Is there a good book to self study calculus?

In summary, these books are good for self-study if you have a strong background in algebra and trigonometry.
  • #1
FeyStein
6
1
Hi, I am looking for a way to self study calculus. I am an eighth grader doing more than grade level stuff, so I am a COMPLETE beginner and need a book which starts with like the 'abc's' of calculus. I know geometry, Algebra 1 & 2 really well, but am not the best at Trig or Precalc, so if there are books to do like a crash course on the topics, that'll be great too, but I am focusing on calculus right now.
 
  • Like
Likes theBin
Physics news on Phys.org
  • #2
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.
 
  • #3
@ProfuselyQuarky Thank You so much
 
  • #4
  • #5
Ssnow said:
Here there is an Insight with title:

''How to Self Study Analysis. Part I: Intro Analysis''

See in:

Reference https://www.physicsforums.com/insights/

I prefer to recommend my insight on how to self-study calculus here.
 
  • Like
Likes Ssnow
  • #6
FeyStein said:
Hi, I am looking for a way to self study calculus. I am an eighth grader doing more than grade level stuff, so I am a COMPLETE beginner and need a book which starts with like the 'abc's' of calculus. I know geometry, Algebra 1 & 2 really well, but am not the best at Trig or Precalc, so if there are books to do like a crash course on the topics, that'll be great too, but I am focusing on calculus right now.
There are since late 1960s, an increasing number of good books for self studying/teaching (infinitesimal) calculus _not to be confused with "analysis"_. Are supplied, inside the book or within a student solutions manual, all the solutions to the exercises, problems & quizes; this criterion excludes the majority of the best textbooks on calculus. _______Second criterion: understanding of all the notions in math and physics of secondary school. _______3th criterion, first year college math prior to calculus, a.k.a. pre-calculus, discrete mathematics ect. _______4th, also learn the stack of notions of the hyperbolic trigonometry.______________________Then you can, on Amazon web sites (.com , .fr ,...), seek for the books on calculus and examine the critics/commentaries. Apostol's old book has presented calculus together with linear algebra. Harold M. Edwards' old book "Advanced Calculus: A Differential Forms Approach" could be your second book to read; only the solutions of odd number problems are supplied. And if you pursue in this most excellent self studies of calculus, don't hesitate to buy a recent book without any solution to the assigned exercises/problems, "Advanced Calculus: A Geometric View" by James J. Callahan. Three others books sould be purshased as complements: 1) "How Round is Your Circle?: Where Engineering and Mathematics Meet" by J. Bryant & C. Sangwin (to be read after your pre-calculus notions); 2) "The Mathematical Mechanic" by M. Levi; 3) "A Geometric Approach to Differential Forms, 2/e" by D. Bachman.
 
  • Like
Likes Joker93
  • #7
FeyStein said:
Hi, I am looking for a way to self study calculus. I am an eighth grader doing more than grade level stuff, so I am a COMPLETE beginner and need a book which starts with like the 'abc's' of calculus. I know geometry, Algebra 1 & 2 really well, but am not the best at Trig or Precalc, so if there are books to do like a crash course on the topics, that'll be great too, but I am focusing on calculus right now.
In nowadays' math, infinitesimal calculus may be compared to a big numerical-control machine-tool! If you wish a much simpler and shorter plan of studies in calculus, here is a low-cost suggestion. "Technical Calculus with Analytic Geometry" by Judith L. Gersting; 528 pp 6.14" x 9.21": ISBN-13: 9780486673431. It contains 6 credits of post secondary education in calculus for technology students with a background in algebra and trigonometry. Answers to all practice problems are given at the back of the book, many with worked-out solutions. Paperback + eBook: 25.25 $US, in the USA.
 
