Reddit mentions of Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics)

I'm 2 years into a part time physics degree, I'm in my 40s, dropped out of schooling earlier in life.

As I'm doing this for fun whilst I also have a full time job, I thought I would list what I'm did to supplement my study preparation.

I started working through these videos - Essence of Calculus as a start over the summer study whilst I had some down time. https://www.youtube.com/playlist?list=PLZHQObOWTQDMsr9K-rj53DwVRMYO3t5Yr

Ive bought the following books in preparation for my journey and to start working through some of these during the summer prior to start

Elements of Style - A nice small cheap reference to improve my writing skills
https://www.amazon.co.uk/gp/product/020530902X/ref=oh_aui_detailpage_o02_s00?ie=UTF8&psc=1

The Humongous Book of Trigonometry Problems https://www.amazon.co.uk/gp/product/1615641823/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1

Calculus: An Intuitive and Physical Approach
https://www.amazon.co.uk/gp/product/0486404536/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

Trigonometry Essentials Practice Workbook
https://www.amazon.co.uk/gp/product/1477497781/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1

Systems of Equations: Substitution, Simultaneous, Cramer's Rule
https://www.amazon.co.uk/gp/product/1941691048/ref=oh_aui_detailpage_o05_s00?ie=UTF8&psc=1

Feynman's Tips on Physics
https://www.amazon.co.uk/gp/product/0465027970/ref=oh_aui_detailpage_o07_s00?ie=UTF8&psc=1

Exercises for the Feynman Lectures on Physics
https://www.amazon.co.uk/gp/product/0465060714/ref=oh_aui_detailpage_o08_s00?ie=UTF8&psc=1

Calculus for the Practical Man
https://www.amazon.co.uk/gp/product/1406756725/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

The Feynman Lectures on Physics (all volumes)
https://www.amazon.co.uk/gp/product/0465024939/ref=oh_aui_detailpage_o09_s00?ie=UTF8&psc=1

I found PatrickJMT helpful, more so than Khan academy, not saying is better, just that you have to find the person and resource that best suits the way your brain works.

Now I'm deep in calculus and quantum mechanics, I would say the important things are:

Algebra - practice practice practice, get good, make it smooth.

Trig - again, practice practice practice.

Try not to learn by rote, try understand the why, play with things, draw triangles and get to know the unit circle well.

Good luck, it's going to cause frustrating moments, times of doubt, long nights and early mornings, confusion, sweat and tears, but power through, keep on trucking, and you will start to see that calculus and trig are some of the most beautiful things in the world.

My main hobby is reading textbooks, so I decided to go beyond the scope of the question posed. I took a look at what I have on my shelves in order to recommend particularly good or standard books that I think could characterize large portions of an undergraduate degree and perhaps the beginnings of a graduate degree in the main fields that interest me, plus some personal favorites.

Neuroscience: Theoretical Neuroscience is a good book for the field of that name, though it does require background knowledge in neuroscience (for which, as others mentioned, Kandel's text is excellent, not to mention that it alone can cover the majority of an undergraduate degree in neuroscience if corequisite classes such as biology and chemistry are momentarily ignored) and in differential equations. Neurobiology of Learning and Memory and Cognitive Neuroscience and Neuropsychology were used in my classes on cognition and learning/memory and I enjoyed both; though they tend to choose breadth over depth, all references are research papers and thus one can easily choose to go more in depth in any relevant topics by consulting these books' bibliographies.

General chemistry, organic chemistry/synthesis: I liked Linus Pauling's General Chemistry more than whatever my school gave us for general chemistry. I liked this undergraduate organic chemistry book, though I should say that I have little exposure to other organic chemistry books, and I found Protective Groups in Organic Synthesis to be very informative and useful. Unfortunately, I didn't have time to take instrumental/analytical/inorganic/physical chemistry and so have no idea what to recommend there.

Biochemistry: Lehninger is the standard text, though it's rather expensive. I have limited exposure here.

Mathematics: When I was younger (i.e. before having learned calculus), I found the four-volume The World of Mathematics great for introducing me to a lot of new concepts and branches of mathematics and for inspiring interest; I would strongly recommend this collection to anyone interested in mathematics and especially to people considering choosing to major in math as an undergrad. I found the trio of Spivak's Calculus (which Amazon says is now unfortunately out of print), Stewart's Calculus (standard text), and Kline's Calculus: An Intuitive and Physical Approach to be a good combination of rigor, practical application, and physical intuition, respectively, for calculus. My school used Marsden and Hoffman's Elementary Classical Analysis for introductory analysis (which is the field that develops and proves the calculus taught in high school), but I liked Rudin's Principles of Mathematical Analysis (nicknamed "Baby Rudin") better. I haven't worked my way though Munkres' Topology yet, but it's great so far and is often recommended as a standard beginning toplogy text. I haven't found books on differential equations or on linear algebra that I've really liked. I randomly came across Quine's Set Theory and its Logic, which I thought was an excellent introduction to set theory. Russell and Whitehead's Principia Mathematica is a very famous text, but I haven't gotten hold of a copy yet. Lang's Algebra is an excellent abstract algebra textbook, though it's rather sophisticated and I've gotten through only a small portion of it as I don't plan on getting a PhD in that subject.

