Math 3152 Calculus II

Mate 3152 – 2019- S2

  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

2019-2020– Semester I

  1. Syllabus S2 2019-20

Due to a virus from China the semester was completed on line as follows:

Tasks for Week 8

  1. View video on partial fractions.
  2. Read Lecture Notes I
  3. Read Lecture Notes II
  4. Do exercises
  5. Submit Homework
  6. Additional Reading

Tasks for Week 9

  1. Review above Sequence Kahn Videos on Improper Integrals
  2. Read and do exercises in items 14, 15 here
  3. Submit Homework 2 — Deadline 11AM Friday April 3

Tasks for Week 10 +

  1. Review Calculus I material on Sequences
  2. Read carefully the class notes on the Convergence of Series
  3. Review the following tests for convergence.
  4. Read class notes on Absolute Convergence
  5. Review this sequence of Kahn Videos on Series <–Link corrected 04/07/2020
  6. Do exercises
  7. Submit Homework 3

Tasks for Week 11+

  1. Review
  2. Read class notes on Power Series
  3. View Kahn Videos on Power Series (see above) 
  4. Submit Homework 4

Tasks for Week 12+

  1. Read class notes on Taylor Series -Posted 04/25
  2. Read class notes on Estimation -Posted 04/25
  3. View this sequence of Kahn Videos on Taylor Series 
  4. Do exercises on Taylor Series
  5. Submit Homework 5 -Posted 04/25

Tasks for Week 13+

  1. View this sequence of Kahn Videos on Curvature
  2. View this sequence of Kahn Videos on Arclength 
  3. Study the examples here. 
  4. Read class notes on Curvature -Posted 04/30
  5. Read class notes on the Cycloid -Posted 04/30
  6. Submit Homework 6 -Posted 04/30

Tasks for Week 14+

  1. View this sequence of Kahn Videos on Polar Coordinates
  2. Do exercises 1-8 on Polar Coordinates -Posted 05/08/2020
  3. Go to Week 15 and Final Exam Review

Tasks for week 15

  1. Prepare for Final Exam: Wednesday May 20 from 11:30-1:30 PM 
  2. Review the class notes, exercises and homeworks at the MATH 3152 Page

Instructions for Final Exam

The exam (in PDF Format) be emailed to you at 11:25AM on the day of the exam. 
The exam will consist  of  20 questions taken from all parts of the course. Each question, whether  trivial or difficult,  will be worth 5 points for a total of 100 points.   The exam should  be answered in dark ink on the exam sheets,  and emailed to me (preferably in PDF format) by 02:00 PM of the same day as the exam.  Exams received after this time will receive no credit.     

Practice Exams

  1. Practice Exam I


  1. The limit of a Sequence
  2. Some Ways to Define Functions
  3. Remarks on Parity
  4. Hyperbolic Sectors
  5. Hyperbolic Functions
  6. Inverse Trigonometric and Hyperbolic Functions
  7. Miscellaneous Trigonometric and Hyperbolic Integrals
  8. Hyperbolic Functions – Examples
  9. Euler’s Formula – Useful Corollaries
  10. Terminal Velocity
  11. The Substitution $t = \tan (x/2)$
  12. Rational Functions
  13. Integration of Rational Functions
  14. Improper Integrals
  15. Convergence of Series
  16. Absolute Convergence
  17. Ratio Test
  18. Cauchy Condensation
  19. Alternating Series
  20. Limit Comparison Test
  21. Power Series-I
  22. Power Series-II
  23. Computing Taylor Series
  24. Exponential Series
  25. The Irrationality of e
  26. Equality up to Order $n$
  27. Limit Superior and Limit Inferior
  28. The Cycloid
  29. Curvature


  1. Limits of Sequences (Calculus I)
  2. Limits of Sequences (Calculus II)
  3. Limits of Functions (Calculus I)
  4. Indeterminate Forms
  5. Logarithmic and ExponentialFunctions
  6. Definite Integrals (Calculus I)
  7. Integration by Parts
  8. Trignometric Functions
  9. Hyperbolic Functions
  10. Ordinary Differential Equations
  11. Rational Functions
  12. Integrals (Calculus II)
  13. Improper Integrals
  14. Series
  15. Taylor Series
  16. Polar Coordinates


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


  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.