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Need a more pedagogic book than Halliday's

  1. Jun 13, 2016 #1
    Can anyone please recommend a more pedagogic book than Halliday's Fundamentals of Physics?

    As a hobby I want to learn QM, so started reading math from scratch three months ago. In order to get a quick overview I just read the curriculum from middle school through high school and has now finished all the lectures of the most demanding beginner's course in calculus at the University of Oslo. But have so far little practice in actively solving particular math assignments. My passive understanding of the general explanations of calculus is relatively good though, which means that I understand all the logical steps explained in the books and lectures.

    With no prior knowledge about physics I need a good book which provides logical step-by-step explanations of how calculus equations are applied and related to dynamic phenomena in the real world. Explanations which include pictures or drawings that will give an intuitive and visual understanding of this relation.

    I read fast and learn quickly if I just see the logic of things, so don't mind if a physics book has 3000 pages or more as long as all the calculus explanations in it secure a steady and relatively quick progress.

    Halliday's book seems okay in one way, but the first chapter about velocity and acceleration does not provide thorough explanations. It's very short, and I don't see how one can use it to solve all the problems in the back of this chapter.

    Have noticed in several math and physics books that some things, that are often basic, are explained really well, but in between there are also explanations (of difficult things) which skip several steps in how a conclusion is reached. This is probably done because the author(s) assume that the reader has prior knowledge, but when I'm reading an introductory book I want to see all the steps from the basic premises to the conclusion. So is there a calculus-based physics book which does that?

    Btw, I know that I must use a lot of time on actively solving particular math problems, so I will do this too, but I'm only learning physics as a hobby, and only started with math three months ago, so it would be nice to know if there is a pedagogic physics book which I can read now without having much training so far in actively solving specific math assignments. Then I can practice on the way, after the book has thorougly explained how to solve particular calculus equations in relation to physics.

    Also know that my path so far has been a bit unusual, because I have almost speed read all the general math explanations without actively solving particular equations yet, but my initial goal is just to get an overview of math and physics, in order to check if I have the necessary IQ to at least get a passive understanding of math at a university level required before studying quantum physics. I don't have much self-confidence regarding math, so didn't want to waste time on it if I didn't even understand the general explanations of it at a university level beginner's course. Now it will be even more motivating to learn math if it is related directly to calculus-based physics, so hope someone has written a book that can be helpful on this track.
  2. jcsd
  3. Jun 13, 2016 #2


    Staff: Mentor

    Last edited by a moderator: May 8, 2017
  4. Jun 13, 2016 #3


    Staff: Mentor

    Passive reading is not a good strategy. To learn the mathematics, you need to do lots of problems.
    I don't believe there are any physics books like this
    As far as I know, there aren't any books like this. A calculus-based physics books presumes that you are knowledgeable in calculus.
    Speed reading mathematics is not a good strategy.
  5. Jun 13, 2016 #4
    Thanks for replies! I will check out Susskind :)

    Regarding the second reply I had hoped that my rather thorough text would have clearly shown that I am well aware that "speed reading" math is not a useful strategy in the long run, but I had virtually no knowledge of math prior to March this year, so I decided to take a relatively quick first run at it, to get an indication of how far my IQ would take me up the increasingly steep math slope, in order to see if I would meet any insurmountable obstacles on the level of just understanding the logic of the general explanations of calculus. So far this has not been a problem. So I will return to scratch again and start actively solving particular equations.

    The above path is unusual, but it took only three months to get an overview which covers both high school math and a university beginner's course in calculus. If one has no self-confidence when it comes to learning math, and have no hurry to learn it, then I will actually recommend this path initially, because one will notice that the general principles and explanations of math are not that difficult, even at a first year university course. That in itself will restore much lost confidence in anyone who thinks he or she is a loser in math, presupposing that one has found math books, lectures and online courses which have good teachers who understand the art of teaching.

    Similarily, I am looking for a high school physics book written by a good teacher.
  6. Jun 13, 2016 #5


    Staff: Mentor

    Based on what you wrote in the first post, it didn't seem to me that you had a very firm grasp on introductory calculus.
    The problems about velocity and acceleration presume some knowledge about how to differentiate an expression, and possibly how to find the antiderivative of an expression. Halliday and Resnick is a staple in university engineering physics courses, and has been in use, with multiple editions, since the 60's or so.

