UNIVERSITY OF CALIFORNIA, LOS ANGELES - SUMMER 2022
MATH 31B:1 - Integration and Infinite Series
Instructor :  Pablo S. Ocal
Office hours :  T 7:00-9:00 am (no appointment necessary)
Teaching Assistant :  Gurkiran Dhaliwal
Office hours :  F 2:00-3:00 pm (no appointment necessary)
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

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.

Tentative Schedule
Aug 1Section 7.4, 7.1,
Introduction. Derivative of the Exponential Function. Notes.
Aug 2Section 7.1, 7.2,
Derivative of the Exponential Function. Inverse Functions. Notes.
Aug 3Section 7.3,
Logarithms and their Derivatives. Notes.
Aug 8Section 7.3, 7.7
Logarithms and their Derivatives. L'Hopital's Rule. Notes.
Aug 9Section 7.8, 7.9, 8.1
Inverse Trigonometric and Hyperbolic Functions. Integration by Parts. Notes.
Aug 10Section 8.1,
Integration by Parts. Notes.
Aug 11Sections 7.1-7.3, 7.7-7.9, 8.1,
Midterm 1.
Aug 15Section 8.5, 9.1,
The Method of Partial Fractions. Arc Length and Surface Area. Notes.
Aug 16Section 9.1, 9.4,
Arc Length and Surface Area. Taylor Polynomials. Notes.
Aug 17Section 8.6,
Improper Integrals. Notes.
Aug 22Section 8.6, 11.1
Improper Integrals. Sequences. Notes.
Aug 23Section 11.1,
Sequences. Notes.
Aug 24Section 11.2,
Summing an Infinite Series. Notes.
Aug 25Sections 8.5-8.6, 9.1, 9.4, 11.1-11.2,
Midterm 2.
Aug 29Section 11.3,
Convergence of Series with Positive Terms. Notes.
Aug 30Section 11.3, 11.4,
Convergence of Series with Positive Terms. Absolute and Conditional Convergence. Notes.
Aug 31Section 11.5, 11.6,
The Ratio and Root Tests. Power Series. Notes.
Sep 5Section 11.6,
Power Series. Notes.
Sep 6Section 11.7,
Taylor Series. Notes.
Sep 7Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, 8.6, 9.1, 9.4, 11.1-11.7,
Review.
Sep 8Sections 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 Mondays at 9:00 am. The assignments will be due the next week, on Friday at 11:59 pm. The assignments, deadlines, and solutions will be posted here.

Aug 1Homework 0.
Deadline: Aug 12.
Aug 8Homework 1.
Deadline: Aug 19.
Aug 15Homework 2.
Deadline: Aug 26.
Aug 22Homework 3.
Deadline: Sep 2.
Aug 29Homework 4.
Deadline: Sep 9.
Aug 29Homework 5.
Deadline: Sep 9.
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 first starred problem will be due on Gradescope on Tuesday at 11:59 pm. The second 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.

Aug 9Discussion 1.1.
Deadline: Aug 9.
Aug 11Discussion 1.2.
Deadline: Aug 11.
Aug 16Discussion 2.1.
Deadline: Aug 16.
Aug 18Discussion 2.2.
Deadline: Aug 18.
Aug 23Discussion 3.1.
Deadline: Aug 23.
Aug 25Discussion 3.2.
Deadline: Aug 25.
Aug 30Discussion 4.1.
Deadline: Aug 30.
Sep 1Discussion 4.2.
Deadline: Sep 1.
Sep 6Discussion 5.1.
Deadline: Sep 6.
Sep 8Discussion 5.2.
Deadline: Sep 8.
Exams

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

Aug 11-12Midterm 1, Solutions,
From 8:00 am to 8:50 am.
Aug 25-26Midterm 2, Solutions,
From 8:00 am to 8:50 am.
Sep 8-9Final Exam,
From 8:00 am to 8:00 am.

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 Math Success Program from the Community Programs Office can be found 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.