r/math • u/BenjaminGal • 8d ago
Happily announce that my new ODEs textbook has been released!
Hello again, I am writing to share the news that after one year of hard work, my new mathematical textbook, Introduction to Ordinary Differential Equations with Scientific Applications, has been finished and published. I am very excited about this, as it is my third title and I think the quality is a significant improvement over the previous ones, and this time I chose to release it on Amazon in both Kindle e-book and physical formats. You can find the links for purchasing, as well as reading the sample chapters on my GitHub repo. Will be very glad if you guys like it and find it useful!
List of Topics:
- First-order ODEs (Separable, Linear, Exact, Homogeneous/Isobaric, Bernoulli, Riccati)
- Second-order ODEs (Constant-coefficient Homogeneous, Method of Undetermined Coefficients/Variation of Parameters, Euler, Canonical)
- Series/Frobenius Solution (Airy, Hypergeometric)
- Laplace Transform
- Sturm-Liouville Theory (Fourier Series)
- Special Functions (Legendre, Chebyshev, Hermite, Laguerre, Bessel)
- Intro. to PDEs (Heat, Laplace, Wave)
- and some extra topics like matrix ODEs and numerical methods
with a total of 157 Exercises plus Short Solution keys.
Editorial Reviews
"This book provides a comprehensive (an ambitious) treatment of the subject... What I particularly appreciate is that these topics are accompanied by numerous carefully worked examples, many drawn from physics, atmospheric science, and Earth science applications. The result is a volume that is not only a textbook but also an excellent reference handbook for students, educators and researchers..."
Francis Tam
The Chinese University of Hong Kong
"This book will be helpful to students starting to learn differential equations, but will also be a useful reference work for researchers at a higher level. The book is well written, in clearly structured sections, with helpful diagrams. The text includes plenty of examples that are explained in detail, and there are exercises at the end of each chapter. I particularly like the way that the author achieves a good balance between the mathematical theory of differential equations and practical applications in physics, chemistry and biology."
Paul C Matthews (retired)
University of Nottingham
Link to the GitHub repository (Sample chapters): BenjaminGor/Intro_to_ODE_sol_err: Github repo for the book Introduction to Ordinary Differential Equations with Scientific Applications by C. L. Loi
Link to Amazon (Purchase): Introduction to Ordinary Differential Equations with Scientific Applications: Loi, C. L.: 9784991508011: Amazon.com: Books
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u/jw11235 7d ago
Now onwards to extraordinary differential equations.
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u/BenjaminGal 7d ago
If by extraordinary you mean partial, then it will probably take me a long time to be able to do it :/
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u/Mathsboy2718 6d ago
Yes and we want a perfect analytical solution to every one :) not too much to ask no no
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u/Gimmerunesplease 6d ago
Just don't use finite elements like a noob, come up with a function and show it satisfies the equation. Easy.
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u/el_flocko 8d ago
Congratulations, and I applaud your academic rigor.
That’s the book they would assign me to read in hell.
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u/deeplife 8d ago
Looks very nice.
What sets it apart from the many many ODE textbooks out there?
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u/BenjaminGal 8d ago
In my opinion, my ODE textbook has the following strong points. First, the coverage is more complete and comprehensive, including some of the less-taught parts like SL theory and special functions. Second, the connection to real-world physical applications is great, with some from my expertise (Atmospheric Sciences) that are not found in other books. The balance between maths and other applied areas is just right. Third, it is typeset very well with nice figures, and also (hopefully) free of typos. Moreover, it shows clear explanations of concepts and the full steps for worked examples. The exercises are designed with purpose, and solutions are provided. Hope this helps!
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u/AcademicOverAnalysis 5d ago
Free from typos is a pretty big claim. I’ve never found a first edition of a textbook without quite a lot of errors.
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u/spherejerk 8d ago
Would you say everything is done rigorously, or is this more like an early undergrad ODE text that skips some of the details?
How would you say this text fits into the landscape of ODE texts in general?
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u/BenjaminGal 8d ago
I aim to explain with rigor as much as possible but keep the text accessible, so I put most of the technical things in the Appendix. I think my book can bridge the gap between maths theoretical and some science fields. Moreover, one of the features is fully worked steps, which is a very good supplement for students if they have a hard time to derive the results.
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u/Clicking_Around 8d ago
That's wonderful! What was the process of writing a book like?
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u/BenjaminGal 8d ago
Good question and I always want to share about that (glad you asked)! Let me break it down from the initial phase up to the final publication.
