## Mate 3152 – 2019- S2

- Course Philosophy
- Generic Course Objectives
- Classroom Behaviour
- On the use of electronic aparati
- Recomendaciones para Estudiantes Nuevos
- In Praise of Lectures

## 2019-2020– Semester I

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

#### Tasks for Week 8

- View video on partial fractions.
- Read Lecture Notes I
- Read Lecture Notes II
- Do exercises
- Submit Homework
- Additional Reading

#### Tasks for Week 9

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

#### Tasks for Week 10 +

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

#### Tasks for Week 11+

- Review
- Read class notes on Power Series
- View Kahn Videos on Power Series (see above)
- Submit Homework 4

#### Tasks for Week 12+

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

#### Tasks for Week 13+

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

#### Tasks for Week 14+

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

#### Tasks for week 15

- Prepare for Final Exam: Wednesday May 20 from 11:30-1:30 PM
- 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

### Notes

- The limit of a Sequence
- Some Ways to Define Functions
- Remarks on Parity
- Hyperbolic Sectors
- Hyperbolic Functions
- Inverse Trigonometric and Hyperbolic Functions
- Miscellaneous Trigonometric and Hyperbolic Integrals
- Hyperbolic Functions – Examples
- Euler’s Formula – Useful
**C**orollaries - Terminal Velocity
- The Substitution $t = \tan (x/2)$
- Rational Functions
- Integration of Rational Functions
- Improper Integrals
- Convergence of Series
- Absolute Convergence
- Ratio Test
- Cauchy Condensation
- Alternating Series
- Limit Comparison Test
- Power Series-I
- Power Series-II
- Computing Taylor Series
- Exponential Series
- The Irrationality of
*e* - Equality up to Order $n$
- Limit Superior and Limit Inferior
- The Cycloid
- Curvature

### Exercises

- Limits of Sequences (Calculus I)
- Limits of Sequences (Calculus II)
- Limits of Functions (Calculus I)
- Indeterminate Forms
- Logarithmic and ExponentialFunctions
- Definite Integrals (Calculus I)
- Integration by Parts
- Trignometric Functions
- Hyperbolic Functions
- Ordinary Differential Equations
- Rational Functions
- Integrals (Calculus II)
- Improper Integrals
- Series
- Taylor Series
- Polar Coordinates

### 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.