Calculus is a foundational subject for any discipline that concerns itself with continuous quantities or quantities that may be approximated as continuous (i.e. every quantitative discipline). It is a rigorous framework for deriving values from geometrical reasoning, and it is an essential prerequisite for probability (and therefore data science). Calculus has a reputation for being a difficult subject. It's certainly true that there are difficult calculus problems, but that simply reflects the capacity of calculus to model a complicated world. Since it is so important, there many well-polished resources for learning calculus. However, as with most applied subjects, the most important thing is to do a variety of exercises. Often, problems in more advanced data science subjects quickly reduce to calculus problems, so any effort you put into mastering calculus will be rewarded many-fold later on.
Calculus: Early Transcendentals
- In-text exercises
- Answers to odd-numbered exercises
- Solution manual available
- Differential Equations
- Partial Derivatives
- Sequences and Series
- Taylor Series
- Vector Calculus
Despite its high price, this is probably the best calculus textbook for most people. This book is typically used for a 2-3 semester calculus sequence, and contains a lot of supplementary material in the appendices, which makes the price more reasonable.
Early transcendentalsrefers to the early introduction of certain important functions. Stewart's book will take you right through calculus I and II and into multivariate calculus and differential equations, which is quite a good foundation for data science. There are books out there for those who desire a more mathematical approach, but what such people really need is a mathematical analysis book, not a calculus book. Stewart's Calculus is extremely well-organized, and it is great for both learning calculus and future reference. Perhaps the best parts of this book are the
Problems Plussections at the end of each chapter, which contain challenging but interesting problems to really test your mastery of the material.