This book and disk package is a supplement to any currently existing introductory text on Ordinary Differential Equations and uses Maple V as a computational tool to further understanding and importance. Maple is a powerful symbolic computer software package with which the student can learn to perform many tasks. This platform allows one to do many mundane tasks quickly and efficiently enabling new ways of illustrating and thinking about difficult concepts which will allow for new depths of understanding. Numerical and graphical information and methods are emphasized along with symbolic results throughout this manual in order to take advantage of the versatility of Maple and to increase the breadth of understanding of the student.

How to Use This Handbook The MATLAB Handbook is a complete reference tool for the MATLAB computation language, and is written for all MATLAB users, regardless of their discipline or field(s) of interest. All the built-in mathematical, graphic, and system-based commands avail­ able in MATLAB 51 are detailed herein. Overall Organization One of the main premises of The MATLAB Handbook is that most MATLAB users ap­ proach the system to solve a particular problem (or set of problems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different categories (e.g., linear equations, ordinary differential equations, sur­ face and volume graphics, etc.) and the commands within a subset are explained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system. In addition, because there is much information about MATLAB that is very difficult to express on a purely command-by-command basis, each subject is prefaced with an introductory section. Here, detailed examples are given, profiling some of the most common applications of the commands in that particular section. There is also an introductory session, titled MATLAB Quick Start, which is intended to get those readers not already familiar with MATLAB off to a flying start.

How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple lan­ guage, and is written for all Maple users, regardless of their discipline or field(s) of interest. All the built-in mathematical, graphic, and system­ based commands available in Maple V Release 4 are detailed herein. Please note that The Maple Handbook does not teach the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together provide a basic overview of the capabil­ ities of Maple, it is highly recommended that you also read a more thorough tutorial such as Introduction to Maple by Andre Heck, or one of standard manuals shipped with Maple V Release 4. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of prob­ lems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different categories, e.g., calculus, algebra, data manipulation, etc.; the commands within a subset are ex­ plained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system.

The Maple ODE Lab Book is intended to provide a thorough introduc­ tion to using symbolic computation software to model, solve, explore, and visualize ordinary differential equations. It is best used as a supplement to existing texts (see the bibliography for some of our recommended texts). Maple was chosen as our software package because of its ease-of-use, affordability, and popularity at many universities and colleges around the world. The version being used is Maple V Release 4. If you have a previous release of Maple, some of the commands shown in this lab book will work differently (or not at all), but the basic groundwork for solving ODEs hasn''t changed. Speak to your system administrator about upgrading to Release 4, or contact: Waterloo Maple Inc. 450 Phillip Street Waterloo, Ontario CANADA N2L 5J2 Phone: (519) 747-2373 FAX: (519) 747-5284 E-mail: info@maplesoft.com WWW: http://www.maplesoft.com 1 2 • Chapter 1. Introduction How This Lab Book Is Organized Each subsequent chapter of this lab book contains information and ex­ amples of how to apply Maple to various elements of ordinary differential equations. It is suggested that you read the chapters with your computer on and Maple V Release 4 running. You can then execute many of the com­ mands yourself and experiment by changing various parameters and/or initial conditions, observing the corresponding changes in the results.

How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple language, and is written for all Maple users, regardless of their dis­ cipline or field(s) of interest. All the built-in mathematical, graphic, and system-based commands available in Maple V Release 3 are detailed herein. Please note that The Maple Handbook does not teach about the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together do provide a basic overview of the capabilities of Maple, it is highly recom­ mended that you also read a more thorough tutorial such as In­ troduction to Maple by Andre Heck or First Leaves: A Tutorial Introduction to Maple V. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of problems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different cate­ gories (e.g., calculus, algebra, data manipulation, etc.) and the com­ mands within a subset are explained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system.

