Table of Contents | |
1. Description | |
2. Class Notes | |
3. Schedule | |
4. Homework | |
5. Discussion | |
6. Exams | |
7. Resources |
Table of Contents | |
1. Description | |
2. Class Notes | |
3. Schedule | |
4. Homework | |
5. Discussion | |
6. Exams | |
7. Resources |
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.
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.
Aug 1 | Section 7.4, 7.1, Introduction. Derivative of the Exponential Function. Notes. |
Aug 2 | Section 7.1, 7.2, Derivative of the Exponential Function. Inverse Functions. Notes. |
Aug 3 | Section 7.3, Logarithms and their Derivatives. Notes. |
Aug 8 | Section 7.3, 7.7 Logarithms and their Derivatives. L'Hopital's Rule. Notes. |
Aug 9 | Section 7.8, 7.9, 8.1 Inverse Trigonometric and Hyperbolic Functions. Integration by Parts. Notes. |
Aug 10 | Section 8.1, Integration by Parts. Notes. |
Aug 11 | Sections 7.1-7.3, 7.7-7.9, 8.1, Midterm 1. |
Aug 15 | Section 8.5, 9.1, The Method of Partial Fractions. Arc Length and Surface Area. Notes. |
Aug 16 | Section 9.1, 9.4, Arc Length and Surface Area. Taylor Polynomials. Notes. |
Aug 17 | Section 8.6, Improper Integrals. Notes. |
Aug 22 | Section 8.6, 11.1 Improper Integrals. Sequences. Notes. |
Aug 23 | Section 11.1, Sequences. Notes. |
Aug 24 | Section 11.2, Summing an Infinite Series. Notes. |
Aug 25 | Sections 8.5-8.6, 9.1, 9.4, 11.1-11.2, Midterm 2. |
Aug 29 | Section 11.3, Convergence of Series with Positive Terms. Notes. |
Aug 30 | Section 11.3, 11.4, Convergence of Series with Positive Terms. Absolute and Conditional Convergence. Notes. |
Aug 31 | Section 11.5, 11.6, The Ratio and Root Tests. Power Series. Notes. |
Sep 5 | Section 11.6, Power Series. Notes. |
Sep 6 | Section 11.7, Taylor Series. Notes. |
Sep 7 | Sections 7.1-7.3, 7.7-7.9, 8.1, 8.5, 8.6, 9.1, 9.4, 11.1-11.7, Review. |
Sep 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. |
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 1 | Homework 0. Deadline: Aug 12. |
Aug 8 | Homework 1. Deadline: Aug 19. |
Aug 15 | Homework 2. Deadline: Aug 26. |
Aug 22 | Homework 3. Deadline: Sep 2. |
Aug 29 | Homework 4. Deadline: Sep 9. |
Aug 29 | Homework 5. Deadline: Sep 9. |
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 9 | Discussion 1.1. Deadline: Aug 9. |
Aug 11 | Discussion 1.2. Deadline: Aug 11. |
Aug 16 | Discussion 2.1. Deadline: Aug 16. |
Aug 18 | Discussion 2.2. Deadline: Aug 18. |
Aug 23 | Discussion 3.1. Deadline: Aug 23. |
Aug 25 | Discussion 3.2. Deadline: Aug 25. |
Aug 30 | Discussion 4.1. Deadline: Aug 30. |
Sep 1 | Discussion 4.2. Deadline: Sep 1. |
Sep 6 | Discussion 5.1. Deadline: Sep 6. |
Sep 8 | Discussion 5.2. Deadline: Sep 8. |
Here the exams and their solutions will be posted. You can find the official UCLA schedule for the final exams here.
Aug 11-12 | Midterm 1, Solutions, From 8:00 am to 8:50 am. |
Aug 25-26 | Midterm 2, Solutions, From 8:00 am to 8:50 am. |
Sep 8-9 | Final Exam, From 8:00 am to 8:00 am. |
The following are practice exams that you may use to prepare:
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:
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.