Table of Contents | |

1. Description | |

2. Class Notes | |

3. Schedule | |

4. Homework | |

5. Discussion | |

6. Exams | |

7. Resources | |

8. Grading Schemes |

UNIVERSITY OF CALIFORNIA, LOS ANGELES - WINTER 2024

MATH 31B:3 - Integration and Infinite Series

Instructor : Pablo S. Ocal

Office hours : W 8:00-9:45 am (MS 6627)

Teaching Assistant : Advika Rajapakse

Office hours : M 2:00-3:00 pm (MS 3974), F 1:00-2:00 pm (MS 2953)

Teaching Assistant : Thomas Martinez

Office hours : R 12:00 am-1:00 pm (MS 3955)

Teaching Assistant : Abin Devassia

Office hours : M 12:00-1:00 pm (MS 3974)

Table of Contents | |

1. Description | |

2. Class Notes | |

3. Schedule | |

4. Homework | |

5. Discussion | |

6. Exams | |

7. Resources | |

8. Grading Schemes |

Description

The course on *Integration and Infinite Series* will treat, among others, methods of differentiation, methods of integration, series and their convergence, and relations between these concepts. The prerequisites required for this course are covered in Math 31A.

The course will have weekly classes on

**Mondays, Wednesdays, and Fridays in MS, room 4000A, from 11:00 to 11:50 am.**

The book we will be following is *Single Variable Calculus (2nd edition)* by Jonathan D. Rogawski. We will be covering material in Chapters 7, 8, 9, and 11. You may find all the information you will need on the **Syllabus**.

Class Notes

The following notes are a formal outline of the material we will be covering. These notes are not comprehensive nor are intended to be a substitute for the textbook or the lectures. If you find mistakes (typographical or other) in these notes, or have comments, please let me know.

The following are additional materials closely related to the class notes.

- Table of trigonometric functions, hyperbolic functions, their inverses, and their derivatives.
- A variant of Problem 11.3.39.
- Problem 11.4.32.
- Guidelines for choosing a test when determining convergence or divergence of series.
- Factoring polynomials by
**Kevin Wortman**. - A guide to partial fractions by
**Joseph Breen**. - Angles, sine, and cosine, in the unit circle by
**Gilles Cazelais**. - Trigonometry in the unit circle by
**Gilles Cazelais**. - Proof of the trigonometric identities for sum and difference angles by
**Gilles Cazelais**. - Binomial Theorem by
**Saylor Academy**.

Tentative Schedule

Jan 8 | Section 7.1, Derivative of the Exponential Function. |

Jan 10 | Section 7.2, Inverse Functions. |

Jan 12 | Section 7.3, Logarithms and their Derivatives. |

Jan 17 | Section 7.7, L'Hopital's Rule. |

Jan 19 | Section 7.8, 7.9, Inverse Trigonometric and Hyperbolic Functions. |

Jan 22 | Section 8.1, Integration by Parts. |

Jan 24 | Section 8.1, 8.5, Integration by Parts (continued), The Method of Partial Fractions. |

Jan 26 | Section 8.5, The Method of Partial Fractions (continued). |

Jan 29 | Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, Review. |

Jan 31 | Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, Midterm 1. |

Feb 2 | Section 9.4, Taylor Polynomials. |

Feb 5 | Section 8.6, Improper Integrals. |

Feb 7 | Section 8.6, Improper Integrals (continued). |

Feb 9 | Section 11.1, Sequences. |

Feb 12 | Section 11.1, Sequences (continued). |

Feb 14 | Section 11.2, Summing an Infinite Series. |

Feb 16 | Section 11.2, Summing an Infinite Series (continued). |

Feb 21 | Sections 8.6, 9.4, 11.1, 11.2, Review. |

Feb 23 | Sections 8.6, 9.4, 11.1, 11.2, Midterm 2. |

Feb 26 | Section 11.3, Convergence of Series with Positive Terms. |

Feb 28 | Section 11.3, Convergence of Series with Positive Terms (continued). |

Mar 1 | Section 11.4, Absolute and Conditional Convergence. |

Mar 4 | Section 11.5, The Ratio and Root Tests. |

Mar 6 | Section 11.6, Power Series. |

Mar 8 | Section 11.6, Power Series (continued). |

Mar 11 | Section 11.7, Taylor Series. |

Mar 13 | Section 11.7, Taylor Series (continued). |

Mar 15 | Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, 8.6, 9.4, 11.1-11.7, Review. |