  • Like
Likes CalcNerd and The Bill
  • #8
@theBin Thank you so much. Your suggestion really helped! :)
 
  • #9
In addition to the Technical Calculus referenced above, I also like
https://www.amazon.com/dp/0312185480/?tag=pfamazon01-20

I also find the following free resources from the following website very informative.

http://betterexplained.com/calculus/

I also like the following older book very much
https://www.amazon.com/dp/1406756725/?tag=pfamazon01-20

I have heard great things about the following text which I have in order (just curious) but haven't read yet myself.
https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20
 
  • Like
Likes atyy and theBin
  • #10
Also, are economical and in pocket-size, from author A.A.Klaf: "Arithmetic Refresher", Trigonometry Refresher" and "Calculus Refresher". Old stuff (like my revised copy of Audel millwright handbook), for high-school trades, e.g. industrial draftsperson, topometry & land-surveying labourer, machinist, landscaping & gardens designer. His book on calculus hasn't enough coverage for a college technology in architecture, civil engineering or electromechanics.
 
  • #11
Try George Simmons' Calculus and Analytic Geometry. The book is really good for the beginners in calculus, and it will take you from the precalculus to single-calculus to multivariable calculus.

Another good book is Courant/John's two-volume classics.
 
  • Like
Likes theBin
  • #12
bacte2013 said:
Try George Simmons' Calculus and Analytic Geometry. The book is really good for the beginners in calculus, and it will take you from the precalculus to single-calculus to multivariable calculus.

Another good book is Courant/John's two-volume classics.
G. Simmons' book first edited in 1982 is excellent; rather indispensable is the ''Student Solutions Manual (...)'' written by the same author. Finding & buying them by internet at decent prices is sometimes difficult. _________________________Courant & John's set of two volumes in infinitesimal calculus, is for those who made well in advanced secondary math, college precalculus and a primer course in calculus. At page 120 appear the first teachings on integral; on page 155, the first teachings on derivative. The two volumes contain about 20 credits of knowledge.
 
  • #13
based on the idea that mastering the background for calculus is more important than jumping right into the calculus, i suggest the book Principles of Mathematics, by Allendoerfer and Oakley. They will start with logic, number systems, a sketch of groups fields, sets and boolean algebra, and progress through functions, algebraic functions, trig functions, exponential and log functions, and then limits, analytic geometry, continuous functions, and finally a brief introduction to the key ideas of calculus, with an indication of the proof of the fundamental theorem. You will then be ready for a more thorough treatment of calculus itself from one of the more advanced books suggested above.

This book is suitable for honors high school students, while Courant and John is suitable for honors level college students, and is considerably more dense and difficult.
 
  • Like
Likes theBin
  • #14
mathwonk said:
based on the idea that mastering the background for calculus is more important than jumping right into the calculus, i suggest the book Principles of Mathematics, by Allendoerfer and Oakley. They will start with logic, number systems, a sketch of groups fields, sets and boolean algebra, and progress through functions, algebraic functions, trig functions, exponential and log functions, and then limits, analytic geometry, continuous functions, and finally a brief introduction to the key ideas of calculus, with an indication of the proof of the fundamental theorem. You will then be ready for a more thorough treatment of calculus itself from one of the more advanced books suggested above.

This book is suitable for honors high school students, while Courant and John is suitable for honors level college students, and is considerably more dense and difficult.

Better version is "Fundamentals of Freshman Mathematics" by Allendoerfer/Oakley. It is almost same as Principles, but Fundamentals has better organizations, proofs, and more materials geared for pre-calculus. I was little confused about how A/O treated the logic at the beginning, though.
 
  • Like
Likes theBin
  • #15
theBin said:
G. Simmons' book first edited in 1982 is excellent; rather indispensable is the ''Student Solutions Manual (...)'' written by the same author. Finding & buying them by internet at decent prices is sometimes difficult. _________________________Courant & John's set of two volumes in infinitesimal calculus, is for those who made well in advanced secondary math, college precalculus and a primer course in calculus. At page 120 appear the first teachings on integral; on page 155, the first teachings on derivative. The two volumes contain about 20 credits of knowledge.

There is a second edition, where Simmons corrected all mistake on the first edition and added more materials for the multivariable calculus and proofs at the Appendix. It is very sad that his book has a huge price...

