Reddit Reddit reviews Ordinary Differential Equations (Dover Books on Mathematics)

We found 32 Reddit comments about Ordinary Differential Equations (Dover Books on Mathematics). Here are the top ones, ranked by their Reddit score.

Science & Math
Books
Mathematics
Differential Equations
Applied Mathematics
Ordinary Differential Equations (Dover Books on Mathematics)
an elementary college textbook for students of math, engineering and the sciences in general
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32 Reddit comments about Ordinary Differential Equations (Dover Books on Mathematics):

u/Lhopital_rules · 64 pointsr/AskScienceDiscussion

Here's my rough list of textbook recommendations. There are a ton of Dover paperbacks that I didn't put on here, since they're not as widely used, but they are really great and really cheap.

Amazon search for Dover Books on mathematics

There's also this great list of undergraduate books in math that has become sort of famous: https://www.ocf.berkeley.edu/~abhishek/chicmath.htm

Pre-Calculus / Problem-Solving

u/M_from_Austin · 12 pointsr/learnmath

Ordinary Differential Equations from the Dover Books on Mathematics series. I Just took my final for Diff Eq a few days ago and the book was miles better than the one my school suggested and is the best written math textbook I have encountered during my math minor. My Diff Eq course only covered about the first 40% of the book so there's still a TON of info that you can learn or reference later. It is currently $14 USD on amazon and my copy is almost 3" thick so it really is a great deal. A lot of the reviewers are engineering and science students that said the book helped them learn the subject and pass their classes no problem. Highly Highly recommend. ISBN-10: 9780486649405

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https://www.amazon.com/gp/product/0486649407/ref=ppx_yo_dt_b_asin_title_o08_s00?ie=UTF8&psc=1

u/CoreyN · 8 pointsr/math

Tenenbaum and Pollard's ODE book made the subject come quite easily when all my $150 textbook did was confuse me.

u/dargscisyhp · 7 pointsr/AskScienceDiscussion

I'd like to give you my two cents as well on how to proceed here. If nothing else, this will be a second opinion. If I could redo my physics education, this is how I'd want it done.

If you are truly wanting to learn these fields in depth I cannot stress how important it is to actually work problems out of these books, not just read them. There is a certain understanding that comes from struggling with problems that you just can't get by reading the material. On that note, I would recommend getting the Schaum's outline to whatever subject you are studying if you can find one. They are great books with hundreds of solved problems and sample problems for you to try with the answers in the back. When you get to the point you can't find Schaums anymore, I would recommend getting as many solutions manuals as possible. The problems will get very tough, and it's nice to verify that you did the problem correctly or are on the right track, or even just look over solutions to problems you decide not to try.

Basics

I second Stewart's Calculus cover to cover (except the final chapter on differential equations) and Halliday, Resnick and Walker's Fundamentals of Physics. Not all sections from HRW are necessary, but be sure you have the fundamentals of mechanics, electromagnetism, optics, and thermal physics down at the level of HRW.

Once you're done with this move on to studying differential equations. Many physics theorems are stated in terms of differential equations so really getting the hang of these is key to moving on. Differential equations are often taught as two separate classes, one covering ordinary differential equations and one covering partial differential equations. In my opinion, a good introductory textbook to ODEs is one by Morris Tenenbaum and Harry Pollard. That said, there is another book by V. I. Arnold that I would recommend you get as well. The Arnold book may be a bit more mathematical than you are looking for, but it was written as an introductory text to ODEs and you will have a deeper understanding of ODEs after reading it than your typical introductory textbook. This deeper understanding will be useful if you delve into the nitty-gritty parts of classical mechanics. For partial differential equations I recommend the book by Haberman. It will give you a good understanding of different methods you can use to solve PDEs, and is very much geared towards problem-solving.

From there, I would get a decent book on Linear Algebra. I used the one by Leon. I can't guarantee that it's the best book out there, but I think it will get the job done.