Mar 21 | Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, 8.6, 9.4, 11.1-11.7, Final Exam. |

Homework

There will be typically weekly homework. The assignments will be posted before Mondays at 9:00 am. The assignments will be due on Gradescope the following week, on Friday at 11:59 pm. The assignments and deadlines will be posted here. You are encouraged to work in groups.

Jan 8 | Homework 0. Deadline: Jan 12. |

Jan 8 | Homework 1. Deadline: Jan 19. |

Jan 15 | Homework 2. Deadline: Jan 26. |

Jan 22 | Homework 3. Deadline: Feb 2. |

Jan 29 | Homework 4. Deadline: Feb 9. |

Feb 5 | Homework 5. Deadline: Feb 16. |

Feb 12 | Homework 6. Deadline: Feb 23. |

Feb 19 | Homework 7. Deadline: Mar 1. |

Feb 26 | Homework 8. Deadline: Mar 8. |

Mar 4 | Homework 9. Deadline: Mar 15. |

Mar 11 | Homework 10. Deadline: Mar 15. |

Discussion

There will be typically weekly discussion sessions. These intend to allocate time for you to work on the homework problems with your peers while having readily available feedback. The starred problem will be due on Gradescope on Thursday at 11:59 pm. The deadlines will be posted here. You are encouraged to work in groups.

Jan 9 | Discussion 1. Deadline: Jan 11. |

Jan 16 | Discussion 2. Deadline: Jan 18. |

Jan 23 | Discussion 3. Deadline: Jan 25. |

Jan 30 | Discussion 4. Deadline: Feb 2. |

Feb 6 | Discussion 5. Deadline: Feb 8. |

Feb 13 | Discussion 6. Deadline: Feb 15. |

Feb 20 | Discussion 7. Deadline: Feb 22. |

Feb 27 | Discussion 8. Deadline: Feb 29. |

Mar 5 | Discussion 9. Deadline: Mar 7. |

Mar 12 | Discussion 10. Deadline: Mar 14. |

Exams

Here the exams and their solutions will be posted. You can find the official UCLA schedule for the final exams **here**.

Jan 31 | Midterm 1, MS 4000A from 11:00 to 11:50 am. |

Feb 23 | Midterm 2, MS 4000A from 11:00 to 11:50 am. |

Mar 21 | Final Exam, WGYOUNG CS24 from 3:00 to 6:00 pm. |

The following are practice exams that you may use to prepare:

Resources

There are many resources available for a student at UCLA, I encourage you to use them and make the most out of them. Here are some materials specific to this course:

- The open office hours at the Student Math Center can be found
**here**. - The open tutoring of Tau Beta Pi can be found
**here**. - The Math Success Program from the
**Community Programs Office**can be found**here**. - The online calculator Wolfram|Alpha can be found
**here**.

Here are some general materials about the Department of Mathematics, the College of Physical Sciences, and UCLA:

- The Campus Resources document maintained by
**Britney Robinson**can be found**here**. - The Frequently Asked Questions of the Undergraduate Math Council can be found
**here**.

I also encourage you to form study groups with your classmates. However, please keep in mind that you will only learn how to do the exercises if you try them on your own: without trying, looking up the solutions or copying others' work is absolutely useless.

Grading Schemes

You can compute your final grade using the calculator below. Please input the average of your homework assignments (out of 100), the average of your discussion assignments (out of 100), the score of your first midterm (out of 100), the score of your second midterm (out of 100), and the score of your final (out of 100). Then, click "Compute grading schemes" to see the three grading schemes (out of 100).