Notes on Diffy Qs: Differential Equations for Engineers
Jirí Lebl, Oklahoma State University
Pub Date: 2014
ISBN 13: 978-1-5056981-9-0
Conditions of Use
The text is not a reference book, but an introduction to differential equations. It contains the topics commonly covered in a standard sophomore 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.
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 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
- First order ODEs
- Higher order linear ODEs
- Systems of ODEs
- Fourier series and PDEs
- Eigenvalue problems
- The Laplace transform
- Power series methods
- Nonlinear systems
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
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.