This should cover most of the mathematical training you need to move onto the intermediate level physics textbooks. There will be some things that are missing, but those are usually covered explicitly in the intermediate texts that use them (i.e. the Delta function). Still, if you're looking for a good mathematical reference, my recommendation is Lua. It may be a good idea to go over some basic complex analysis from this book, though it is not necessary to move on.

Intermediate

At this stage you need to do intermediate level classical mechanics, electromagnetism, quantum mechanics, and thermal physics at the very least. For electromagnetism, Griffiths hands down. In my opinion, the best pedagogical book for intermediate classical mechanics is Fowles and Cassidy. Once you've read these two books you will have a much deeper understanding of the stuff you learned in HRW. When you're going through the mechanics book pay particular attention to generalized coordinates and Lagrangians. Those become pretty central later on. There is also a very old book by Robert Becker that I think is great. It's problems are tough, and it goes into concepts that aren't typically covered much in depth in other intermediate mechanics books such as statics. I don't think you'll find a torrent for this, but it is 5 bucks on Amazon. That said, I don't think Becker is necessary. For quantum, I cannot recommend Zettili highly enough. Get this book. Tons of worked out examples. In my opinion, Zettili is the best quantum book out there at this level. Finally for thermal physics I would use Mandl. This book is merely sufficient, but I don't know of a book that I liked better.

This is the bare minimum. However, if you find a particular subject interesting, delve into it at this point. If you want to learn Solid State physics there's Kittel. Want to do more Optics? How about Hecht. General relativity? Even that should be accessible with Schutz. Play around here before moving on. A lot of very fascinating things should be accessible to you, at least to a degree, at this point.

Advanced

Before moving on to physics, it is once again time to take up the mathematics. Pick up Arfken and Weber. It covers a great many topics. However, at times it is not the best pedagogical book so you may need some supplemental material on whatever it is you are studying. I would at least read the sections on coordinate transformations, vector analysis, tensors, complex analysis, Green's functions, and the various special functions. Some of this may be a bit of a review, but there are some things Arfken and Weber go into that I didn't see during my undergraduate education even with the topics that I was reviewing. Hell, it may be a good idea to go through the differential equations material in there as well. Again, you may need some supplemental material while doing this. For special functions, a great little book to go along with this is Lebedev.

Beyond this, I think every physicist at the bare minimum needs to take graduate level quantum mechanics, classical mechanics, electromagnetism, and statistical mechanics. For quantum, I recommend Cohen-Tannoudji. This is a great book. It's easy to understand, has many supplemental sections to help further your understanding, is pretty comprehensive, and has more worked examples than a vast majority of graduate text-books. That said, the problems in this book are LONG. Not horrendously hard, mind you, but they do take a long time.

Unfortunately, Cohen-Tannoudji is the only great graduate-level text I can think of. The textbooks in other subjects just don't measure up in my opinion. When you take Classical mechanics I would get Goldstein as a reference but a better book in my opinion is Jose/Saletan as it takes a geometrical approach to the subject from the very beginning. At some point I also think it's worth going through Arnold's treatise on Classical. It's very mathematical and very difficult, but I think once you make it through you will have as deep an understanding as you could hope for in the subject.

u/gerschgorin · 6 pointsr/math

An Introduction to Ordinary Differential Equations - $7.62

Ordinary Differential Equations - $14.74

Partial Differential Equations for Scientists and Engineers - $11.01

Dover books on mathematics have great books for very cheap. I personally own the second and third book on this list and I thought they were a great resource, especially for the price.

u/Banach-Tarski · 5 pointsr/Physics

Learn math first. Physics is essentially applied math with experiments. Start with Calculus then Linear Algebra then Real Analysis then Complex Analysis then Ordinary Differential Equations then Partial Differential Equations then Functional Analysis. Also, if you want to pursue high energy physics and/or cosmology, Differential Geometry is also essential. Make sure you do (almost) all the exercises in every chapter. Don't just skim and memorize.