    There are physics textbooks out there that don't require calculus.
    Last edited: Jun 13, 2016
  7. Jun 13, 2016 #6
    After only three months of math it is difficult to store, through deep understanding, all the calculus rules in the long-term memory of the brain, so I consider myself a newbie in the field of math, of course.

    But I was surprised how easy it was to follow the logic of calculus when the teacher at the University of Oslo didn't skip steps. However, there is a big difference between 1) passively understanding the general rules of math when a good teacher shows you all the logical steps, and 2) actively applying these rules to a particular problem, because then one must know which rules to pick up among a myriad of rules, and know how to translate a textual problem into a mathematical equation. But just having a passive, and thereby superficial, understanding of first year university math has at least restored much of my confidence that it is worth spending more time on this hobby, and learn it the proper way, through active problem solving.

    Hope to find a physics book written by an author who is equally pedagogical as the excellent teachers who have taught me math. But perhaps that is too much to ask? The Sussskind lectures look very promising though. Downloading it on iTunes U now. And if I don't find a suitable physics book on the level of calculus now, then I just have to start with a pre-calculus book, like everyone else who is new to physics :)
  8. Jun 14, 2016 #7

    Vanadium 50

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    Your problem is simple. You're not learning the math, and that's keeping you from learning the physics. You're not learning the math because you've found a resource that lets you think you've understood it without putting the necessary effort in. Now you want something similar for physics. I don't think such a thing exists, and I don't think it would help you if it did. You need to slow down, roll up your sleeves, and start working on problems.
    Last edited: Jun 14, 2016
  9. Jun 14, 2016 #8
    As stated several times, l'm aware that my understanding of math is superficial, which is not surprising since I have only studied it the last three months. Many math students have in common that they think they have understood a lecture or a chapter in a math book, only to discover that they are not able to solve the related math problems on their own, unless they spend much time on it.

    But I will still claim that many math and physics books are not written in a pedagogic way. For example, the first chapter in Halliday's book is full of trivia, but in the second chapter he throws equations at you and rewrites them without explaining them properly or providing much context. If he had been a good teacher he would have skipped the trivia and used these pages on thoroughly explaining that which is difficult, by using more examples and showing the reader when to use each equation. It's also not helpful that he just refers to equations mentioned several pages ago, so that the reader must look back and forth in the book to see what he is talking about.

    Similarily, Susskind spends almost an hour in his first lecture on thoroughly explaining basic things. It was boring. He even apologizes to his students for spending time on easy stuff they already know. But then suddenly he presents a much more difficult equation and says that those students who didn't understand what he just said, should go home afterwards and figure it out themselves. There and then he failed his mission as a teacher.

    I have had good teachers, so I know that math can be explained in a pedagogic way. But so far my subjective impression is that many math and physics teachers/authors seem to know so little about "theory of mind" that one is tempted to think that they are almost on the autism spectrum.

    It seems more likely, however, that there is a more or less prevalent attitude in the math and physics community that being pedagogic is almost the same as "spoon-feeding" and "holding the hands" of students who are too lazy or stupid to "put in the hard work".

    In one way I get this rather elitist attitude, because if you want to become a professional engineer, for example, you will remember things better if you have really struggled to solve a problem on your own, without much help.

    From this perspective one may actually be considered a good teacher if one just throws students in the water and let them swim. It's "tough love" and "the Zen master with a bamboo stick". It's a good way to quickly see who has the right stuff to become a professional.

    But please understand that all the rest of us, who are studying math and physics as a hobby, on our spare time, will get frustrated if it's really true that there are almost no books which can fill the gap between "popular science" and hardcore physics books.

    This is the Internet, so expect that perhaps some may reply with comments like "Oh, cry me river!" But relax, I will do the hard work. Have the academic discipline to do that. But have read advanced commentaries on Kant, Heidegger and Levinas, for example, which are written in a much more pedagogic way than high school math books used by teachers in my own country, Norway. And that's a problem if one of the goals is to increase scientific awareness in the general population.

    Fortunately, there are many online resources today that can help students if they don't understand a cryptic book or teacher. These resources are amazing. Truly grateful that they exist.
  10. Jun 14, 2016 #9


    Staff: Mentor

    The operative statement here is, "they think they have understood..."
    I have a copy of Halliday and Resnick, "Physics, Parts I and II," Second Printing, 1967. I used this book in a year-long sequence of engineering physics courses. There have been a number of editions since then, so the book you're referring to is likely a much newer version than the one I have. In my version, the first chapter is titled "Measurement," and is only about a dozen pages. The second chapter is titled "Vectors," and isn't much longer.

