# Notes on Diffy Qs: Differential Equations for Engineers

Jirí Lebl, Oklahoma State University

Copyright Year: 2014

Last Update: 2020

ISBN 13: 9781505698190

Publisher: Jirí Lebl

Language: English

## Formats Available

## Conditions of Use

Attribution-NonCommercial-ShareAlike

CC BY-NC-SA

## Reviews

The selection of topics is extensive and well chosen, and the material is easily viewed and accessed from the table of contents at the left. The coverage is broad enough to give the instructor freedom to design various course outlines, depending... read more

The selection of topics is extensive and well chosen, and the material is easily viewed and accessed from the table of contents at the left. The coverage is broad enough to give the instructor freedom to design various course outlines, depending on the needs and interests of the students.

The content is accurate and well explained. The figures and examples are beautifully integrated into the explanations to help the reader understand why the techniques work and how to use them.

Yes, this is relevant to modern-day problems, with real-world examples and explanations. The text is enhanced with figures drawn with modern software that makes the concepts clear and easy to visualize. The book will remain current for many years but is also easy to update if needed.

Clarity, lucidity, and readability are highlights of this book. The style is friendly, pleasant, and easy to learn from. There is a perfect balance between conciseness and completeness that keeps the reader engaged and wanting to read more.

The notation and layout of the headings, examples, and figures is clean, consistent, and easy to follow.

The text is nicely subdivided into sections and subsections, with the examples and figures clearly marked. It is easy to look back or ahead and find what one is looking for.

The flow of ideas is natural and engaging, keeping the reader’s interest in every section. Ideas in later sections refer conveniently to topics in previous sections. There are meaningful applications in every part of the book.

The navigation is easy and effortless, and the displays are beautifully presented.

The excellent grammar and friendly, colloquial style are perfect for engaging with undergraduate readers.

The book is beautifully presented for anyone interested in learning about differential equations and its applications.

This is an amazingly well crafted book. Thank you to the author for making it available!

The book covers all the material one might want in an introductory Differential Equations course aimed at engineering students. The book provides plenty of examples and well-constructed exercise sets. Overall, the textbook is well-organized and... read more

The book covers all the material one might want in an introductory Differential Equations course aimed at engineering students. The book provides plenty of examples and well-constructed exercise sets. Overall, the textbook is well-organized and written in the form of lecture notes. Even though the table of contents is well-structured, I would still have the existence and uniqueness section as a separate section of the first chapter and I would also mention Peano's existence theorem in that section.

The book is well written and edited. I found the presentation of the material to be objective and clear.

The text is up to date.

The text of this book is clear and easy to understand.

The notation seems consistent.

The textbook is divided into chapters, sections, and subsections with plenty of excises at the end of each section.

The text is organized in a clear fashion. My personal preference would be to have the existence and uniqueness section as a separate section of the first chapter.

As for a pdf book, navigation is fairly easy.

I found the text to be clear and I did not notice any grammatical errors throughout the book.

The text covers the standard differential equations topics aimed at engineering students. The book does not have any cultural issues.

This is a good book for the intended course. It has a few nice features. In particular, it is concise and written in the form of lecture notes with a lot of exercises of different levels at the end of each section.

The text is written in a comprehensive way although it is an extension of the class notes. It covers required topics as the first of differential equations for engineering students. This is a useful book, but many concepts are not explained in... read more

The text is written in a comprehensive way although it is an extension of the class notes. It covers required topics as the first of differential equations for engineering students. This is a useful book, but many concepts are not explained in detail. It’s good if students read this text as well as follow another textbook, e.g., “Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling” to understand the concepts clearly.

The content seems accurate.

The text covers differential equations for undergraduate students and will not be obsolete within a short period of time.

The text is an extension of the class notes. Overall, the content is easy to understand although some materials are not explained in detail.

The text seems consistent.

The modularity of the text is quite well. The sections of the book are mostly independent to each other.

The topics in the text are presented in a fairly, organized way.

There are no significant interface issues.

The text seems almost free of grammatical errors.

The text covers differential equations for engineering students. The book does not have any cultural issues.

This is a well-written, well-organized text that was initiated from the class notes. This text can be used as a one-semester first course on differential equations, especially for engineering students. This text could be used as a stand-alone textbook. But students would read this text as well as a comprehensive textbook, such as “Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling” or “Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems” to understand the concepts clearly.

The text is not a reference book, but an introduction to differential equations. It contains the topics commonly covered in a standard sophomore level undergraduate course. The index appears to be effective. Further, at the start of each section... read more

The text is not a reference book, but an introduction to differential equations. It contains the topics commonly covered in a standard sophomore level undergraduate course. The index appears to be effective. Further, at the start of each section the author references corresponding chapters in two of the commonly used books: Boyce and DiPrima’s "Elementary Differential Equations and Boundary Value Problems" and Edwards and Penney's "Differential Equations and Boundary Value Problems: Computing and Modeling."

On a high level the book appears to be mostly error free - the main theorems are stated correctly, mathematical notation is used in the standard way, and historical attribution is accurate. I have not read every section closely, but the in sections that I have the calculations and examples appear to be error free.

This is standard material for an undergraduate course in Ordinary Differential Equations. I don't think the text will become obsolete in the near future.