This is a lot of math to learn, but if you are determined enough you can probably master Calculus to Real Analysis, and that will give you a big head start and a deeper understanding of university-level physics.

u/[deleted] · 4 pointsr/math

I got Ordinary Differential Equations by Tenenbaum and Pollard. This was a book I saw get thrown around as a great self-study book. I have to say it's great because nearly all the answers to problems are provided.

Link: http://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407

u/commutant · 3 pointsr/math

The second book that gerschgorin listed is very good, though a little old fashioned.

Since you are finishing up your math major, I'd recommend Hirsch & Smale & Devaney, an excellent book if you have a little bit of mathematical background.

There is also a video series I'm making meant to be a quick overview of many of the key topics. Maybe useful, maybe not. Also, the MIT lectures are excellent.

u/DomMk · 3 pointsr/math

I used Tenenbaum. One of my favorite undergrad books. Only downside that it doesn't use any Linear Algebra

u/BattleFriendly · 3 pointsr/EngineeringStudents

Definitely split up the load and take classes over the summer. I often hear people say Calculus II is the hardest of the EPIC MATH TRILOGY. I certainly agree. If you've done well in Calc I and II and have a notion of what 3d vectors are (physics should of covered this well) then you'll have no problem with Calc III (though series' and summations can be tough).

Differential equations will be your first introduction to hard "pure"-style math concepts. The language will take some time to understand and digest. I highly recommend you purchase this book to supplement your textbook. If you take notes on each chapter and work through the derivations, problems, and solutions, you'll be golden.

In my experience, materials is not math heavy for ME's. All of my tests were multiple choice and more concept based. It's not too bad.

Thermodynamics and Engineering Dynamics will be in the top three as far as difficulty goes. Circuits or Fluids will also be in there somewhere. Make sure you allow plenty of time to study these topics.

Good luck!

u/misplaced_my_pants · 3 pointsr/math

Some possibilities:

Calc I & II: Spivak's Calculus

Calc III and a bit of linear algebra: Hubbard & Hubbard's Vector Calculus

LA: Axler or Shilov or both

ODE: Morris Tanenbaum


Discrete/Combinatorics/etc.: Knuth's Concrete Mathematics

For book suggestions beyond concerning Analysis, Algebra, and Topology, the search box will turn up a ton of previous conversations.

u/EulerANDBernoulli · 3 pointsr/math
u/beaverteeth92 · 3 pointsr/math

I'm a particular fan of Tenenbaum and Pollard. It's both really well-explained and cheap.

u/brickrickslick · 2 pointsr/EngineeringStudents

The one and only , if you're willing to dedicate the time

Ordinary Differential Equations (Dover Books on Mathematics)
https://www.amazon.com/dp/0486649407/

u/solve-for-x · 2 pointsr/math

With regards to your edit, if your friend is still incarcerated after reading his calculus text, send him Ordinary Differential Equations by Tenenbaum and Pollard. It contains zillions of worked problems showing how ODEs can be applied to physical problems.

u/0xd4e · 2 pointsr/EngineeringStudents

I've used Tenenbaum to teach myself ODEs. Got an A in my class. Arnold is cannon, but you need mathematical maturity so YMMV.

u/captainmeanyface · 2 pointsr/learnmath

Aye, I hate that book. I liked This one much better. I feel like the worse fad in math text books is trying to make them "more conversational." In my experience, more conversational = convoluted.

u/Periflux · 2 pointsr/EngineeringStudents

http://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407/ref=mt_paperback?_encoding=UTF8&me=

Stay away from Youtube and Khan Academy unless you need reinforcement on a specific topic. Go through this book, page by page, learn the material, and do every problem.

u/jnethery · 2 pointsr/funny

15! Well then, you have plenty of time to figure this out. Well, a few years, in any case.

