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.
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.
3. Techniques for finding limits , Update 16-02 4. What is a derivative , Update 15-09 5. Derivatives formulas and rules , Update 15-09 9. Related rates , Update 16-04 10. Maxima and minima of functions Update 16-04
11. Optimization problems , Update 16-04 12. Proofs
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
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