Integration and Infinite Series

UNIVERSITY OF CALIFORNIA, LOS ANGELES - FALL 2021

MATH 31B:1 - Integration and Infinite Series

Instructor : Pablo S. Ocal

Office hours : M 9:00-10:30 am (no appointment necessary)

Teaching Assistant : Eric Kim

Office hours : T 9:00-10:00 am (or by appointment)

Teaching Assistant : Gurkiran Dhaliwal

Office hours : T 4:10-5:10 pm (or by appointment)

Teaching Assistant : Zeshun Zong

Office hours : R 10:30 am-12:30 pm (or by appointment)

	Table of Contents
	1. Description
	2. Class Notes
	3. Schedule
	4. Homework
	5. Exams
	6. Resources

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 8:00 to 8:50 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.

MATH 31B Class Notes.

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

Tentative Schedule

Sep 24	Section 7.4, Introduction.
Sep 27	Section 7.1, Derivative of the Exponential Function. Office hours.
Sep 29	Section 7.2, Inverse Functions.
Oct 1	Section 7.3, Logarithms and their Derivatives.
Oct 4	Section 7.3, Logarithms and their Derivatives (continued). Office hours.
Oct 6	Section 7.7, L'Hopital's Rule.
Oct 8	Section 7.8, 7.9, Inverse Trigonometric and Hyperbolic Functions.
Oct 11	Section 8.1, Integration by Parts. Office hours.
Oct 13	Section 8.1, Integration by Parts (continued). Office hours.
Oct 15	Section 8.5, The Method of Partial Fractions.
Oct 18	Section 9.1, Arc Length and Surface Area. Office hours.
Oct 20	Section 9.4, Taylor Polynomials.
Oct 22	Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, Review.
Oct 25	Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, Midterm 1. Office hours.
Oct 27	Section 8.6, Improper Integrals.
Oct 29	Section 8.6, Improper Integrals (continued).
Nov 1	Section 11.1, Sequences. Office hours.
Nov 3	Section 11.1, Sequences (continued).
Nov 5	Section 11.2, Summing an Infinite Series.
Nov 8	Section 11.3, Convergence of Series with Positive Terms. Office hours.
Nov 10	Section 11.3, Convergence of Series with Positive Terms (continued).
Nov 12	Sections 8.6, 9.1, 9.4, 11.1, Review.
Nov 15	Sections 8.6, 9.1, 9.4, 11.1, Midterm 2. Office hours.
Nov 17	Section 11.4, Absolute and Conditional Convergence.
Nov 19	Section 11.5, The Ratio and Root Tests.
Nov 22	Section 11.6, Power Series. Office hours.
Nov 24	Section 11.6, Power Series (continued).
Nov 29	Section 11.7, Taylor Series. Office hours.
Dec 1	Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, 8.6, 9.1, 9.4, 11.1-11.7, Review.
Dec 3	Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, 8.6, 9.1, 9.4, 11.1-11.7, Review (continued).
Dec 8	Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, 8.6, 9.1, 9.4, 11.1-11.7, Final Exam.

Homework

There will be typically weekly homework. The assignments will be posted before Tuesdays at 9:00 am. The assignments will be due the next week, on Wednesday at 9:00 am. The assignments, deadlines, and solutions will be posted here.

Sep 21	Homework 0. Deadline: Sep 29.
Sep 28	Homework 1. Deadline: Oct 6.
Oct 5	Homework 2. Deadline: Oct 13.
Oct 12	Homework 3. Deadline: Oct 20.
Oct 19	Homework 4. Deadline: Oct 27.
Oct 26	Homework 5. Deadline: Nov 4.
Nov 2	Homework 6. Deadline: Nov 10.
Nov 9	Homework 7. Deadline: Nov 19.
Nov 16	Homework 8. Deadline: Nov 29.
Nov 23	Homework 9. Deadline: Dec 1.
Nov 30	Homework 10. Deadline: Dec 8.

Exams

Here the exams and their solutions will be posted. You can find the official UCLA schedule for the final exams here. You are required to bring two scantrons 882-ES/882-E to each exam.

Oct 25	Midterm 1, Solutions, MS 4000A from 8:00 to 8:50 am.
Nov 15	Midterm 2, Solutions, MS 4000A from 8:00 to 8:50 am.
Dec 8	Final Exam, Solutions, AU Grand Ballroom from 11:30 am to 2:30 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 peer learning facilitator from the Academic Advancement Program is Susanna Tovmasyan.
The Math Success Program from the Community Programs Office can be found here. You can go to their drop-in hours (no appointment necessary). You can also set up an appointment here.
The online calculator Wolfram|Alpha 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.