1. Syllabus
2. Classroom Behaviour
3. Generic Course Objectives

Topic 1. Review of Calculus 1

1. Chain rule
2. Definition of the integral 
3. The fundamental theorem of calculus.

Topic 2. Transcendental Functions – Continued

1. The derivative of the logarithm function – geometric version   
2. The logarithm and exponential functions using the Fundamental Theorem of Calculus,

Topic 3. Integration by Parts

1. Integration by parts – Exercises
2. Trigonometrical Function.  
3. Integrals involving the Secant Function
4. Laissant’s Formula

Topic 4. Hyperbolic functions and some applications

1. Trigonometrical and Hyperbolic Functions – A Comparison
2. Hyperbolic Functions – Exercises.

Topic 5. Rational Functions, Improper Integrals

1. Rational Functions and Exercises
2. Integration of Rational Functions
3. Improper Integrals

Topic 6. Differential Equations

1. Introduction to ODE’s
2. Terminal Velocity

Topic 7. Sequences and Series

1. Review Calculus I material on Sequences

Topics 8-9 . Convergence of Series

1. Convergence of Series.
2. Power Series

Topics 11-12 Conic Sections

1. Salas, Hille and Anderson

Topic 13-14 Cuves

1. Curvature in 2 dimensions
2. The Cycloid

Topics 14- 15. Polar Coordinates

1. Polar Coordinate Exercises
2. Polar Coordinates

Supplementary Notes

1. Some Ways to Define Functions
2. Remarks on Parity
3. Exponential Series

Practice Exercises

1. Limits of Sequences Exercises
2. Limits of Functions Exercises
3. Indeterminate Forms Exercises
4. Definite Integrals – Exercises
5. Trignometric Integrals – Exercises
6. Ordinary Differential Equations – Exercises
7. Integrals – Exercises

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 and Anderson, Calculus, One and Several Variables, John Wiley.
7. (Free) Precalculus Book by David Santos
8. (Free) Ossifrage-And-Algebra-2007 by David Santos
9. (Free) Pre-y Cálculo Criollos (Spanish Version) by David Santos
10. (Free) Andragogic Propaedeutic Mathematics by David Santos
11. (Free) The Elements of Infinitesimal Calculus by David Santos
12. Michael Spivak, Calculus, Publish or Perish Inc., 1968.

Practice Exams

1. Practice Exam I