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Calculus Any Calculus Starter Textbook suggestions?

  1. Feb 25, 2017 #1
    I would like to start learning my calculus course before in school. Are here any textbooks or science reading books that would help me with the situation?
  2. jcsd
  3. Feb 25, 2017 #2
    I strongly recommend George Simmon's "Calculus with Analytic Geometry". He writes very clear, sophisticated exposition for both high schools and beginning undergraduates. He also has excellent problems sets. I also recommend APEX Calculus, which is free to download and also has fascinating exposition.
  4. Feb 25, 2017 #3
    Thanks I'll try them
  5. Feb 25, 2017 #4
    Simmons as suggested above is good. I have a lot of other favorites.

    There is a small and fun to read book that makes the basics strong. https://www.amazon.com/Hitchhikers-Guide-Calculus-Michael-Spivak/dp/0883858126
    For Applications, you cannot beat https://www.amazon.com/No-bullshit-guide-math-physics/dp/0992001005
    Great way to quickly learn calculus https://www.amazon.com/gp/product/0471827223
    Great book (Q&A style) https://www.amazon.com/gp/product/0486203700
    A really fun book to read https://www.amazon.com/gp/product/0691161909
    Really good Calculus books: https://www.amazon.com/gp/product/0691130884 and https://www.amazon.com/gp/product/0312185480
    Oldies but goldies https://www.amazon.com/gp/product/B00GMPZBGA, https://www.amazon.com/gp/product/0201048108, https://www.amazon.com/gp/product/0030892686 - These are much better (along with Simmons) than nay of the current calculus books.
    A Tutoring Book https://www.amazon.com/gp/product/0879421835
    An Infinitesimal approach https://www.amazon.com/gp/product/0486484521
    The book that allegedly taught Feynman https://www.amazon.com/Calculus-Practical-Man-J-Thompson/dp/1406756725
    For Problems https://www.amazon.com/gp/product/1592575129
    Lastly, there is the best of the best https://www.amazon.com/Calculus-4th-Michael-Spivak/dp/0914098918 (although in my opinion it serves the best as the second book rather than the first)

    Hope you find something interesting in the above list. If I were you, I would opt for a non traditional textbook and have some fun reading through it. You will have to go through textbooks when they teach you at school anyways. You cannot really go wrong with any of the books I suggested or Simmons.
    Last edited by a moderator: May 8, 2017
  6. Feb 25, 2017 #5
    Thanks! Your information is massive!
    Last edited by a moderator: May 8, 2017
  7. Apr 2, 2017 #6
  8. Apr 2, 2017 #7


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    Last edited by a moderator: May 8, 2017
  9. Apr 2, 2017 #8
    I can vouch for the Moise Calculus book. Really great book with interesting problems. Shows you the why and how. It is at a bit lower level than Spivak but above Thomas.
  10. Apr 5, 2017 #9
    No list is complete without Apostol's calculus.
  11. Apr 5, 2017 #10
    M. Spivak
    Really an awesome book
  12. Apr 6, 2017 #11


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    But it's really much more than calculus. It's also linear algebra, probability theory, ...
  13. Apr 6, 2017 #12
    Spivak and Apostol are great books and so are Courant and john's calculus books, I in fact suggested Spivak in my post above with a caveat. However, I do not believe Apostol or Spivak should be used as a first calculus book for High School Students.

    Spivak https://www.amazon.com/Hitchhikers-Guide-Calculus-Michael-Spivak/dp/0883858126/that will be appropriate as a great companion for a real text book - the only reason I did not suggest it above is I do not think this book should be used stand alone and it costs way too much ($48 in Amazon) for what it is.
    Last edited by a moderator: May 8, 2017
  14. Apr 7, 2017 #13
    You really should stop recommending Spivak or Apostol for high school students who have no clue what calculus is. Those of us who understand it find them to be lovely books but I can't think of a better way to make a new student hate math than to suggest to him that those books are representative of what they will likely do with calculus.
  15. Apr 7, 2017 #14
  16. Apr 7, 2017 #15
    He did offer a word of caution about Spivak/Apostol.

    My suggestion would be to get Moise: Calculus. It is between Courant and Stewart/Thomas. It goes over topics, like the Induction Principle, and Well Ordering Principle. Has neat problems. The writing in the text is lucid and clear, and Moise makes the ideas connect in elegant and beautiful ways. He also discusses topics that should be familiar from previous math classes, in a very thoughtful and meaningful way. Why do we call a coordinate system right handed? How did people define the trigonometric functions? It talks about the Winding Function, something that was new to me. Limit laws are clear. Proofs are very clear and offer a lot of insight as to why the theorems hold. A very excellent book!

    Get Moise and maybe Thomas/Finnly 9th ed. Use Moise as the main text and Thomas as a supplement.
  17. Apr 7, 2017 #16
    People above are recommending them. They really are inappropriate for a kid asking to learn calculus but every time the question comes up the same answers are given.

  18. Apr 7, 2017 #17
    I am sorry. I recommended that book because other people were recommending all types of books except this one, so I thought I would complete the list.
  19. Apr 8, 2017 #18


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    Well, to recommend good university books for freshmen to highschool students is good advice. When I was about in the 8th grade, I had big trouble with mathematics, and I couldn't make sense of my school book nor with the explanations of my teachers. Then I was lucky to find some textbook called "Mathematics for Engineers", which covered the stuff (I think it was elementary Euclidean geometry about triangles, sin, cos, tan, and all that) I had trouble with in a clear and lucid way. It was far from being a strict mathematicians' math textbook, but full with applications and exercises with solutions in the appendix. From that day on math was my favorite subject, and I had good marks too. I even started to self-study math ahead of class getting an idea about calculus (differentiation and integration) quite early. I never could make sense of what was in the school books, but these university books were the door opener for understanding math, and pretty soon I also read introductory textbooks on "true math" with real strict proofs of theorems, a discipline that had not much in common with what's called "math" in school. So good introductory university books can definitely help to motivate high school students to learn a subject, because they teach the subject without hiding it behind well-intended but flawed didactics!
  20. Apr 11, 2017 #19


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    Can you tell now more precisely what exactly was wrong with their way of teaching?
  21. Apr 11, 2017 #20
    I am assuming most of the high school textbook, were full of pictures,diagrams, non related math jargon, and only the calculation aspect. Maybe no explanation from the high school authors as to why we do such and such, and why its important, etc.
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