Revisiting Single-Variable Calculus after Multi-

In summary, the conversation is about someone wanting to strengthen their knowledge of Calculus after finishing a Multivariable Calculus course in high school. They have already taken the AP Calculus BC Exam and used the textbook Stewart. They are interested in revisiting the topics in a more rigorous and proof-focused manner and have heard good things about Spivak and Apostol. They have also been reading Linear Algebra Done Right and are open to recommendations for their situation. Some suggestions include Apostol, Courant, Spivak, and Understanding Analysis by Abbot. Additionally, they are advised to look into the multivariable Analysis book by Hubbard and Hubbard once they have a good understanding of the generalized Reiman Integral.
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Hello all! I was thinking about strengthening my knowledge of Calculus after I finish the course I am taking in Multivariable Calculus. I am in a particularly unique situation, as I am only going to enter high school next year.

I took the AP Calculus BC Exam last year and got a 5. The course I took was through John Hopkins Center for Talented Youth, and the textbook was Stewart. I also used Stewart for Multi, but I would love to revisit all of the topics in a more rigorous and proof-focused manner.

I have heard many good things about Spivak and Apostol, but I am open to other possibilities as well. I have recently been reading Linear Algebra Done Right by Axel after watching Gil Strang's 18.06 lectures, and am finding the proofs very enlightening. What would you recommend for my situation? I eagerly await all responses!
 
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Maybe try either Apostol/Courant/Spivak? Out of these, I find Apostol easier to read.

However, you can start learning Analysis if you find Linear Algebra Done Right readable. A good intro is Understanding Analysis by Abbot.

Once you get up the section before the generalized Reiman Integral (or you can cover it too), have a look at the multivariable Analysis book by Hubbard and Hubbard.
 
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FAQ: Revisiting Single-Variable Calculus after Multi-

What is single-variable calculus?

Single-variable calculus is a branch of mathematics that deals with the study of change in one variable at a time. It involves concepts such as limits, derivatives, and integrals, and is used to model and analyze continuous change in various fields such as physics, engineering, and economics.

Why is it important to revisit single-variable calculus after studying multi-variable calculus?

Revisiting single-variable calculus after studying multi-variable calculus allows for a deeper understanding of the fundamental concepts and techniques used in both branches. It also helps in developing a strong foundation for more advanced topics in mathematics and other fields that heavily rely on calculus.

What are some key differences between single-variable and multi-variable calculus?

The main difference between single-variable and multi-variable calculus is the number of variables involved. Single-variable calculus deals with functions of one variable, while multi-variable calculus deals with functions of two or more variables. This leads to differences in concepts and techniques, such as the use of partial derivatives in multi-variable calculus.

How can revisiting single-variable calculus benefit my understanding of other mathematical concepts?

Single-variable calculus is the basis for many other mathematical concepts, such as differential equations, linear algebra, and optimization. Revisiting it can help strengthen your understanding of these topics and make it easier to apply them in various fields.

What are some resources for revisiting single-variable calculus?

There are many resources available for revisiting single-variable calculus, including textbooks, online courses, and video lectures. Some popular textbooks include "Calculus: Early Transcendentals" by James Stewart and "Calculus" by Michael Spivak. Online platforms like Khan Academy and Coursera also offer free courses on single-variable calculus.

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