I think what you should do is learn some programming as soon as possible (assuming you don't already). It's easy, trust me. Start with C, C++, Python or Java. Personally, I started with C, so I'll give you the tutorials I learned from: http://www.cprogramming.com/tutorial/c/lesson1.html

You should also try out some electronics. There's too much theory for me to really explain here, but try and maybe get a starter's kit with a book of tutorials on basic electronics. Then, move onto some more complicated projects. It wouldn't hurt to look into some circuit theory.

For mechanical, well... that one is kind of hard to get practical experience for on a budget, but you can still try and learn some of the theory behind it. Start with learning some dynamics and then move onto statics. Once you've got that down, try learning about the structure and property of materials and then go to solid mechanics and machine design. There's a lot more to mechanical engineering than that, but that's a good starting point.

There's also, of course, chemical engineering, civil engineering, industrial engineering, aerospace engineering, etc, etc... but the main ones I know about are mechanical (what I'm currently studying), electrical and computer.

Hope this helped. I wasn't trying to dissuade you from pursuing engineering, but instead I'm just forewarning you that a lot of people go into it with almost no actual engineering skills and well, they tend to do poorly. If you start picking up some skills now, years before college, you'll do great.

EDIT: Also, try learning some math! It would help a lot to have some experience with linear algebra, calculus and differential equations. This book should help.

u/greatBigDot · 2 pointsr/math

Ordinary Differential Equations by Tenenbaum and Pollard is a classic. I thought it explained things well and was more rigorous than some other treatments of subject that I've come across.

u/B-80 · 2 pointsr/math

There seems to often be this sort of tragedy of the commons with the elementary courses in mathematics. Basically the issue is that the subject has too much utility. Be assured that it is very rich in mathematical aesthetic, but courses, specifically those aimed at teaching tools to people who are not in the field, tend to lose that charm. It is quite a shame that it's not taught with all the beautiful geometric interpretations that underlie the theory.

As far as texts, if you like physics, I can not recommend highly enough this book by Lanczos. On the surface it's about classical mechanics(some physics background will be needed), but at its heart it's a course on dynamical systems, Diff EQs, and variational principles. The nice thing about the physics perspective is that you're almost always working with a physically interpretable picture in mind. That is, when you are trying to describe the motion of a physical system, you can always visualize that system in your mind's eye (at least in classical mechanics).

I've also read through some of this book and found it to be very well written. It's highly regarded, and from what I read it did a very good job touching on the stuff that's normally brushed over. But it is a long read for sure.

u/SoTopological · 2 pointsr/learnmath

I've never really used MIT OCW however I've used Paul's OMN a lot back when I was studying multivar calc. I do recommend books, though. I have books both on multivar calc and differential equations and they're both well, however, I've moved on from calculus (that is, I don't actively study it anymore) so I can't really say much more.


The books I have:

> https://www.amazon.com/Multivariable-Calculus-Clark-Bray/dp/1482550741/ref=sr_1_3?s=books&ie=UTF8&qid=1500976188&sr=1-3&keywords=multivariable+calculus

> https://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407/ref=sr_1_1?s=books&ie=UTF8&qid=1500976233&sr=1-1&keywords=differential+equations

u/Yuushi · 2 pointsr/learnmath

For ODEs, I'd seriously suggest buying this. Lots and lots of exercises, and full solutions. Plus, at $15, it hopefully won't break the bank too badly.

u/kem3 · 1 pointr/EngineeringStudents

I had a hard time getting through dif eq also, because the book was unreadable (to me). I also hate reading anything by Hibbler. The Munson fluid mechanics book is... barely tolerable. When that happens, I tend to look, with more vigor than usual, for other sources. Dif eq: I was lucky, and our tutoring center has dif eq tutors. Fluids: I found a wonderful lecture series done by UC Irvine OpenCourseWare. Hibbler... well, I've been S.O.L. on that so far. Generally, I also try to find a solutions manual. If I'm having a terrible time with a problem, I work through it and check myself each step of the way. I often try to find a different book, too. The only reason you need the required book is so you know what to look for in your chosen book.