I think Courant/John really cared about the applications of analysis, especially in physics. The modern treatment quite similar to C/J is gigantic 2-volume sets by Zorich. He emphasizes the physical motivation and intuition, particularly on the foundations of calculus on physical phenomena.
 
  • Like
Likes theBin
  • #16
mathwonk said:
based on the idea that mastering the background for calculus is more important than jumping right into the calculus, i suggest the book Principles of Mathematics, by Allendoerfer and Oakley. They will start with logic, number systems, a sketch of groups fields, sets and boolean algebra, and progress through functions, algebraic functions, trig functions, exponential and log functions, and then limits, analytic geometry, continuous functions, and finally a brief introduction to the key ideas of calculus, with an indication of the proof of the fundamental theorem. You will then be ready for a more thorough treatment of calculus itself from one of the more advanced books suggested above.

This book is suitable for honors high school students, while Courant and John is suitable for honors level college students, and is considerably more dense and difficult.
Exactly. _____ ''trig functions, exponential'' including the teachings on the hyperbolic ''and log functions'' because the mature/true equation of the curve of the suspended chain needs be built with an hyperbolic-trigonometric function.
 
  • #17
theBin said:
G. Simmons' book first edited in 1982 is excellent; rather indispensable is the ''Student Solutions Manual (...)'' written by the same author. Finding & buying them by internet at decent prices is sometimes difficult. _________________________Courant & John's set of two volumes in infinitesimal calculus, is for those who made well in advanced secondary math, college precalculus and a primer course in calculus. At page 120 appear the first teachings on integral; on page 155, the first teachings on derivative. The two volumes contain about 20 credits of knowledge.
They don't contain 20-credit of knowledge but if one makes some extra readings in the books mentionned as reference or source, the learning will expand.
 
  • #18
Why is this book so expensive?
 
  • #19
officed
smodak said:
Why is this book so expensive?
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.
 
  • #22
why would you want the second edition? the first edition is always preferable, both for quality and price. to be blunt, only suckers, i.e. students required to do so, buy later editions. the 1st edition is usually what the author intended. 99% of the time, later editions are mandated by the publisher to be able to sell more copies for more money. do you really think professor simmons worked all those years to write his book, then after finally publishing it, realized oops i forgot something super important, i better put in the second edition? and that you cannot do without that trivial addendum? i coulld be wrong since i am not physically comoparing the two, but i suggest you get the 1st edition, based on a lifetime (50+ years) of experience in such matters.
 
  • Like
Likes theBin
  • #23
mathwonk said:
why would you want the second edition? the first edition is always preferable, boith for quality and price. to be blunt, only suckers, i.e. students required to do so, buy later editions. the 1st edition is usually what the author intended. 99% of the time, later editions are mandated by the publisher to be able to sell more copies for more money. do you really think professor simmons worked all those years to write his book, then after finally publishing it, realized oops i forgot something super important, i better put in the second edition? and that you cannot do without that trivial addendum?

I believe the second edition has significantly added materials, e.g. Diff. Equations in addition to proofs.
 
  • Like
Likes theBin
  • #24
is a section on diff eq is worth $65 extra? the average person never fiunishes a calc book in a lifetime; i myself at age 73 am still reading the courant i bought in 1960; i guarantee you the first edition has more than you can learn in a really long time. we are recommending for an eighth grader here.
 
  • #25
mathwonk said:
is a section on diff eq is worth $65 extra? the average person never fiunishes a calc book in a lifetime; i myself at age 73 am still reading the courant i bought in 1960; i guarantee you the first edition has more than you can learn in a really long time. we are recommending for an eighth grader here.

I understand where you are coming from, but I still stand with the 2nd edition. Having read both 1st and 2nd (borrowed 1st one from the library), I can say that Professor Simmons added significantly more materials on the series & sequence, differentia equations, and more information about the multivariable calculus and intro. vector analysis.

This is my personal opinion, but I think the money should not be a big issue when purchasing great masterpiece such as Simmons. Those classic books will be very expensive in future, which sadly is a case for other classic books such as Dugundji and Engelking.
 
