# Introduction to GNU Octave: A brief tutorial for linear algebra and calculus students

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Jason Lachniet, Wytheville Community College

Pub Date: 2017

Publisher: Independent

Language: English

## Conditions of Use

Attribution-ShareAlike

CC BY-SA

## Table of Contents

Contents

Preface

1 Basic operation

1.1 Introduction

1.2 Matrices and vectors

1.3 Plotting

Chapter 1 Exercises

2 Matrices and linear systems

2.1 Linear systems

2.2 Polynomial curve fitting

2.3 Matrix transformations

Chapter 2 Exercises

3 Calculus

3.1 Limits, sequences, and series

3.2 Numerical integration

3.3 Parametric and polar plots

3.4 Special functions

Chapter 3 Exercises

4 Eigenvalue problems

4.1 Eigenvalues and eigenvectors

4.2 Markov chains

4.3 Diagonalization

4.4 Singular value decomposition

4.5 Gram-Schmidt and the QR algorithm

Chapter 4 Exercises

5 Additional topics

5.1 Three dimensional graphs

5.2 Multiple integrals

5.3 Vector fields

5.4 Statistics

5.5 Differential equations

Chapter 5 Exercises

A MATLAB compatibility

B List of Octave commands

References

Index

## About the Book

This guide is heavy on linear algebra and makes a good supplement to a linear algebra textbook. But, it is assumed that any college student studying linear algebra will also be studying calculus and differential equations, maybe statistics. Therefore it makes sense to apply the Octave skills learned for linear algebra to these subjects as well. Chapters 3 and 5 have several applications to calculus, differential equations, and statistics. The overarching objective is to enhance our understanding of calculus and linear algebra using Octave as a tool for computations. For the most part, we will not address issues of accuracy and round-off error in machine arithmetic. For more details about numerical issues, refer to [1], which also contains many useful Octave examples.

To get started, read Chapter 1, without worrying too much about any of the mathematics you don't yet understand. After grasping the basics, you should be able to move into any of the chapters or sections that interest you.

Every chapter concludes with a set of problems, some of which are routine practice, and some of which are more extended applied projects.

Most examples assume the reader is familiar with the mathematics involved. In a few cases, more detailed explanation of relevant theorems is given by way of motivation, but there are no proofs. Refer to the linear algebra and calculus books listed in the references for background on the underlying mathematics. In the spirit of openness, all references listed are available for free under GNU or Creative Commons licenses and can be accessed using the links provided.

## About the Contributors

### Author

**Jason Lachniet**, Wytheville Community College