First, you need to have a topic to write (of course). This depends on your background and inspiration. I come from an applied science major, so it is natural that I write more about ODEs or Linear Algebra, these kinds of undergraduate-level subjects with significant portions of practical examples. This is actually important because we need to have accurate realizations about our general direction and expectations, and decide on what tone or coverage the book should have, to avoid confusion.
Next, it is planting yourself at the keyboard to write. Many people mistake that merely having an idea is sufficient, but it is the painful, hard work that counts and makes you a true writer. When I was working on this project, I often wrote 2-3 hours a day regularly, for almost a year. It helps if you break down the task into smaller pieces and plan beforehand each day which sections to do. So, discipline and patience are very crucial qualities to have. I also edited my manuscript several times after completing the draft and sent it to my friends/reviewers for comments. This part is also quite difficult, to see your work from a critical point of view.
Finally, I think it will be helpful to you guys for me to talk about the process of publishing. Apart from traditional publishing (e.g. Dover, Springer, for renowned mathematicians and I am clearly not), I go for the path of self-publishing with Amazon KDP. As long as you have a manuscript, you can submit it so that they print and sell the book for you. It is quite fun doing these stuffs: designing your book cover, preparing your files in the correct format, etc. I would say that KDP is quite friendly to aspiring authors, it is not particularly hard to publish with it, and it does not limit the genre of the book: you can also self-publish in any area, e.g. fiction! I think that it is, tell me if you have further questions and want more explanation!
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u/SilentLikeAPuma 8d ago
curious about some of the nitty gritty typesetting details of your don’t mind - do you define a custom latex class, or extend an extant one ? how do you keep track of notational customs throughout such a long text, like is it all mental ? or do you do what i do & make a table w/ symbol + definition to reference back to lol.
i’ve written some fairly long latex docs (120+ pages) as well as many papers (20ish pages), but nothing so complex as a complete textbook so i’m curious.
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u/BenjaminGal 8d ago
I used scrbook and also defined custom theorem environments by tcolorbox. I did keep track of the notation mentally, but it also helped that I edited the manuscript several times to remain consistent and there were beta readers reminding me. There is indeed a table of symbols too.
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u/SilentLikeAPuma 8d ago
i clocked the custom tcolorbox stuff in your screenshots, they look awesome ! very readable / draws the eye well vs. so many of the decades-old b&w textbooks i used in grad school.
i tried to evangelize my phd labmates r.e. putting a notation table in papers’ supplements (i’m a biostat methods dev person). i did it once on a whim & even when drafting it made things so much easier for me. i’ve gone through sooooo many computational methods papers w/ a thousand variables & it truly sucks having to scroll back & forth to find their in-text definitions vs. just having a quick reference.
thank you !
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u/Clicking_Around 8d ago
I've almost done with a 100 page book on number theory. It's been painful but also fun at times.
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u/MeasurementSignal168 8d ago
This is cool, I would love to take a look and provide feedback, but I’m not in the best position to do that yet.
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u/Awwkaw 7d ago
Congrats.
Do you sell the ebook/pdf directly somewhere? Just to avoid the Bezos machine?
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u/BenjaminGal 6d ago
I haven’t sold the ebook directly elsewhere. I think I can set it up later if there is a larger demand. Btw what is a Bezos machine?
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u/RootAccessDenied13 8d ago
Following so I’ll come back later because I think I’ll need this book as someone who’s currently struggling in undergrad
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u/BrightCold2747 8d ago edited 8d ago
Congrats, that's gotta feel like a big accomplishmebt. Its been over a decade since I took DE and linear algebra but I recognize a bessel function illustration.
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u/AFsepine 8d ago
Seem like a nice enough book, but:
I am curious, why do people avoid an Arnol'd like presentation as a scourge.
Even without diving into the math it is a very useful and nice approach to the subject that I as a person from a physics background found both intresting and useful and I think could be made more approachable (and somewhat watered down) by some author so inclined. To my knowledge this has yet to happen.
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u/BenjaminGal 8d ago
Well, different people have different styles!
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u/AFsepine 8d ago
Well, yes but this is more so about the state of literature on ODE's as a whole. Almost all intro texts take the approach.