I recently discovered there is a very highly-rated dif eq book available used on Amazon for about $13, so I ordered it in the hopes that it will be readable, as I now need to brush up on dif eq and can't stand the book we used in class.

u/freyrs3 · 1 pointr/math

For DEs try:
Ordinary Differential Equations by Tennenbaum

Its a great book with a TON of worked examples and solutions to all the exercises. This text was my holy book during my undergrad engineering courses.

u/HigherMathHelp · 1 pointr/math

LIST OF APPLICATIONS IN MY DIFF EQ PLAYLIST
Have you seen the first video in my series on differential equations?

I'm still working on the playlist, but the first video lists a bunch of applications that you might not have seen before. My goal was to provide a sample of the diversity of applications outside of mathematics, and I chose fairly concrete examples that include applications in engineering.

I don't go into any depth at all regarding any of the particular applications (it's just a short introductory video), but you might find the brief introduction to be helpful.

If you find any one of the applications interesting, then a Google search will reveal more detailed resources.

A COUPLE OF FREE OR INEXPENSIVE BOOKS
Also, off the top of my head, the books below have quite a few applications that you might not see in the more standard textbooks.

  • Differential Equations and Their Applications: An Introduction to Applied Mathematics, Martin Braun (Amazon, PDF)
  • Ordinary Differential Equations, Morris Tenenbaum and Harry Pollard (Amazon)

    I think you can find other legal PDFs of Braun's third edition, too. Pollard and Tenenbaum is an inexpensive paperback from Dover, and I actually found a copy at my local library.

    ENGINEERING BOOKS
    Of course, the books I listed are strictly devoted to differential equations, but you can find other applications if you look for books in engineering. For example, I used differential equations in a course on signals and systems that I tutored last semester (applications included electrical circuits and mass-spring-damper systems).

    NEAT VIDEO (SOFT BODY MODELING)
    By the way, here's a cool video of various soft body simulations based on mass-spring-damper systems modeled by differential equations.

    Here's a Wikipedia article on soft body dynamics. This belongs to the field of computer graphics, so I'm not sure if you're interested, but mass-spring-damper systems come up a fair amount in engineering courses, and this is an application of those ideas that might open your mind a bit to other possible applications.

    Edit: typo
u/lordpie314 · 1 pointr/NoStupidQuestions

That helps a little. I'm not too familiar with that world (I'm a physics major), but I took a look at a sample civil engineering course curriculum. If you like learning but the material in high school is boring, you could try self-teaching yourself basic physics, basic applied mathematics, or some chemistry, that way you could focus more on engineering in college. I don't know much about engineering literature, but this book is good for learning ODE methods (I own it) and this book is good for introductory classical mechanics (I bought and looked over it for a family member). The last one will definitely challenge you. Linear Algebra is also incredibly useful knowledge, in case you want to do virtually anything. Considering you like engineering, a book less focused on proofs and more focused on applications would be better for you. I looked around on Amazon, and I found this book that focuses on applications in computer science, and I found this book focusing on applications in general. I don't own any of those books, but they seem to be fine. You should do your own personal vetting though. Considering you are in high school, most of those books should be relatively affordable. I would personally go for the ODE or classical mechanics book first. They should both be very accessible to you. Reading through them and doing exercises that you find interesting would definitely give you an edge over other people in your class. I don't know if this applies to engineering, but using LaTeX is an essential skill for physicists and mathematicians. I don't feel confident in recommending any engineering texts, since I could easily send you down the wrong road due to my lack of knowledge. If you look at an engineering stack exchange, they could help you with that.

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You may also want to invest some time into learning a computer language. Doing some casual googling, I arrived at the conclusion that programming is useful in civil engineering today. There are a multitude of ways to go about learning programming. You can try to teach yourself, or you can try and find a class outside of school. I learned to program in such a class that my parents thankfully paid for. If you are fortunate enough to be in a similar situation, that might be a fun use of your time as well. To save you the trouble, any of these languages would be suitable: Python, C#, or VB.NET. Learning C# first will give you a more rigorous understanding of programming as compared to learning Python, but Python might be easier. I chose these three candidates based off of quick application potential rather than furthering knowledge in programming. This is its own separate topic, but my personal two cents are you will spend more time deliberating between programming languages rather than programming if you don't choose one quickly.