This book and disk package is a supplement to any currently existing introductory text on Ordinary Differential Equations and uses Maple V as a computational tool to further understanding and importance. Maple is a powerful symbolic computer software package with which the student can learn to perform many tasks. This platform allows one to do many mundane tasks quickly and efficiently enabling new ways of illustrating and thinking about difficult concepts which will allow for new depths of understanding. Numerical and graphical information and methods are emphasized along with symbolic results throughout this manual in order to take advantage of the versatility of Maple and to increase the breadth of understanding of the student.

How to Use This Handbook The MATLAB Handbook is a complete reference tool for the MATLAB computation language, and is written for all MATLAB users, regardless of their discipline or field(s) of interest. All the built-in mathematical, graphic, and system-based commands avail­ able in MATLAB 51 are detailed herein. Overall Organization One of the main premises of The MATLAB Handbook is that most MATLAB users ap­ proach the system to solve a particular problem (or set of problems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different categories (e.g., linear equations, ordinary differential equations, sur­ face and volume graphics, etc.) and the commands within a subset are explained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system. In addition, because there is much information about MATLAB that is very difficult to express on a purely command-by-command basis, each subject is prefaced with an introductory section. Here, detailed examples are given, profiling some of the most common applications of the commands in that particular section. There is also an introductory session, titled MATLAB Quick Start, which is intended to get those readers not already familiar with MATLAB off to a flying start.

How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple lan­ guage, and is written for all Maple users, regardless of their discipline or field(s) of interest. All the built-in mathematical, graphic, and system­ based commands available in Maple V Release 4 are detailed herein. Please note that The Maple Handbook does not teach the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together provide a basic overview of the capabil­ ities of Maple, it is highly recommended that you also read a more thorough tutorial such as Introduction to Maple by Andre Heck, or one of standard manuals shipped with Maple V Release 4. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of prob­ lems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different categories, e.g., calculus, algebra, data manipulation, etc.; the commands within a subset are ex­ plained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system.

The Maple ODE Lab Book is intended to provide a thorough introduc­ tion to using symbolic computation software to model, solve, explore, and visualize ordinary differential equations. It is best used as a supplement to existing texts (see the bibliography for some of our recommended texts). Maple was chosen as our software package because of its ease-of-use, affordability, and popularity at many universities and colleges around the world. The version being used is Maple V Release 4. If you have a previous release of Maple, some of the commands shown in this lab book will work differently (or not at all), but the basic groundwork for solving ODEs hasn''t changed. Speak to your system administrator about upgrading to Release 4, or contact: Waterloo Maple Inc. 450 Phillip Street Waterloo, Ontario CANADA N2L 5J2 Phone: (519) 747-2373 FAX: (519) 747-5284 E-mail: info@maplesoft.com WWW: http://www.maplesoft.com 1 2 • Chapter 1. Introduction How This Lab Book Is Organized Each subsequent chapter of this lab book contains information and ex­ amples of how to apply Maple to various elements of ordinary differential equations. It is suggested that you read the chapters with your computer on and Maple V Release 4 running. You can then execute many of the com­ mands yourself and experiment by changing various parameters and/or initial conditions, observing the corresponding changes in the results.

How to Use This Handbook The Maple Handbook is a complete reference tool for the Maple language, and is written for all Maple users, regardless of their dis­ cipline or field(s) of interest. All the built-in mathematical, graphic, and system-based commands available in Maple V Release 3 are detailed herein. Please note that The Maple Handbook does not teach about the mathematics behind Maple commands. If you do not know the meaning of such concepts as definite integral, identity matrix, or prime integer, do not expect to learn them here. As well, while the introductory sections to each chapter taken together do provide a basic overview of the capabilities of Maple, it is highly recom­ mended that you also read a more thorough tutorial such as In­ troduction to Maple by Andre Heck or First Leaves: A Tutorial Introduction to Maple V. Overall Organization One of the main premises of The Maple Handbook is that most Maple users approach the system to solve a particular problem (or set of problems) in a specific subject area. Therefore, all commands are organized in logical subsets that reflect these different cate­ gories (e.g., calculus, algebra, data manipulation, etc.) and the com­ mands within a subset are explained in a similar language, creating a tool that allows you quick and confident access to the information necessary to complete the problem you have brought to the system.