Math 3151 Calculus I

  1. Syllabus – Semester I, 2023
  2. Generic Course Objectives
  3. Classroom Behaviour

Calendar of Lectures

Week I — Review of Precalculus

  1. Review

Week II — Limits of sequences and functions

  1. The Limit of a Sequence
  2. Exercises on the Limit of a Sequence
  3. Limits using Epsilon and Delta – Example.
  4. Exercises on the Limit of a Function

Week III — Continuity

  1. Exercises on Continuity

Week IV — The derivative

  1. Homework I on the Derivative
  2. Homework II on the Derivative
  3. Rectilinear Motion

Week V — The derivative, Part II

  1. The Chain Rule
  2. Rate of Change Example

EXAM I

  1. Review for Exam I

Week VI — Implicit differentiation, related rates

  1. Implicit Derivatives and Rate of Change Problems

Week VII — Logarithms

  1. Derivative of the Natural Logarithm

Week VIII — The Mean Value Theorem and Consequences

  1. Mean Value Theorem
  2. Points of Inflexion
  3. Exercises on the Mean Value Theorem

Week IX — Optimization

  1. Optimization (Application to Optics)
  2. Exercises on Optimization with Constraints

EXAM II

  1. Review for Exam II

Week X — Antiderivatives

  1. Antiderivative Formulae
  2. Exercises on Antiderivatives

Week XI — Antiderivatives Part II

  1. Substitution – more examples
  2. Harder Substitution Examples
  3. Antiderivatives Involving the Secant Function

Week XII — The definite Integral

  1. The Definite Integral
  2. Applications of the Definite Integral
  3. Exercises on the Definition of the Integral

Week XIII — The Fundamental Theorem of Calculus (FTC)

  1. The Fundamental Theorem
  2. Exercises on the Definite Integral
  3. Exercises on Area
  4. Volume

EXAM III

  1. Review for Exam III

Week XIV — Logarithmic and Exponential Functions

  1. Application of the FTC to Logarithms
  2. Exercises on Exponential Growth and Decay

Week XV — Applications

  1. Applications of the Definite Integral
  2. Work

Exam IV

  1. Review for Exam IV

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.