How appropriate that our first new free textbook of 2021 was released on January 1. And, how exciting it was to receive an email from the author letting us know!

Elementary Calculus is Michael Corral’s third open textbook. His other’s are Vector Calculus and Trigonometry. He is an Adjunct faculty member of the Schoolcraft College Department of Mathematics. He earned his BA in Mathematics from the University of California and earned his MA in Mathematics and his MS in Industrial & Operations Engineering from the University of Michigan.

This textbook includes materials for both Calculus I & II. To prepare for these courses, students should have completed high school courses in algebra, geometry and trigonometry. The text is suitable for both high school and college calculus students. Students will get plenty of practice as they work the included 943 exercises – yes, answers and hints are provided for selected exercises.

## Table of Contents for Elementary Calculus Open Textbook

- 1. The Derivative
- Introduction
- The Derivative: Limit Approach
- The Derivative: Infinitesimal Approach
- Derivatives of Sums, Products and Quotients
- The Chain Rule
- Higher Order Derivatives
- 2. Derivatives of Common Functions
- Inverse Functions
- Trigonometric Functions and Their Inverses
- The Exponential and Natural Logarithm Functions
- General Exponential and Logarithmic Functions
- 3. Topics in Differential Calculus
- Tangent Lines
- Limits: Formal Definition
- Continuity
- Implicit Differentiation
- Related Rates
- Differentials
- 4. Applications of Derivatives
- Optimization
- Curve Sketching
- Numerical Approximation of Roots of Functions
- The Mean Value Theorem

- 5. The Integral
- The Indefinite Integral
- The Definite Integral
- The Fundamental Theorem of Calculus
- Integration by Substitution
- Improper Integrals

- 6. Methods of Integration
- Integration by Parts
- Trigonometric Integrals
- Trigonometric Substitutions
- Partial Fractions
- Miscellaneous Integration Methods
- Numerical Integration Methods
- 7. Analytic Geometry and Plane Curves
- Ellipses
- Parabolas
- Hyperbolas
- Translations and Rotations
- Hyperbolic Functions
- Parametric Equations
- Polar Coordinates
- 8. Applications of Integrals
- Area Between Curves
- Average Value of a Function
- Arc Length and Curvature
- Surfaces and Solids of Revolution
- Applications in Physics and Statistics

- 9. Infinite Sequences and Series
- Sequences and Series
- Tests for Convergence
- Alternating Series
- Power Series
- Appendix A: Answers and Hints to Selected Exercises
- NU Free Documentation License
- History
- Index

View this Free Online Material at the source:

Elementary Calculus