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)
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.

Tentative Schedule
Jan 8Section 7.1,
Derivative of the Exponential Function.
Jan 10Section 7.2,
Inverse Functions.
Jan 12Section 7.3,
Logarithms and their Derivatives.
Jan 17Section 7.7,
L'Hopital's Rule.
Jan 19Section 7.8, 7.9,
Inverse Trigonometric and Hyperbolic Functions.
Jan 22Section 8.1,
Integration by Parts.
Jan 24Section 8.1, 8.5,
Integration by Parts (continued), The Method of Partial Fractions.
Jan 26Section 8.5,
The Method of Partial Fractions (continued).
Jan 29Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5,
Review.
Jan 31Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5,
Midterm 1.
Feb 2Section 9.4,
Taylor Polynomials.
Feb 5Section 8.6,
Improper Integrals.
Feb 7Section 8.6,
Improper Integrals (continued).
Feb 9Section 11.1,
Sequences.
Feb 12Section 11.1,
Sequences (continued).
Feb 14Section 11.2,
Summing an Infinite Series.
Feb 16Section 11.2,
Summing an Infinite Series (continued).
Feb 21Sections 8.6, 9.4, 11.1, 11.2,
Review.
Feb 23Sections 8.6, 9.4, 11.1, 11.2,
Midterm 2.
Feb 26Section 11.3,
Convergence of Series with Positive Terms.
Feb 28Section 11.3,
Convergence of Series with Positive Terms (continued).
Mar 1Section 11.4,
Absolute and Conditional Convergence.
Mar 4Section 11.5,
The Ratio and Root Tests.
Mar 6Section 11.6,
Power Series.
Mar 8Section 11.6,
Power Series (continued).
Mar 11Section 11.7,
Taylor Series.
Mar 13Section 11.7,
Taylor Series (continued).
Mar 15Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, 8.6, 9.4, 11.1-11.7,
Review.
Mar 21Sections 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 8Homework 0.
Deadline: Jan 12.
Jan 8Homework 1.
Deadline: Jan 19.
Jan 15Homework 2.
Deadline: Jan 26.
Jan 22Homework 3.
Deadline: Feb 2.
Jan 29Homework 4.
Deadline: Feb 9.
Feb 5Homework 5.
Deadline: Feb 16.
Feb 12Homework 6.
Deadline: Feb 23.
Feb 19Homework 7.
Deadline: Mar 1.
Feb 26Homework 8.
Deadline: Mar 8.
Mar 4Homework 9.
Deadline: Mar 15.
Mar 11Homework 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 9Discussion 1.
Deadline: Jan 11.
Jan 16Discussion 2.
Deadline: Jan 18.
Jan 23Discussion 3.
Deadline: Jan 25.
Jan 30Discussion 4.
Deadline: Feb 2.
Feb 6Discussion 5.
Deadline: Feb 8.
Feb 13Discussion 6.
Deadline: Feb 15.
Feb 20Discussion 7.
Deadline: Feb 22.
Feb 27Discussion 8.
Deadline: Feb 29.
Mar 5Discussion 9.
Deadline: Mar 7.
Mar 12Discussion 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 31Midterm 1,
MS 4000A from 11:00 to 11:50 am.
Feb 23Midterm 2,
MS 4000A from 11:00 to 11:50 am.
Mar 21Final Exam,
TBD 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.

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).