# Tutorials

These introductory notebooks are the main source for you to learn Euler Math Toolbox. The tutorial files are installed with EMT in form of notebooks and as web pages exported from the notebooks. You can load the notebooks into the program using the item in the help menu.

## Introduction

• First Steps
This tutorial contains a first introduction into EMT.

## Syntax and Data Types

• The Syntax of Euler
Contains everything you need to know about the syntax of commands and expressions, including the symbolic expressions.
• The Matrix Language
The matrix language is the basic tool for efficient computations in EMT. For short and quick ways to solve problems you should be familiar with this way to handle numerical computations.
• Complex Numbers
Besides real numbers, EMT can handle complex numbers, find zeros of complex polynomials, and solve complex equations.
• Intervals
Interval arithmetic, together with the exact scalar product, is the main tool to get guaranteed inclusions for solutions of linear and non-linear equations or differential equations.
• Maxima
This tutorial introduces symbolic expressions and the interface to Maxima. EMT seamlessly incorporates Maxima using a special syntax for symbolic expressions and functions.
• Maxima Introduction
Examples from the recommended book of W. Haager, translated to EMT.

## Algorithms and Functions

• 2D Plots
All about plots of one variable, curves, or implicit plots in the plane.
• 3D Plots
All about plots of two variables, surfaces, or implicit plots in the 3D space.
• Linear Algebra
Shows how to solve linear systems, compute least square fits, eigenvalues or singular values, using numerical and symbolic arithmetic.
• Numerical Analysis
EMT can solve non-linear equations and systems, or integrals.
• Differential Equations
Shows numerical and symbolic solutions of differential equations
• Input and Output
Read and write from files or from the Internet.
• Statistics
Statistics is a perfect application for EMT. This tutorial introduces statistical distributions, functions, and special plots for statistics. Moreover, it shows how to do Monte-Carlo simulations in EMT.
• Optimization
A tutorial about linear, non-linear, and integer optimization. EMT contains the efficient LPSOLVE package for linear optimization.
• Large Systems
EMT can handle large and sparse systems. The tutorial contains examples connected to graph theory.
• Fast Fourier Transform
This explains FFT and how to produce or analyze sound in EMT.

## Programming Language

• Programming Euler
All there is to say about the programming language of Euler.
• Compiled Code
A tutorial about C code in Euler. Euler comes with the TinyC compiler.
• Python in Euler
Python can be used as a scripting language in EMT. Functions in Python can be called from EMT and vice versa. This includes might packages like MatPlotlib.

## More in Euler

• Povray and Euler
Tutorial on using Povray from Euler with many examples.
• Media Files