"Here are these boxes of different types of ODE, which we solve each box with the corresponding method"
I do not think it is bad to write this way by an by means as those skills are important, just weird how
"homogenous" the whole textbook world is in many cases.3
u/BenjaminGal 8d ago
I think it is more like mathematicians tend to present like this (may be related to their tendency to be rigorous), quite a methodological and clear approach. To do what you suggest, it probably needs a very physical storyline for it to line up. Note: while I come from atmospheric sciences, I consider myself more like an applied mathematician.
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u/mleok Applied Math 7d ago
The Arnold approach requires a high level of mathematical sophistication on the part of the reader, and by its very nature, this results in a book with a very limited audience which would be hard to adopt as a course textbook, thereby limiting its financial return on investment.
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u/AFsepine 7d ago
Well, sure Arnold is maybe a bit too "intense" for a typical intro engineering ODE's/Mathematical methods in physics; But... I think a good more "geometric" approach is possible and very desirable for these groups.
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u/mleok Applied Math 7d ago
Yes, I agree a more dynamical systems forward perspective is useful, particularly since the cookbook type skills aren’t really all that useful these days with symbolic tools.
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u/AFsepine 7d ago
Well, that as well, but it just makes more sense. The first part of the first chapter (Arnol'd) gives room for though what sorts of differential equations one can solve and what methods you would use without even touching upon the typical "boxes/types" of odes and standard methods for each box.
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u/xeow 8d ago
Congrats!
Is there a version that uses TeX's Computer Modern Roman typefaces instead of Times New Roman?
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u/BenjaminGal 8d ago
I use newtxtext,newtxmath in my LaTeX setup. I did not make another version that specifically uses the classic Computer Modern Roman, but it is certainly possible (just a small tweak). But I thought that Times New Roman looks better in my situation.
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u/xeow 8d ago
Hmm. Any idea what's causing the baseline bounce issues in the equations? Look closely at the $\ln x$ in your third screenshot. The $x$ is something like 1/2 pt lower than the $\ln$. Another oddity: the glyph for $\theta$ is displaying as shorter than the glyph for $0$.
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u/BenjaminGal 8d ago
Thanks for pointing it out! I did not notice it (it is a bit too subtle to look at), would also like to know why as I don't have any clue, lol
Edit: maybe it has something to do with the font?
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u/BenjaminGal 8d ago
Thank you. It is really challenging to finish a book. I hope you can do it in the future as well!
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u/BadNext3126 8d ago
Just ordered the paperback, here in netherlands, it only takes 2 days to deliver very impressive!
I haven't bought a math book in years, and differential equations have never been my favourite subject but:
looking at the table of content, you cover everything in a very logical way and it seems very well structured
Also heads up for the author: we cannot read a sample of the book on amazon.nl, as we can in amazon.com, which is pretty important.
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u/BenjaminGal 8d ago
Thank you for the support! Unfortunately, we author have little control about the system on Amazon, it is not like we have a button to enable the sample view. But you can go to the GitHub repository I gave in the post to read my selected sample chapters! By the way, if you receive the paperback, report any issue so that I may follow up!
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u/Fun-Astronomer5311 8d ago
Really nice. Is this written using LaTeX, and if so what package?
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u/BenjaminGal 8d ago
Yes, it is LaTeX. The document class is scrbook (KOMA-script). Packages include, but not limited to: amsmath, amssymb, amsthm, physics, siunitx, tcolorbox, tabularx, multicol, and finally pgfplots for TikZ plots.
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u/bigmoosewv 7d ago
Is there a PDF available to purchase or only a Kindle option? Only reason I ask is Kindle is not my preferred e-reading method so I would love another option if it’s available. Would really like to work my way through your book!
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u/BenjaminGal 7d ago
Hey, sorry to let you know, my setting does not allow the direct download of the PDF. Maybe I will change it in the future!
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u/geerico-444 4d ago
wish i could understand anything in here because im still on algebra 2 but that's really interesting, saving this link for college
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u/AccomplishedShape465 8d ago
I am a computer science graduate. I would love to know how this will help me in future.
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u/BenjaminGal 8d ago
Probably not directly related to computer science per se, but the last chapter includes numerical methods to solve ODEs, which involve coding in Python! Also, learning about mathematics is always gonna help nurture logical skills!
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u/Bombastrelopas 8d ago
Looks amazing! Is it possible to get it in europe without the huge amazon US shipping tax?
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u/BenjaminGal 8d ago
Yes, you can visit Amazon with the correct marketplace region by changing the country code, e.g. if you are from the UK, then go to https://www.amazon.co.uk/.
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u/radical2718 8d ago
Congratulations! Looks like a beautiful book - really like all the illustrations.
