Elementary Calculus

Michael Corral

Digital versions PDF
Latex source Yes
Exercises Yes, with answers and hints to odd numbered problems
Solutions No
License Gnu Free Documentation License

The book is designed for students in science and engineering. It motivates the concepts of calculus with physical examples and uses infinitesimals in a way that aligns with what students see in their physics and engineering classes.

This text offers a clear alternative to the commercial textbooks that the author finds “…far too bloated and filled with fluff…”. There are plenty of exercises but not so many as to overwhelm the instructor making homework assignments. The exercises grouped into easy, moderate, and challenging categories. There are answers and some hints for many of the odd-numbered problems and for some of the even-numbered problems. A few exercises require the student to write programs for numerical approximations. Algorithms are presented in pseudocode and some examples of code are given in Java, Python, Sage, and Octave.


  1. The Derivative
  2. Derivatives of Common Functions
  3. Topics in Differential Calculus
  4. Applications of Derivatives
  5. The Integral
  6. Methods of Integration
  7. Analytic Geometry of Plane Curves
  8. Applications of Integrals
  9. Infinite Sequences and Series