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What might be the best option is contacting a professor at the college you will be attending and asking for advice. You could email said professor with something along the lines of, "Hi Professor X! I'm a recently accepted student to Y college, and I'm really excited to study engineering. I want to do some rigorous learning about Z subject, but I don't know where to start. Could you help me?" Your message would be more formal than that, but I suspect you get the gist. Being known by your professors in college is especially good, and starting in high school is even better. These are the people who will write you recommendations for a job, write you recommendations for graduate school (if you plan on it), put you in contact with potential employers, help you in office hours, or end up as a friend. At my school at least, we are on a first name basis with professors, and I have had dinner with a few of mine. If your professors like you, that's excellent. Don't stress it though; it's not a game you have to psychopathically play. A lot of these relationships will develop naturally.

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That more or less covers educational things. If your laziness stems from material boredom, everything related to engineering I can advise on should be covered up there. Your laziness may also just originate from general apathy due to high school not having much impact on your life anymore. You've submitted college applications, and provided you don't fail your classes, your second semester will probably not have much bearing on your life. This general line of thought is what develops classic second semester senioritis. The common response is to blow off school, hang out with your friends, go to parties, and in general waste your time. I'm not saying don't go to parties, hang out with friends, etc., but what I am saying is you will feel regret eventually about doing only frivolous and passing things. This could be material to guilt trip yourself back into caring.

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For something more positive, try to think about some of your fun days at school before this semester. What made those days enjoyable? You could try to reproduce those underlying conditions. You could also go to school with the thought "today I'm going to accomplish X goal, and X goal will make me happy because of Y and Z." It always feels good to accomplish goals. If you think about it, second semester senioritis tends to make school boring because there are no more goals to accomplish. As an analogy, think about your favorite video game. If you have already completed the story, acquired the best items, played the interesting types of characters/party combinations, then why play the game? That's a deep question I won't fully unpack, but the simple answer is not playing the game because all of the goals have been completed. In a way, this is a lot like second semester of senior year. In the case of real life, you can think of second semester high school as the waiting period between the release of the first title and its sequel. Just because you are waiting doesn't mean you do nothing. You play another game, and in this case it's up to you to decide exactly what game you play.

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Alternatively, you could just skip the more elegant analysis from the last few paragraphs and tell yourself, "If I am not studying, then someone else is." This type of thinking is very risky, and most likely, it will make you unhappy, but it is a possibility. Fair warning, you will be miserable in college and misuse your 4 years if the only thing you do is study. I guarantee that you will have excellent grades, but I don't think the price you pay is worth it.

u/Chade_Fallstar · 1 pointr/learnmath

Tenenbaum and Pollard's book is fine. It is cheap too (published by Dover methinks)
https://www.amazon.com/Ordinary-Differential-Equations-Dover-Mathematics/dp/0486649407

u/ThroughTheForests · 1 pointr/math
u/wowSuchPotato · 1 pointr/getdisciplined

General Advice

  • Try to put in a consistent amount of work daily.
  • Make sure you're doing exercises (not just reading watching videos)

    Specific Advice

  • Videos/Course: MIT Calculus Course. Watch the videos, supplement with notes if you need to. Do the assignments and check your solutions. Work towards getting passing grades in the exams. It's not important to get this done before college, just work on it and you will be more prepared.
  • ODE Textbook: Love this book, working my way through it now, not sure if a better ODE book exists. It's also fairly simple but you might want to do some work on the MIT course first. It's not legally free, but...


u/ndat · 1 pointr/webdev

I just bought this for $10. Not all textbook companies are jokes. Just most.