To effectively understand calculus, foundational knowledge in algebra, geometry, trigonometry, and logarithms is essential. "Basic Mathematics" by Lang is recommended as a comprehensive resource for elementary mathematics, although it may be challenging for beginners. For those needing a gentler introduction, Gelfand's books on trigonometry, functions, and coordinates are suggested as preparatory materials. Mastering these subjects will facilitate a smoother transition into calculus concepts.
PREREQUISITESStudents preparing for calculus, educators seeking teaching resources, and anyone looking to strengthen their mathematical foundation before tackling advanced topics.
Thanks so much! I am going with the latter book followed by Lang'smicromass said:It all depends on what you mean with "understand". This isn't just a smartass comment though. You can easily pick up "calculus made easy" and work through it. You won't need much prerequisite knowledge. On the other hand, you have understanding at the level of Spivak's calculus, this requires a lot more effort and prerequisite knowledge.
A good book here is "Basic Mathematics" by Lang. This book contains everything you need in order to start learning calculus. It covers elementary mathematics in a concise and non-spoonfeeding manner. However, if you've never seen these kind of mathematics before, then this book might be difficult.
If the book is too difficult, then I highly recommend the books by Gelfand. Here is the first volume: https://www.amazon.com/dp/0817636773/?tag=pfamazon01-20
He has other books on trigonometry, functions and graphs, method of coordinates. It would be good to work through all of these books before starting calculus. And it would be good to work through Lang too.