference

public static double backwardDifference(Expression f, Argument x, double x0)
Backward difference(1) operator (at x = x0).
Parameters:
`f` - the expression
`x` - the argument name
`x0` - x = x0
Returns:
Backward difference value calculated at x0.
• ### backwardDifference

public static double backwardDifference(Expression f, Argument x)
Backward difference(1) operator (at current value of argument x)
Parameters:
`f` - the expression
`x` - the argument name
Returns:
Backward difference(1) value calculated at the current value of argument x.
• ### forwardDifference

public static double forwardDifference(Expression f, double h, Argument x, double x0)
Forward difference(h) operator (at x = x0)
Parameters:
`f` - the expression
`h` - the difference
`x` - the argument name
`x0` - x = x0
Returns:
Forward difference(h) value calculated at x0.
• ### forwardDifference

public static double forwardDifference(Expression f, double h, Argument x)
Forward difference(h) operator (at the current value of the argument x)
Parameters:
`f` - the expression
`h` - the difference
`x` - the argument name
Returns:
Forward difference(h) value calculated at the current value of the argument x.
• ### backwardDifference

public static double backwardDifference(Expression f, double h, Argument x, double x0)
Backward difference(h) operator (at x = x0)
Parameters:
`f` - the expression
`h` - the difference
`x` - the argument name
`x0` - x = x0
Returns:
Backward difference(h) value calculated at x0.
• ### backwardDifference

public static double backwardDifference(Expression f, double h, Argument x)
Backward difference(h) operator (at the current value of the argument x)
Parameters:
`f` - the expression
`h` - the difference
`x` - the argument name
Returns:
Backward difference(h) value calculated at the current value of the argument x.
`f` - Function given in the Expression form
`x` - Argument
`a` - Left limit
`b` - Right limit
`eps` - Epsilon value (accuracy)
`maxSteps` - Maximum number of iterations