Is there a good book to self study calculus?

[NathanaelNolk]

Never use solutions manuals. It hampers the learning process. Most upper division courses, at a good school or an excellent professor, will give problems sets you cannot google search the answer. Most students fail these courses, because they always used solutions manuals.

The problem isn't with the solution manuals but with people not being able to work through the exercises without taking a peek at the solutions.
If you just started university and you go through calculus almost alone (or worse yet, if you're a self-learner), a solutions manual is a great way to check whether you're actually understanding the material or not. The fact that some people lack the proper discipline to use it correctly has nothing to do with that.

 

[MidgetDwarf]

The problem isn't with the solution manuals but with people not being able to work through the exercises without taking a peek at the solutions.
If you just started university and you go through calculus almost alone (or worse yet, if you're a self-learner), a solutions manual is a great way to check whether you're actually understanding the material or not. The fact that some people lack the proper discipline to use it correctly has nothing to do with that.

No it is not. I never used a solutions manual and I do good in my classes. Solutions manual hampers the learning process. It is better to post of physicsforum, and have one of the members on this site help you. To understand what I am saying, and maybe for you to challenge your previous notions, I suggest to read the great book by Polya: How to Solve It.

 

[micromass]

No it is not. I never used a solutions manual and I do good in my classes. Solutions manual hampers the learning process. It is better to post of physicsforum, and have one of the members on this site help you. To understand what I am saying, and maybe for you to challenge your previous notions, I suggest to read the great book by Polya: How to Solve It.

I disagree. A solution manual can be a lot of help. You just need to use it correctly.

 

[NathanaelNolk]

No it is not. I never used a solutions manual and I do good in my classes. Solutions manual hampers the learning process. It is better to post of physicsforum, and have one of the members on this site help you. To understand what I am saying, and maybe for you to challenge your previous notions, I suggest to read the great book by Polya: How to Solve It.

You're missing the point. A solutions' manual directly tells you whether you got problems wrong or not. This adds motivation and helps learners make sure they actually know the material. No one is going to post every problem set they work through on PF, people aren't devoid of shyness.
Furthermore, your personal example isn't going to solidify your claim. The fact that you do well without a solutions' manual is great for you, but that doesn't necessarily apply to everyone else. What's more, not everyone has the luxury to learn everything they want in university (or even go to university in the first place). A lot of university students and self-learners most likely don't even know about PhysicsForums. The audience you're targeting is very tiny indeed, in comparison to all the learners out there. To add to this, PhysicsForums is an English-speaking community so you're automatically ruling out people who don't have the necessary grasp of the language. I think that's not exactly the best advice out there to people just starting on their studies.

As a matter of fact, I am aware of Polya's book and read parts of it; it is very interessant indeed, but it bears little importance in the actual discussion, in my opinion.

 

[mathwonk]

obviously there are many respected persons who differ on this, but i agree that solutions manuals do little to most people good and actually are harmful. they are seductive though and it is tempting to wonder whether one got the same answer as the solutions m,anual. notice i do not say right answer since solutions manuals are just one persons solution and need not be right. i have found numerous wrong answers in solutions manuals as well as poor methods used in those that give methods.

i recommend thinking of a second method for doing a problem and seeing if you get the same result, in order to verify correctness. that is all you are doing in using a solutions manual, if it only gives answers and not explanations. i.e. a solutions manual answer is just a second opinion. the real harm is getting used to the existence of a solutions manual when in the real world there is no such crutch available an you have to figure out whether or not your answer is right on your own, by its internal logic. If you have understood the problem then you should be able to know it is right.

if you want a second opinion, a much better way is to work with a friend and compare results, then try to convince each other when you differ.

still if you feel helped by one, then use it, but i recommend working to wean yourself off this crutch. The solutions manual for EP Calculus that I was given was used in my office only as a doorstop, except I admit that once in 20 years I bent over and picked it up to look up a quick answer. I feel guilty about that even now though.