  • Like
Likes theBin
  • #26
As a beginner too, I recommend Calculus For Dummies
 
  • Like
Likes debajyoti datta
  • #27
FeyStein said:
Hi, I am looking for a way to self study calculus. I am an eighth grader doing more than grade level stuff, so I am a COMPLETE beginner and need a book which starts with like the 'abc's' of calculus. I know geometry, Algebra 1 & 2 really well, but am not the best at Trig or Precalc, so if there are books to do like a crash course on the topics, that'll be great too, but I am focusing on calculus right now.
In the "Demystified" series. <> ''Precalculus Demystified"; or ''College Algebra Demystified'' + ''Trigonometry Demystified''. <> ''Discrete Mathematics Demystified'', or ''Logic Demystified'' + ''Probability Demystified'' + ''Math Proofs Demystified''. <> Then, these books in such sequence: ''Calculus Demystified'' ---> ''Linear Algebra Demystified'' ---> ''Advanced Calculus Demystified'' ---> ''Differential Equations Demystified'' ---> ''Complex Variables''. The ''Demystified'' series is also composed of several books on physics; notions that can help to find a better/specilized job. _________________ Or if you want to save space on shelves, and a few dollars, why not buying an acclaimed hardcovered manual on calculus with the relevant prerequisites, also called ''pre-calculus', e.g. the second edition of the above-mentionned book of Simmons. And don't neglect to buy the student solutions manual, and the study guide, if they were published.
 
  • #28
terryds said:
As a beginner too, I recommend Calculus For Dummies
May I quote Ryan's review of July 26, 2008 on Amazon.com, concerning ''Calculus II for Dummies'' ? << Most of (...) (pg 1-283 out of 368 pgs including index) is covered in the first "Calculus for Dummies'' book.>>
 
  • #29
For self-study I have always been a big fan of the Shaum's Outline series. They have many worked examples and practice exercises. There is one for trig and one for calculus.
 
  • Like
Likes theBin
  • #30
I wonder why nobody mentioned about Thomas' Calculus...
 
  • #31
debajyoti datta said:
I wonder why nobody mentioned about Thomas' Calculus...
Thomas' , also Thomas & Finney's calculus textbooks have already been recommended in other discussions. The problem is to find a dealer who offers the student solutions manual, and the study guide, when the editor doesn't sell them anymore. Whithout the official high school top education in math, and the appropriate college pre-calculus course(s), one will fully understand only the first two/three chapters.
 
  • #32
Thomas Calculus with Analytical Geometry 3rd ed.

Moise is also nice, but can be hard for a reader if he is strong in algebra, trig, geometry.
 
  • #33
I have to second the Thomas suggestion. I've been using the second edition alongside Lang's First Course in Calculus as my first exposure, and I feel they supplement each other pretty well.
 
  • #34
The book "Advanced Calculus" by J.Callahan is a book full of treasures(insights!). Do not hesitate to check it out. It's a must-have supplement for any book on vector/multivariable calculus. Truly great
 
  • #35
theBin said:
Thomas' , also Thomas & Finney's calculus textbooks have already been recommended in other discussions. The problem is to find a dealer who offers the student solutions manual, and the study guide, when the editor doesn't sell them anymore. Whithout the official high school top education in math, and the appropriate college pre-calculus course(s), one will fully understand only the first two/three chapters.

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.
 

Similar threads

  • Science and Math Textbooks
Replies
26
Views
3K
  • Science and Math Textbooks
Replies
3
Views
2K
  • Science and Math Textbooks
Replies
17
Views
2K
  • Science and Math Textbooks
Replies
3
Views
2K
  • Science and Math Textbooks
Replies
2
Views
695
  • Science and Math Textbooks
Replies
14
Views
4K
  • Science and Math Textbooks
Replies
4
Views
1K
  • Science and Math Textbooks
Replies
16
Views
2K
  • Science and Math Textbooks
Replies
7
Views
3K
  • Science and Math Textbooks
Replies
2
Views
1K
Back
Top