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Radarithm
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What introductory calculus textbook do you recommend? Is Spivak's book good or is it too hard? What about Ron Larson's?
jgens said:Spivak is an excellent intro book. Depending on your interests it might be more theory-oriented than you care for, but regardless it contains most of the important information.
Radarithm said:The 4th edition is the best one, correct?
Also, does it explain the information thoroughly?
edit: Apostol's seems good. Should I get it or stay with Spivak?
Radarithm said:If I don't know what a Dedekind-ordered field is, should I go for an easier book?
I'll get a used or new (but cheaper) copy of another textbook along with it. Spivak's will be good to have when I'm good enough at calculus.mathwonk said:Spivak is a very hard, very abstract book, suitable mostly for those who already know a lot of math and who are very motivated and strong theoretically. For the right audience it is superb, but it helps to have a teacher.
I personally think it is not at all an introductory book, but you will find out by reading it. I say all this only so that you are not discouraged if it is not right for you. Many other books are much easier and more appropriate for most people to begin with.
I like Cruse and Granberg for instance, but it is hard to find.
Spivak and Larson's textbooks are known for their rigorous and thorough approach to teaching calculus. They focus on developing a deep understanding of the subject through challenging problems and proofs, rather than just memorizing formulas. They also include historical context and real-world applications to make the material more engaging.
While some basic knowledge of algebra and trigonometry is helpful, Spivak and Larson's textbooks are designed for beginners and do not assume any prior knowledge of calculus. They provide a solid foundation in the fundamentals of calculus and gradually build upon them to more advanced concepts.
Yes, both Spivak and Larson's textbooks cover both single and multivariable calculus. They begin with the basics of single variable calculus and then move on to more advanced topics such as vector calculus and differential equations.
Yes, both Spivak and Larson's textbooks include numerous practice problems and solutions to help students reinforce their understanding of the material. They also provide challenging problems to help students develop their problem-solving skills.
While having a teacher or tutor can be helpful, Spivak and Larson's textbooks are designed to be used for self-study. They provide clear explanations and examples, as well as exercises and solutions, allowing students to learn at their own pace and track their progress.