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/
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.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.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.
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.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.
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.
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.
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.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.
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.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.
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.smodak said:Why is this book so expensive?
Was talking about the second edition of Simmonsmathwonk said:nor is Simmons:
http://www.abebooks.com/servlet/BookDetailsPL?bi=15997784025&searchurl=bi=0&ds=30&sts=t&bx=off&sortby=17&tn=calculus&an=george%20simmons&recentlyadded=all
what book's price are you complaining about?
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?
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.
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.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.
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.>>terryds said:As a beginner too, I recommend Calculus For Dummies
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.debajyoti datta said:I wonder why nobody mentioned about Thomas' Calculus...
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.