Calculus for Everyone

I wrote a free Calculus I textbook (Differential Calculus) as part of Brooklyn College's contribution to CUNY's Open Education Resources (OER) at CUNY. The College supported this effort by giving faculty participating in OER a 3-credit course release for Spring 2015. At some point in the future I will also write a free Calculus II textbook (Integral Calculus).


Side note: If you are looking for Tintin Comics Professor Calculus click here. If you are looking for Marvel's Young God Calculus click here. Then come back here to see why Calculus can "predict with near-total accuracy the outcome of future events and how to manipuate events in order to achieve a desired result."


The first draft is available below. It may help to read the preface before reading the chapters since that is where I describe my views on how to make Calculus textbooks accessible to a wide audience and discuss the various types of Calculus courses.

The following excerpt from Skimming a Century of Calculus has guided my approach.

On page 48, R. G. Helsel and T. Radů pondered (MAA 55 1948, pp. 28-29) the question Can We Teach Good Mathematics To Undergraduates? They cited three ingredients of good mathematics: relevancy (calculus, for example, is overflowing with relevancy), rigor (all of the reasons must be given), and elegancy (not to deprive the students of the very thing that affords us our greatest pleasure).

Consistency, I thought, they did not mention consistency. Clearly the question at hand is that of good mathematics presentation. For a good course, consistency in style is a prerequisite. It could be a trifle. For example, if during the first few weeks Professor conditions the students by emphasizing important ideas with a chalk of red color, and then comes to a lesson without his implements, many students will be bound to miss something important.

Consistency is something that I found missing in textbooks and it is not just the layout of the material, but a consistency of thinking style, consistency of ideas and of how to start with something simple and build up from there. I paid attention to consistency as best as I could.

If you read the book (or portions of it) or use it in your class, I would love to hear from you. Constructive criticism would be much appreciated. You can send me email at Sandra Kingan (skingan@brooklyn.cuny.edu). As I correct and update chapters I will post the updated chapters right next to the original chapters to make it easy for the reader to get the most updated version.


Calculus I: Differential Calculus


Preface

1. What is a limit?

2. Continuous functions

3. Techniques for finding limits , Update 16-02

4. What is a derivative , Update 15-09

5. Derivatives formulas and rules , Update 15-09

6. More derivative formulas

7. Implicit differentiation

8. LíHopitalís rule

9. Related rates , Update 16-04

10. Maxima and minima of functions Update 16-04

11. Optimization problems , Update 16-04

12. Proofs


Calculus II: Integral Calculus


1. What is integration?

2. Integration formulas

3 Integration by substitution

4. More integration techniques

5. Integration using partial fractions

6. Numerical methods for integration

7. Areas and volumes

8. Arc lengths and surfaces of revolution

9. Sequences and series

10. Tests of convergence - I

11. Tests of convergence - II

12. Taylor and MacLaurin Series


© 2015 S. R. Kingan All Rights Reserved