- Course Philosophy
- Generic Course Objectives
- Classroom Behaviour
- On the use of electronic aparati
- Recomendaciones para Estudiantes Nuevos
- In Praise of Lectures
- UPR Regulations concerning Academic Integrity and Reasonable Accommodation”

### Syllabus

### Notes

- The Limit of a Sequence
- The epsilon-delta definition of a limit -From Brilliant.org
- Limits using Epsilon and Delta – Example.
- Derivative of the Natural Logarithm
- The Chain Rule
- Points of Inflexion
- Rates of Change
- Rectilinear Motion
- Mean Value Theorem
- Optimization (Application to Optics)
- Antiderivative Formulae
- Substitution – more examples
- Antiderivatives Involving the Secant Function
- Telescoping Series
- The Definite Integral
- The Fundamental Theorem
- Application of the FTC to Logarithms
- Applications of the Definite Integral
- Work
- Harder Substitution Examples
- The Irrationality of
*e*

### Exercises

- Limits of Sequences
- Limits of Functions
- Differentiation
- Differentiation
- Exponential Growth
- Rate of Change Problems
- Optimization with Constraints
- Antiderivatives (Indefinite Integrals)
- Definite Integrals
- Area

### Text

George B. Thomas Jr. Maurice D. Weir, and Joel R. Hass, Calculus, 12th Edition.

### Bibliography

- K. Kodaira, (Editor), Basic Analysis, Japanese Grade 11. AMS
- Y. M. Chow et. al., College Mathematics Volume 2, Syllabus C, Pan Pacific Publications, ISBN 9971-63-863-0.
- Stewart and Tall,
*Foundations of Mathematics, Ed. 1*, Oxford University Press. - Serge Lang,
*A First Course in Calculus,*Addison Wesely, 1968. - Serge Lang,
*A Second Course in Calculus,*Addison Wesely, 1968. - Salas, Hille y Anderson,
*Calculus, One and Several Variables*, John Wiley. - Lecture Notes
- (Free) Precalculus Book by David Santos
- (Free) Ossifrage-And-Algebra-2007 by David Santos
- (Free) Pre-y Cálculo Criollos (Spanish Version) by David Santos
- (Free) Andragogic Propaedeutic Mathematics by David Santos
- (Free) The Elements of Infinitesimal Calculus by David Santos
- Michael Spivak,
*Calculus*, Publish or Perish Inc., 1968.