    Can you give an example of the equations that are thrown at you in Ch. 2 of your book?

    As far as not being written in a pedagogic way, I disagree. In the preface of my book it says
    It seems clear to me that the intended audience for this book is not people who have at most a limited mathematical background.
    As I mentioned before, there are physics textbooks that are geared for students who are not taking calculus. Such books are sometimes referred to disparagingly as "Physics for Poets." Given that the level of H & R is explicitly stated in the preface, it does not seem reasonable to me to expect such a book to show the steps in solving every equation to the level of a beginning student in algebra.
    The alternative would be to never refer to a previously written equation, but instead write it again. The book I have is 1214 pages, plus about 100 pages in supplementary topics and appendices. It's already quite thick; to reprint each previously written equation would necessarily add to the bulk of this book, which would make it more costly to print. If your plan is to study advanced physics (and the prerequisite math needed to understand the physics), you're going to find that virtually every book refers to previously discussed equations, usually by a number.
    Are you referring to the online videos that jedishrfu cited, on Quantum Mechanics? If so, this is not an easy subject, and there are many prerequisite concepts in mathematics and physics that have to be mastered before understanding QM. Without that prerequisite knowledge, it is unreasonable for a student to expect to be able to understand.
    What many students don't realize is that mathematics is hierarchical in nature, with arithmetic at the lowest level, and with geometry and algebra at a somewhat higher level, and trigonometry higher yet, and so on, up through calculus, differential equations, linear algebra, and many other areas of more advanced mathematics. A student who doesn't understand arithmetic has no hope of understanding algebra. In the same vein, a student who doesn't have a firm grasp on algebra will not be able to understand trig or calculus.

    What you're suggesting here in your description of pedagogy seems to me to be saying that every algebra textbook should start off with a complete discourse on arithmetic, every calculus book should include complete presentations of arithmetic and algebra, and in short, every mathematics textbook should include complete presentations of whatever foundational mathematics comes before it. That seems eminently unreasonable to me.
    From Wikipedia (https://en.wikipedia.org/wiki/Royal_Road),
    IMO there's a world of difference between books on philosophy and books on mathematics or any of the sciences.
  11. Jun 14, 2016 #10
    Hi, thanks for reply! :)

    Books have different audiences, but I read that Halliday could be used by high school students, so I started reading it, found it to be somewhat on a level beyond my knowledge, so came here to ask if anyone can recommend a good high school physics book which includes basic derivation and integration. If I myself had been clearer, more pedagogic so to speak, I would have stressed in my first post that l'm simply looking for an easier book than Halliday's, a book that average high school students can read. Then I can read that while also working on math problems.

    Anyway, as a noob I have to be humble when judging Halliday's book. I never expected that the book should explain everything all the way back to basic algebra. But the book so far has a mix of easy stuff and difficult things that are not explained. I guess that it's this mix that has given me an inadequate idea about what I can expect from it. I'm like: "Why waste space on presenting and explaining the easy stuff when the same pages could have been used to properly explain that which is difficult?" Of course, one answer is that Halliday is also a reference book it seems, and then it makes more sense. I accept that, but then I need another physics book which includes basic calculus.

    The Susskind lecture was the first intro to classical mechanics. Halliday now has a new chapter two, about motion. Here is a photo of five equations which are presented without properly explaining when one should use each of them, as seen for example in the section above Eq 2-16:


    I'm not looking for any royal road, only a book that explain things in a logical way, step-by-step, with enough examples and drawings to visualise the dynamics of physics. Besides philosophy I have studied neuroscience, law, psychology and political science, and all the university textbooks I have read are more pedagogic than the high school math books I have used. However, don't get me wrong, I'm genuinely impressed by those who have the IQ to be professional physicists, but want to be part of the fun and therefore prefer books that make it as simple as possible, but not simpler.
  12. Jun 14, 2016 #11
    HRW is a good introduction. What you need is a calculus text to work through before/concurrently.
  13. Jun 14, 2016 #12
    But is there a better calculus-based physics book for high school students than HRW (by which I assume you mean their book Fundamentals of Physics)?
  14. Jun 14, 2016 #13


