Derivatives & Integrals

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The tutorial consists of more than 200 live examples from 50 sections. Each of the examples can be copied and run on your own environment. In addition, mXparser provides an extensive collection of over 500 built-in math functions, expressions and symbols. Familiarize yourself with the scope and the syntax. Live testing is the best way to learn. Good luck! 🙂

Tutorial Math Collection API spec Download

Below is the code for JAVA, the code for C# is almost identical. To copy the code, double-click inside the frame.

Case 1: General derivative – at given point

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Expression e = new Expression("cos(1) - der(sin(x), x, 1)");
mXparser.consolePrintln("Res: " + e.getExpressionString() + " = " + e.calculate());
[mXparser-v.5.2.1] Res: cos(1) - der(sin(x), x, 1) = 8.588628E-10

Case 2: General derivative – point given by argument value

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Argument x = new Argument("x = 1");
Expression e = new Expression("cos(x) - der(sin(x), x)", x);
mXparser.consolePrintln("Res: " + e.getExpressionString() + " = " + e.calculate());
[mXparser-v.5.2.1] Res: cos(x) - der(sin(x), x) = 8.588628E-10

Case 3: Left / right derivative – at given point

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Expression e1 = new Expression("der-(abs(x), x, 0)");
Expression e2 = new Expression("der+(abs(x), x, 0)");

mXparser.consolePrintln("Res 1: " + e1.getExpressionString() + " = " + e1.calculate());
mXparser.consolePrintln("Res 2: " + e2.getExpressionString() + " = " + e2.calculate());
[mXparser-v.5.2.1] Res 1: der-(abs(x), x, 0) = -1.0
[mXparser-v.5.2.1] Res 2: der+(abs(x), x, 0) = 1.0

Case 4: Left / right derivative – point given by argument value

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Argument x = new Argument("x = 0");
Expression e1 = new Expression("der-(abs(x), x)", x);
Expression e2 = new Expression("der+(abs(x), x)", x);
         
mXparser.consolePrintln("Res 1: " + e1.getExpressionString() + " = " + e1.calculate());
mXparser.consolePrintln("Res 2: " + e2.getExpressionString() + " = " + e2.calculate());
[mXparser-v.5.2.1] Res 1: der-(abs(x), x) = -1.0
[mXparser-v.5.2.1] Res 2: der+(abs(x), x) = 1.0

Case 5: Derivative from more complex function – at given point

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...

/* Derivative from Taylor series approximation of sin(x)*/
Expression e1 = new Expression("cos(1) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x, 1)");
mXparser.consolePrintln("Res 1: " + e1.getExpressionString() + " = " + e1.calculate());

Expression e2 = new Expression("cos(2) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x, 2)");
mXparser.consolePrintln("Res 2: " + e2.getExpressionString() + " = " + e2.calculate());

Expression e3 = new Expression("cos(3) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x, 3)");
mXparser.consolePrintln("Res 3: " + e3.getExpressionString() + " = " + e3.calculate());
[mXparser-v.5.2.1] Res 1: cos(1) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x, 1) = 8.588628E-10
[mXparser-v.5.2.1] Res 2: cos(2) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x, 2) = -2.6459193E-9
[mXparser-v.5.2.1] Res 3: cos(3) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x, 3) = -1.5994834E-9

Case 6: Derivative from more complex function – point given by argument value

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Argument x = new Argument("x = 1");

/* Derivative from Taylor series approximation of sin(x)*/
Expression e = new Expression("cos(x) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x)", x);
mXparser.consolePrintln("Res 1: " + e.getExpressionString() + " = " + e.calculate());

x.setArgumentValue(2);
mXparser.consolePrintln("Res 2: " + e.getExpressionString() + " = " + e.calculate());

x.setArgumentValue(3);
mXparser.consolePrintln("Res 3: " + e.getExpressionString() + " = " + e.calculate());
[mXparser-v.5.2.1] Res 1: cos(x) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x) = 8.588628E-10
[mXparser-v.5.2.1] Res 2: cos(x) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x) = -2.6459193E-9
[mXparser-v.5.2.1] Res 3: cos(x) - der( sum(k,0,10,(-1)^k*(x^(2*k+1))/(2*k+1)!), x) = -1.5994834E-9

Case 7: Integrals – calculating pi by integration sqrt(1-x^2)

// JAVA: import org.mariuszgromada.math.mxparser.*;
// C#: using org.mariuszgromada.math.mxparser;
// ...
Expression e = new Expression("2 * int( sqrt(1-x^2), x, -1, 1 )");
mXparser.consolePrintln("Res: " + e.getExpressionString() + " = " + e.calculate());
[mXparser-v.5.2.1] Res: 2 * int( sqrt(1-x^2), x, -1, 1 ) = 3.1415920928388927
Nuget – Package Manager

Install-Package MathParser.org-mXparser -Version 6.0.0

Nuget – .NET CLI

dotnet add package MathParser.org-mXparser --version 6.0.0

Nuget – Package Reference

<PackageReference Include="MathParser.org-mXparser" Version="6.0.0"/>

Maven – Dependency

<dependency>
<groupid>
org.mariuszgromada.math</groupid>
<artifactid>
MathParser.org-mXparser</artifactid>
<version>
6.0.0</version>
</dependency>

Maven – Gradle

implementation 'org.mariuszgromada.math:MathParser.org-mXparser:6.0.0'

Maven – Gradle (Kotlin)

implementation("org.mariuszgromada.math:MathParser.org-mXparser:6.0.0")

GitHub

git clone https://github.com/mariuszgromada/MathParser.org-mXparser

OTHER DOWNLOAD OPTIONS

Download latest release – v.6.0.0 Picon: .NET bin onlyDownload latest release – v.6.0.0 Picon: JAVA bin onlyDownload latest release – v.6.0.0 Picon: bin + doc

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