Textbook on calculus with the best application exercises

Question

I have finished the first half of Tom Apostol's Calculus vol. 1. While the theory is explained well, it doesn't teach much how you could apply the techniques you learn. I think I get a feeling for mathematics only when I see how I can apply it in solving real-life problems from different domains or deriving important physical equations.

While I intend to continue reading Apostol's works, I would like to have a second textbook that would be more down-to-earth and would contain a lot of interesting applications of calculus not only in physics, but in all sort of domains. I am considering the popular texts like Larson & Edwards, Thomas, Stewart and so on.

Can you tell me which one of these texts contain the best examples of applied calculus and the best application exercises. How it teaches theory is not important. Or recommend another textbook.

Answer 1

You are looking application oriented texts.

The two volumes of calculus

Introduction to Calculus and Analysis, by Richard Courant, Fritz John

theoretically as well as practically would be good sources for you. As far as I remembered, these two volumes were "especially" written with application purpose. This is some part of preface of his volume 1.

....While it differs markedly in form and content from the original, it is animated by the same intention: To lead the student directly to the heart of the subject and to prepare him for active application of his knowledge. It avoids the dogmatic style which conceals the motivation and the roots of the calculus in intuitive style. To exhibit the interaction between mathematical analysis and its various applications and to emphasize the role of intuition remains an important aim of this new book.....

Answer 2

The Courant is a great choice for application. Calculus: Early Transcendentals by Dennis Zill and Warren Wright is also very good. You have to consider also that the Introduction to Calculus and Analysis has a much more formal approach than Calculus: Early Transcendentals. Zill's book has some difficult (or tricky) examples.

Have a look at the Calculus books written by Jon Rogawski (they have difficult examples that are great to practise the techniques of calculus and the applications) or the ones by George B. Thomas.

Warning: If you want to learn about the applications do not read A course of pure mathematics by G. H. Hardy. It has no applications of Calculus. However, it is still one of the best books to learn the formal aspects of Calculus and some other related areas of Mathematics.