Computer Science: For artificial intelligence and related areas, Russell and Norvig's Artificial Intelligence: A Modern Approach's text is a standard and good text, and I also liked Introduction to Information Retrieval (which is available online by chapter and entirely). For processor design, I found Computer Organization and Design to be a good introduction. I don't have any recommendations for specific programming languages as I find self-teaching to be most important there, nor do I know of any data structures books that I found to be memorable (not that I've really looked, given the wealth of information online). Knuth's The Art of Computer Programming is considered to be a gold standard text for algorithms, but I haven't secured a copy yet.

Physics: For basic undergraduate physics (mechanics, e&m, and a smattering of other subjects), I liked Fundamentals of Physics. I liked Rindler's Essential Relativity and Messiah's Quantum Mechanics much better than whatever books my school used. I appreciated the exposition and style of Rindler's text. I understand that some of the later chapters of Messiah's text are now obsolete, but the rest of the book is good enough for you to not need to reference many other books. I have little exposure to books on other areas of physics and am sure that there are many others in this subreddit that can give excellent recommendations.

Other: I liked Early Theories of the Universe to be good light historical reading. I also think that everyone should read Kuhn's The Structure of Scientific Revolutions.

There are a lot of good classics on /u/thebenson's list. I want to highlight the books that are good for what you'll be learning, and give you a sense of how the sequence works. And I'll add a few.


Calculus books: Thomas' Calculus, Calculus by James Stewart (not multivariable), and this cheap easy read by Morris Kline.

Have you learned calculus in the past? It sounds like you'll need it for at least one of those courses, but either way, it will definitely help you conceptually for the others. You should really try to get solid on this before you need to use it.



Intro physics books: Fundamentals of Physics (Halliday & Resnick), Physics for Scientists and Engineers (Serway & Jewett), Physics for Scientists and Engineers (Tipler & Mosca), University Physics (Young), and Physics for Scientists and Engineers (Knight) are all good. Gee, they get really unoriginal with the names, huh?

Each of these books assumes no background in physics, but you do need to use calculus. If you're going to take a class in basic mechanics that doesn't involve any calculus, you may find it more useful to get a book at that level. The only such book that I'm familiar with is Physics: Principles with Applications by Giancoli. I know there are many others, but I can't speak for them.



Mathematical methods: Greenberg is way more than you need here. I think you would find Engineering Mathematics by Stroud & Booth more useful as a reference, since it covers a lot of the less advanced stuff that you may need a refresher on.



Sequence: it's typical to start learning physics by learning about Newtonian mechanics, with or without calculus. After that, one often goes on to thermodynamics or to electricity and magnetism. It sounds like this is roughly how your program is going to work.

If you are learning mechanics with calculus, you can expect E&M to be even heavier on the calculus and thermodynamics to be less so. More calculus is not a bad thing. People often get scared of it, but it actually makes things easier to understand.

It is very typical that you will use only one book (from the intro books above) for all of these topics. You shouldn't need to get any books on specific topics.

**

The other books on /u/thebenson's list are all great textbooks, but I think you should avoid them for now. They generally assume a healthy background in basic physics, and they may not be very relevant to the physics you'll be studying.

But I do want to give some mention to Spacetime Physics* by Taylor and Wheeler, since I don't want to imply that this is a background-heavy book. On the contrary, this is one of the most beginner-friendly physics books ever written, and it is my favorite introduction to special relativity. Special relativity is probably not something you need to learn about right now, but if you have any interest, I seriously recommend finding an old used copy of this book—it's a fun read aside from any other uses!

Textbooks (calculus): Fundamentals of Physics: http://www.amazon.com/Fundamentals-Physics-Extended-David-Halliday/dp/0470469080/ref=sr_1_4?ie=UTF8&qid=1398087387&sr=8-4&keywords=fundamentals+of+physics ,

Textbooks (calculus): University Physics with Modern Physics; http://www.amazon.com/University-Physics-Modern-12th-Edition/dp/0321501217/ref=sr_1_2?ie=UTF8&qid=1398087411&sr=8-2&keywords=university+physics+with+modern+physics

Textbook (algebra): [This is a great one if you don't know anything and want a book to self study from, after you finish this you can begin a calculus physics book like those listed above]: http://www.amazon.com/Physics-Principles-Applications-7th-Edition/dp/0321625927/ref=sr_1_1?ie=UTF8&qid=1398087498&sr=8-1&keywords=physics+giancoli

If you want to be competitive at the international level, you definitely need calculus, at least the basics of it.
Here is a good book: http://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/ref=sr_1_1?ie=UTF8&qid=1398087834&sr=8-1&keywords=calculus+kline
It is quite cheap and easy to understand if you want to self teach yourself calculus.