As the word "notes" in the title suggests the book is fairly terse when compared to other textbooks. When used in a classroom setting I think this is fine. However, for self study a text with longer explanations may be preferable.

The notation seems consistent.

The nature of mathematics restricts the ability for the book to be completely modular. However, the author describes the interdependency between the chapters in the introduction.

There are no issues with the book's organization/structure/flow.

I saw no "interface" issues.

I noticed no grammatical errors that significantly impacted the readability of the text.

not applicable.

I have not used this text as an instructor. The last time I taught an differential equations course I used Boyce and DiPrima’s "Elementary Differential Equations and Boundary Value Problems" (which is the standard text at the institution I was teaching at). Through out the quarter, I also read through Jirí Lebl's text to see if it would appropriate to use the next time I taught the course. Overall I think Lebl's book compares well to Boyce and DiPrima’s text and the next time I teach I will probably use Lebl's book. The book has several attractive features. First, there are many problems given in each section. Second, each section contains a reference to the corresponding material in two of the standard textbooks in ordinary differential equations. As an instructor this makes it easy to update lectures if one switches from one of these text. For students, this gives them as easy to find reference for an alternative approach or more detailed discussion. Perhaps the most attractive feature is that the book will never go out of print and there will be no pressure to update to a new edition.

The book covers many of the material that is usually covered on an undergraduate engineering course on Differential Equations. It also was an extensive index. However, the book does not cover some important topics (e.g., more applications of the... read more

The book covers many of the material that is usually covered on an undergraduate engineering course on Differential Equations. It also was an extensive index. However, the book does not cover some important topics (e.g., more applications of the theory of ODEs, study of non-diagonalizable systems of DE). Overall, the material main material is there but it sometimes lacks depth in the presentation.

This are lecture notes, not exactly a book. As lecture notes they do emphasize on the most important parts of the material. However there are some explanations that required revision (e.g., discussion on antiderivatives, hypothesis on some theorems). I think this lecture notes will benefit of a proper definition of concepts and a careful statement of theorems. I would not recommend this lectures for self study since they lack of some precision for the careful reader.

This is a classic material and will hardly get obsolete

While most of the books is written in a lucid and accessible way. Some parts of the book are written in an informal way (e.g., “Do note that the definite integral and the indefinite integral (antidifferentiation) are completely different beast” or “Here is a good way to make fun of your friends taking second semester calculus. Tell them to find the closed form solution. Ha ha ha (bad math joke). It is not possible (in closed form)”). Also, there are some explanations that need further improvement.

I could not find inconsistencies in terminology while doing a fast read of the book. There are however many typos in the text and theorems.

As lecture notes (not book) the modularity of the are very good. There is a natural flow of the material.

Overall, the organization of the material is standard. However, I found that the books goes back and forth in the topic of partial differential equations (PDEs). I prefer the more classical approach where the theory of PDEs are presented after covering ordinary differential equations (e.g., Boyce-Di Prima’s book). But this might be a matter of taste.

The images on the book are good. I think the book could benefit of a more interactive interface with back and forth interlinks. Also, it will be nice to have reference to the web material produce by the author (see additional comments at the end)

I could find some minor grammatical errors.

Is hard to attest cultural relevance on mathematics notes like this ones. I could not find relevant culturally plural examples.

There are two very useful and important highlights about this book that I did not mentioned before. First, the LATEX code of the notes are provided by the author on his website. That in itself, makes the book a great contribution since it will allow improvements and extensions in a very smooth fashion. Actually, as mentioned on the author’s website there are already Portuguese notes that are a partial translation of this ones. Second, the author provides with many SAGE demos to illustrate some parts of the theory (e.g., Euler’s method, mechanical vibrations, resonances, etc). I would be nice if the additional material is mentioned when relevant during the text.

## Table of Contents

- 1. First order equations
- 2. Higher order linear ODEs
- 3. Systems of ODEs
- 4. Fourier series and PDEs
- 5. More on eigenvalue problems
- 6. The Laplace transform
- 7. Power series methods
- 8. Nonlinear systems
- A. Linear algebra

## Ancillary Material

## About the Book

A one semester first course on differential equations, aimed at engineering students. Prerequisite for the course is the basic calculus sequence. This free online book (e-book in webspeak) should be usable as a stand-alone textbook or as a companion to a course using another book such as Edwards and Penney, Differential Equations and Boundary Value Problems: Computing and Modeling or Boyce and DiPrima, Elementary Differential Equations and Boundary Value Problems (section correspondence to these two is given). I developed and used these notes to teach Math 286/285 at the University of Illinois at Urbana-Champaign Sample Dirichlet problem solution (one is a 4-day-a-week, the other a 3-day-a-week semester-long course). I have also taught Math 20D at University of California, San Diego with these notes (a 3-day-a-week quarter-long course). There is enough material to run a 2-quarter course, and even perhaps a two semester course depending on lecturer speed.

## About the Contributors

### Author

**Jirí Lebl, **Mathematician at OSU, wearer of hats and colored socks (odd pairs only). Degrees: PhD from UCSD (2007), BA and MA are from SDSU (2001, 2003). Spent 2007-2010 as a postdoc at UIUC, the 2010-2011 year visiting UCSD, and 2011-2013 postdocing again at UW-Madison.