
Uses everyday experiences to reveal the hidden calculus behind a typical day's events, showing how math naturally emerges from simple observations such as how hot coffee cools down, and demonstrating that calculus can be both useful and fascinating.
When it comes to Calculus most people get traumatized due to the excessive rigor and abstraction many teachers/books start with in the beginning. There is the Heine discrete sequence approach that is far easier to understand (see https://news.ycombinator.com/item?id=49312120) than the standard epsilon-delta definition but for some reason it is not emphasized. Add the fact that many mindlessly recommend Spivak/Apostol etc. books which are highly rigorous and a beginning student is lost and starts to develop an aversion to the subject.
For some motivation see Everyday Calculus: Discovering the Hidden Math All around Us by Oscar Fernandez - https://press.princeton.edu/books/paperback/9780691175751/ev...
People should have at the minimum a conceptual idea of Calculus. A good motivation is Everyday Calculus: Discovering the Hidden Math All around Us by Oscar E. Fernandez - https://press.princeton.edu/books/paperback/9780691175751/ev...
> And if you do learn it, do so with rigor so you actually learn it
This is not strictly necessary for everybody. The conceptual ideas are what are important; else you are merely doing "plug-and-chug" Maths without any understanding. You need to focus on rigor only based on your needs and at your own pace. Concepts come first Formalism comes second.
A good example; In the Principia Newton actually uses the phrase Quantity of Motion for what we define today as Momentum. The phrase is evocative and beautifully captures the main concept instead of the bland p = m x v definition which though correct and needed for calculations conveys no mental imagery.
In Mathematics one should always approach a concept/idea from multiple perspectives including (but not limited to) Imagination, Conceptual, Graphical, Symbolic, Relationship, Applications, Definition/Theorem/Proof.
A Programmer's Introduction to Mathematics by Jeremy Kun is wide ranging and appropriate if there is also interest in programming.
Nature and Growth of Modern Mathematics by Edna Kramer is a wonderful book if history is a passion as well.
Elements of Mathematics by John Stillwell is a broad overview of subjects. It has a crisp mathematical feel to it.
Vector Calculus, Linear Algebra, and Differential Forms by John & Barbara Hubbard is a beautiful introduction to the multi-dimensional aspects, but it is a book that should happen after knowing one dimensional calculus. .
If your child hasn't been exposed to Guesstimation, then a book on that is highly recommended. The book with that title by Weinstein and Adams is a nice guide to investigating that realm.
If the child does arithmetic from right to left, as is sadly too common, the book Speed Mathematics Simplified by Edward Stoddard is a great remedy for that.
Everyday Calculus by Oscar Fernandez could also be worth a look.
https://www.amazon.com/Everyday-Calculus-Discovering-Hidden-...