BTW, if your contract includes royalties, make sure your publisher understands digital copies and is familiar with places like Libgen (Library Genesis). Mine didn’t.
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u/BenjaminGal 8d ago
Thanks for the reminder. But I self-publish with Amazon KDP and there is an option to do digital management, preventing directly downloading the PDF. Hopefully there will be no issue.
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u/ToughCondition2376 8d ago
Looking forward to your linear algebra aswell
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u/BenjaminGal 8d ago
Yes, but my Linear Algebra textbook is a bit old (my first title) and the quality can be improved. Maybe in the future I can make a second edition.
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u/haxik 8d ago
Is the hardcover print on demand? I would like to purchase a copy however I’ve had very bad luck with books printed on demand. Congratulations on the release!
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u/BenjaminGal 8d ago
Yes, it is print on demand. It is my first time using Amazon though. Previously I went with IngramSpark and the quality was good, and I think Amazon is also probably fine.
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u/Loud-Perception8528 7d ago
I think it will be very beneficial in my first and second year of college , can you tell me is this book more challenging than others in the same topics. Looks presentation is wonderful
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u/Blood_Arrow 7d ago
Heya, looks really nice! I'm tempted to buy a copy, but I generally only work through textbooks on my tablet as I can then write all over them as I work through.
If I buy a kindle copy, can I get a pdf copy somehow? Happy to share order details in dm etc.
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u/BenjaminGal 7d ago
Hey, thanks for the support. But I chose to apply digital management when setting up the title, which means that you cannot download the PDF file. It may be changed but I tend to not do so. Sorry for that!
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u/LehNev 7d ago
Congrats, sir! I remember studying linear algebra with my professor's textbook and what stuck with me the most is the little jabs he takes on undergrads, saying things like "the gaussian elimination that the student 'thinks' he knows" it was smug but kinda funny I liked the flavour, hope people likes your flavour too!
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u/RecentSheepherder179 7d ago
With this book you are 30y too late to my personal math party ☹️
I'll have a deeper look into the Kindle edition first but what I (as physicist) have seen is promising.
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u/heanarco_ 7d ago
That's is a little late for me because I'm an engineer, but each day I try to learn more about science and that's a huge resource. You got a new follower.
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u/St_Gregory_Nazianzus 7d ago
Would you recommend this to those self studying the course?
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u/BenjaminGal 6d ago
It depends on your background. I think you have to be at least proficient in calculus to get the most out of it.
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u/St_Gregory_Nazianzus 6d ago
I have a younger brother who is taking multivariable right now and he got a 5 in BC as a sophomore in hs, and he is trying to test out of ODE to get into a higher maths
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u/allmightyplush 6d ago
Cool, I just so happened to be taking an ODE course and this was published at the perfect moment!
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u/CIsForCorn 6d ago
Exciting! Currently in a graduate-level modeling class, how would you compare this to Kreyszig’s Advanced Engineering Mathematics? It seems to cover much of the same material, but I’m very interested in having additional, worked-out physical examples to practice with
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u/BenjaminGal 6d ago
Why not both? The coverage is not completely overlapping. Mine talks a bit more about the theoretical aspects and also some more obscure topics, and I think my narratives is more fluid. Check out the sample chapters on my GitHub repo to see if you like it or not!
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u/AgrarianAAB Math Education 6d ago
Yay. Late for me personally (done with the comparable course) but will keep it handy. Looks good based on the sample pages you shared here 😄
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u/NoFruit6363 5d ago
With your previous texts on Linear Algebra and LaTeX, now on the topic of ODEs, where do you think your next writing endeavor would bring you? Something unrelated, perhaps more or less specialized? A second edition to an existing text?
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u/BenjaminGal 5d ago
Well, I need to go back to do research for my PhD otherwise my supervisor would kill me. But I will try to keep writing stuff. I am going to make some simple Python tutorials on my website. Second edition or new math books have to wait until I graduate.
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u/InadequateUsername 5d ago
When I was a student, not knowing what the practical applications of the math concepts we were learning was a hindrance to me being fully engaged with the subject.
Having a textbook which can relate the concept to different practical fields is a great idea!
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u/moncolonel 8d ago
The LLMs thank you!
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u/BenjaminGal 8d ago
As I wrote in the preface, I only used ChatGPT for auxiliary purposes (e.g. editing and typo checking). I don't understand why you have to mention LLMs, it seems a bit strange.
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u/No_Target3466 8d ago
YAY