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    I will suggest a couple of books for you.
    Physics the Easy Way: It is a fairly easy Physics paperback workbook.
    Physics for Dummies (any /all of them): You can work through one of these paperbacks fairly easily.
    Physics Demystified (other titles too ie Modern): Similar to Physics for Dummies, but sounds better.
    or The High School edition of the text you now are using (buy an older edition to save money)
    Or buy another author's text (again an older edition, as you will find them much less)
    You might even buy some home school edition science books (beware, some are worse than not reading at all!): I won't even comment other than saying these books exist and are as pedagogico_O as you desire.
    If you manage to read and finish any of the above with proper understanding, you will have gained approximately the understanding of a first year freshman student in a physics 1 course and quite possibly a good understanding or at least a good portion of a physics II. However, whenever someone decides to self educate themselves, they have to be aware that there is the possibility that they could have just as easily mislead themselves as well. That is the caution and red flags many of the previous posters are trying to get across to you about your wants for a "Royal Road" to Physics. None of us have found it.
  15. Jun 14, 2016 #14
    Halliday and Resnick is the best book you can find. Seriously, you can't do the physics without first understanding the math 100%. So start now by seriously working through the math and only THEN can you do the physics.
  16. Jun 14, 2016 #15
    In high school one reads math and physics at the same time, so why not learn it simultaneously? I could just buy a Norwegian high school book about physics, but they are expensive and have a not so good reputation. Prefer an introductory book in English since all the advanced books are in English.

    Read a bit more in Halliday and the first pages about vectors are just basic stuff, like covering high school algebra. In this chapter he even has several illustrations of all the easy things. But expect that he soon will present a difficult equation without explaining it thoroughly. It's like climbing a mountain with a guide that helps you through the easy areas but then let you hang on a cliff wall. That develops strength which is good if you want to become a professional, but it's just annoying if you want to have math and physics as a hobby.

    But no worries really, just have to postpone reading Halliday until I have solved a ton of math problems. Never expected to avoid intense problem solving anyway :)
  17. Jun 14, 2016 #16
    Seeing these five equations just written out(along with definitions of the variables, which are indeed present on that page) should be more than enough of a proper explanation. The fact that you think it isn't says to me that you need to work out a lot of applied algebra practice problems. If your pre-college algebra skills were honed, you'd probably think that page was too wordy, if anything.

    You need to work lots of algebra problems for yourself, then work some basic calculus problem sets. Get used to how variables interact in equations, how to rearrange an equation using the rules of algebra.
  18. Jun 14, 2016 #17
    After having studied math for only three months, just to get an overview, I definitely need a lot of active problem solving in algebra, and the rest. Will start with that now.

    However, when Halliday spends pages on illustrating basic vector rules and have pictures of other trivial things, why couldn't he have used that space to provide illustrations of how more difficult things, like the five equations above, look like on a graph in relation to real world phenomena? Probably because he thinks the entire second chapter is easy enough for college students, and that's fine, but that still leaves me with the original question: can you guys recommend some really good high school physics books which have enough illustrations and pictures to get an excellent visual understanding of how equations relate to dynamics in the real world? The best answer so far has been the post from CalcNerd. I will try to find the high school edition of Halliday's book :)

    Since I learn math and physics on my own I depend on pedagogic books and lectures in order to feel confident about having actually understood the subject. Hope to find more books that provide a middle way between mathematical rock climbing and the royal road. But if they don't exist I fortunately have the time and stuborness to do it the hard way, like the rest of you professionals.
    Last edited: Jun 14, 2016
  19. Jun 14, 2016 #18

    The five equations you mentioned have nothing to do with physics. That is, if you don't understand them, then you're having problems with your math. As long as you won't fix your math, you'll never make it. The explanation that Halliday provides is already way too long.
  20. Jun 14, 2016 #19
    I certainly can't disagree with you that I need more experience in algebra. Guess that when I start solving particular equations in a math book I will meet lots of examples where acceleration, velocity, time and position are used as variables, but being new to physics I just didn't see that equations about motion, presented in a physics book, have basically so little to do with physics that illustrations and graphs (in relation to the real world) are unnecessary, as you seem to claim. So the best option, it seems, is to get an algebra-based physics book while working on algebra problems, and then find a high school physics book which is suitable when solving derivations and integrations on a high school level.
  21. Jun 14, 2016 #20
    What graphs? You should be able to make graphs of these equations yourself. Being spoonfed everything is not the way to approach physics. If you don't know how to draw these graphs, then you're missing very fundamental math even before calculus.
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