Math 3151 Calculus I

  1. Course Philosophy
  2. Generic Course Objectives
  3. Classroom Behaviour
  4. On the use of electronic aparati
  5. Recomendaciones para Estudiantes Nuevos
  6. In Praise of Lectures
  7. UPR Regulations concerning Academic Integrity and Reasonable Accommodation”

Syllabus

Syllabus S1 2020

Notes

  1. The Limit of a Sequence
  2. The epsilon-delta definition of a limit -From Brilliant.org
  3. Limits using Epsilon and Delta – Example.
  4. Derivative of the Natural Logarithm
  5. The Chain Rule
  6. Points of Inflexion
  7. Rates of Change
  8. Rectilinear Motion
  9. Mean Value Theorem
  10. Optimization (Application to Optics)
  11. Antiderivative Formulae
  12. Substitution – more examples
  13. Antiderivatives Involving the Secant Function
  14. Telescoping Series
  15. The Definite Integral
  16. The Fundamental Theorem
  17. Application of the FTC to Logarithms
  18. Applications of the Definite Integral
  19. Work
  20. Harder Substitution Examples
  21. The Irrationality of e

Exercises

  1. Limits of Sequences
  2. Limits of Functions
  3. Differentiation
  4. Differentiation
  5. Exponential Growth
  6. Rate of Change Problems
  7. Optimization with Constraints
  8. Antiderivatives (Indefinite Integrals)
  9. Definite Integrals
  10. Area

Text

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

Bibliography

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