Another option would be this book:http://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918/ref=sr_1_1?ie=UTF8&qid=1398087878&sr=8-1&keywords=spivak
If you can finish self teaching that to yourself, you will be ready for anything that could face you in mathematics in university or the IPhO. (However it is a difficult book)

Problem books: Irodov; http://www.amazon.com/Problems-General-Physics-I-E-Irodov/dp/8183552153/ref=sr_1_1?ie=UTF8&qid=1398087565&sr=8-1&keywords=irodov ,

Problem Books: Krotov; http://www.amazon.com/Science-Everyone-Aptitude-Problems-Physics/dp/8123904886/ref=sr_1_1?ie=UTF8&qid=1398087579&sr=8-1&keywords=krotov

You should look for problem sets online after you have finished your textbook, those are the best recourses. You can get past contests from the physics olympiad websites.

Definitely agree with the people recommending Calculus Made Easy by Silvanus P. Thompson. Often imitated, never equalled.

Another book similar to that is The Calculus for the Practical Man by J.E. Thompson. Besides its fame for being the book that Richard Feynman used to teach himself calculus, it has a completely nonstandard proof that the derivative of sin(x) is cos(x), using an argument based on arc length, which I haven't seen in any other book.

For more modern books I'd recommend Kline's book, which is underrated in my opinion. I'd avoid Spivak's book, which I feel is vastly overrated; it makes calculus even drier than the standard books do.

Calculus: An Intuitive and Physical Approach (Second Edition) (Dover Books on Mathematics) https://www.amazon.com/dp/0486404536/ref=cm_sw_r_cp_apip_qmMduBiBKxeqD


This book currently. I learned precalculus using Kahn academy over the year along with trig.

:D
http://betterexplained.com/

http://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/ref=sr_1_1?ie=UTF8&qid=1422649729&sr=8-1&keywords=calculus+an+intuitive&pebp=1422649747330&peasin=486404536

The first site is fun, because it teaches you how to intuitively understand math. I love it. Second is a book that makes you think. Read the reviews for it. I really hope it helps because it's helped me, and I didn't even like math that much in the beginning, now I'm all excited for it :D

If you're on a budget, check out Calculus: An Intuitive and Physical Approach by Morris Kline.

I had the misfortune of teaching calculus from the Anton/Bivens/Davis book. That book is filled with so much needless fluff - not to mention contrived "applications" and convoluted explanations - that I will never use it again. I much prefer Calculus: An Intuitive and Physical Approach by Morris Kline. I think it's the best of the calculus texts still being published, and gives a much better feel for the subject than the standard books.

I dont know much about boot camp, but it sounds like having a physical book will be your best bet.

Personally, my favorite text book to use is Calculus: an Intutitive Approach by Morris Kline, but you might want something more advanced than that.

What text are you using?

Edit: Most calc II or multivariable textbooks that I've encountered (e.g.: this one, this one, this one, or this one) are full of examples, problems, and sections dealing with physical applications, if that's what you mean by outside the classroom.

From what I recollect, Calc II was mostly about developing facility with integration techniques, with some extensions of the concept of integration to boot. Although some of the material may seem to be of little relevance, think of it as an important stepping stone. It is preparing you for some super interesting subjects (like line integrals on vector fields!) that are used to model physical systems.

An invaluable book when I took calculus the second time: Precalculus Mathematics in a Nutshell

I took calc a second time, because I had taken it previously over ten years before. My instructor at the time was quite the hardass and didn't allow calculators on his tests or homework. I remember doing integration by parts where problems would take two whole sheets of handwritten work.

Consequently, I have a bit of a "been there, done that" attitude towards calculus...

EDIT - My instructor was a big fan of Kline

https://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536

A good intro book on calculus I found helpful was Calculus: A Physical and Intuitive Approach by Morris Kline. Jumping right into Spivak, while doable, is not for the faint of heart. (But one should definitely approach it eventually!)

Edit: spelling

Whew, not looking for Stewart or spivak? That's the two ends of the spectrum as far as calculus is concerned.

Maybe check out Morris Kline. Its intuitive and sounds right up your alley (I think)! For vector calc you may need to pick up something more advanced. I hope this helps :)

http://www.amazon.com/gp/aw/review/0486404536/RTE3I14V7OSHN/ref=cm_cr_dp_mb_rvw_1?ie=UTF8&cursor=1

A true classic that will make you a beast at calculus:

Calculus: An Intuitive and Physical Approach by Morris Kline

It's old-school but totally awesome. Gives you great explanations for why we use what we use in the mathematical world.