 

[smodak]

I disagree. A solution manual can be a lot of help. You just need to use it correctly.

I could not agree more.

 

[Pablo Blanco]

Trigonometry is ever so important in Calculus. Calculus is like a pot of soup where parts of algebra, geometry, and trig all come to work together. Pre-Calc is a good teaser on what calculus will be like, so you should try that too. I've already recommended this for another person, but try the fifth edition of Trigonometry by McKeague and Turner. It's very simplistic.

It can be downloaded here https://archive.org/details/Trigonometry_Seventh_Edition_by_Charles_P._McKeague_Mark_D._Turner

 

[Aufbauwerk 2045]

Since you are in 8th grade, you might find Bob Miller's books very helpful. He specializes in teaching math to high school students. I think he is outstanding. His books are fun, but you are also learning serious math. He also has some good advice on how to learn math.

His books cover all the high school prerequisites for calculus, as well as AP and university level calculus.

His books are not expensive. For a tight budget, it's easy to find used copies on Amazon along with the new copies.

Based on your background, I think the book you want to get started with is Bob Miller's Calc for the Clueless: Precalc (including Trigonometry). Just search on Amazon. I would provide a link but I don't want to step on the PF affiliate link system. Maybe they already have a link? I don't have time to look for it.

Don't worry about the title. He is just trying to put you at ease. He never insults your intelligence. Quite the contrary.

He other books include algebra, geometry, Calc I, Calc II, and Calc III.

Remember, there are no shortcuts in learning math. Just be patient and master the topics in order.

 

[amorrow]

There is a new resource on the web:
https://en.wikiversity.org/wiki/Calculus_I
It is a fast, lean-and-mean introduction to Calculus.
If you like it, then tell others about it, like other math students and faculty.

 

[leadpencil]

officed Some masterpieces are out of print, and not yet reprinted at very low cost, as does e.g. Dover Publishing Company. Until there, many salespersons who opereate on web platforms like Amazon, AbeBooks etc, will try their best to make outrageous profits. Before the 1980s, generaly speaking, the academic manuals were suffering of underdevelopment in every aspects. The didactics of infinitesimal calculus and linear algebra, also of physics, have taken a century to correct pitfalls, traps and ambiguities. The American Government took very long to awake & realized that, in order to promote math & physics in the brain of the Youth, big money should be every year invested in expensive paper, colours, hardcovering etc, not only in aerospace missions to other planet(s) with rockets. Before 1982, the Bibles, a handful of reputated dictionaries & encyclopedia, the Life magazine, the manuscripts at notary/chapel/city-hall or at land-surveyer office, etc were alone of high qualities; not the manuals for school, college & university. ____________ I own a copy of ''Calculus and Analytic Geometry" edited in 1982, written by Mizrahi & Sullivan. In the preface the authors admit that there were many good books on calculus already, but they aren't interesting: they are done to please to the eventual teachers. So they did a very interesting manual and easy-to-read manual, built for the student.

The 3rd edition of your late-mentioned book of Mizrahi & Sullivan contains 150 more pages. My leitmotive is to give preference to the third edition of any contemporary textbook on mathematics for engineering and physics. Thus, I bought on Internet the sole new copy, at a very low cost, of: "Thomas' Calculus: A Transcendental Approach" 3rd custom edition for the Rensselaer Polytechnic Institute, published in 2011. (This institute, located in Troy, state of New York, is the eldest technical university in the USA.) Unfortunately the softcovered manuals for all the answers aren't for sale; while the solutions manuals, much too expensive, also almost no dealer ships them to Canada. It looks to me that this Thomas' Calculus: A (...)" should be preferred by more teachers. maybe the teachers are reluctant to the customized edition of textbook?

 

[amorrow]

I had to shift my page on my very fast introduction to initial Calculus to

http://thermo4thermo.org/calculus_quickstart.html