Made me the man I am today.

http://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536

That's great, it reminds me a lot of Calculus by Kline. He takes a similar approach and his introduction perfectly foresaw 60 years ago the problems with math education now.

https://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536

Unfortunately, many books like Spivak or Thomas are going to be very expensive, although you can find scans of them online if you look hard enough.

Dover books are cheap and are often classics, for example Calculus by Kline.

Spivak would be worth it if you plan to go on to study mathematics. It's going to have the rigor (and interesting stuff from a mathematical standpoint) that are omitted or hidden in other texts.

http://www.amazon.com/Calculus-Intuitive-Physical-Approach-Mathematics/dp/0486404536/ref=sr_1_1?s=books&ie=UTF8&qid=1405668438&sr=1-1&keywords=calculus+an+intuitive+and+physical+approach

Starts out with a brief history of calculus in chapter 1.

Chapter 2 is derivatives.

Chapter 3 is anti-derivatives

Chapter 4 talks about the geometric importance of the derivative...etc..

Chapter 21 talks about multivariable functions and geometric representation then 22 is over partial differentiation, 23 multiple integrals then an introduction to diff eq.

I don't know if that's what you're looking for.. but its been an excellent read so far, and it tends to be written in layman's terms(great for me) rather than math speak.

Hello! I'm interested in trying to cultivate a better understanding/interest/mastery of mathematics for myself. For some context:

 




To be frank, Math has always been my least favorite subject. I do love learning, and my primary interests are Animation, Literature, History, Philosophy, Politics, Ecology & Biology. (I'm a Digital Media Major with an Evolutionary Biology minor) Throughout highschool I started off in the "honors" section with Algebra I, Geometry, and Algebra II. (Although, it was a small school, most of the really "excelling" students either doubled up with Geometry early on or qualified to skip Algebra I, meaning that most of the students I was around - as per Honors English, Bio, etc - were taking Math courses a grade ahead of me, taking Algebra II while I took Geometry, Pre-Calc while I took Algebra II, and AP/BC Calc/Calc I while I took Pre-Calc)

By my senior year though, I took a level down, and took Pre-Calculus in the "advanced" level. Not the lowest, that would be "College Prep," (man, Honors, Advanced, and College Prep - those are some really condescending names lol - of course in Junior & Senior year the APs open up, so all the kids who were in Honors went on to APs, and Honors became a bit lower in standard from that point on) but since I had never been doing great in Math I decided to take it a bit easier as I focused on other things.

So my point is, throughout High School I never really grappled with Math outside of necessity for completing courses, I never did all that well (I mean, grade-wise I was fine, Cs, Bs and occasional As) and pretty much forgot much of it after I needed to.

Currently I'm a sophmore in University. For my first year I kinda skirted around taking Math, since I had never done that well & hadn't enjoyed it much, so I wound up taking Statistics second semester of freshman year. I did okay, I got a C+ which is one of my worse grades, but considering my skills in the subject was acceptable. My professor was well-meaning and helpful outside of classes, but she had a very thick accent & I was very distracted for much of that semester.

Now this semester I'm taking Applied Finite Mathematics, and am doing alright. Much of the content so far has been a retread, but that's fine for me since I forgot most of the stuff & the presentation is far better this time, it's sinking in quite a bit easier. So far we've been going over the basics of Set Theory, Probability, Permutations, and some other stuff - kinda slowly tbh.

 




Well that was quite a bit of a preamble, tl;dr I was never all that good at or interested in math. However, I want to foster a healthier engagement with mathematics and so far have found entrance points of interest in discussions on the history and philosophy of mathematics. I think I could come to a better understanding and maybe even appreciation for math if I studied it on my own in some fashion.

So I've been looking into it, and I see that Dover publishes quite a range of affordable, slightly old math textbooks. Now, considering my background, (I am probably quite rusty but somewhat secure in Elementary Algebra, and to be honest I would not trust anything I could vaguely remember from 2 years ago in "Advanced" Pre-Calculus) what would be a good book to try and read/practice with/work through to make math 1) more approachable to me, 2) get a better and more rewarding understanding by attacking the stuff on my own, and/or 3) broaden my knowledge and ability in various math subjects?

Here are some interesting ones I've found via cursory search, I've so far just been looking at Dover's selections but feel free to recommend other stuff, just keep in mind I'd have to keep a rather small budget, especially since this is really on the side (considering my course of study, I really won't have to take any more math courses):
Prelude to Mathematics
A Book of Set Theory - More relevant to my current course & have heard good things about it
Linear Algebra
Number Theory
A Book of Abstract Algebra
Basic Algebra I
Calculus: An Intuitive and Physical Approach
Probability Theory: A Concise Course
A Course on Group Theory
Elementary Functional Analysis