**Course: MATH 31B, Integration and Infinite Series**, Lecture 3,
Spring 2015

**Prerequisite:** MATH 31A, with a grade of C- or
better.

**Course Content:** Transcendental functions (such as the
exponential and logarithm functions); methods and applications of
integration; sequences and series.

**Syllabus:** here.
*Last update:* 11 May 2015

**Instructor:** Steven Heilman, heilman(@-symbol)ucla.edu

**Office Hours:** Mondays, 9AM-111AM, Wednesdays 1PM-2PM, MS 7370

**Lecture Meeting Time/Location:** Monday, Wednesday and Friday,
3PM-350PM, MS 4000A

**TA:** ,
Iyer, G. S., geoff.iyer(@-symbol)gmail.com; Coley, I. A.,
iacoley(@-symbol)math.ucla.edu; Barnicle, M. G.,
barnicle(@-symbol)ucla.edu

**TA Office Hours:**Iyer, Thursdays
2PM-3PM, MS 6160;
Coley, Thursdays 1130AM-1230PM, MS 3903; Barnicle, Thursdays 10AM-11AM, MS
2954

**Discussion Session Meeting Time/Location:**

- 3A, Tuesday, 3PM-350PM, MS 5117. Iyer, G. S. http://www.math.ucla.edu/people/grad/gsiyer
- 3B, Thursday, 3PM-350PM, MS 5117. Iyer, G. S. http://www.math.ucla.edu/people/grad/gsiyer
- 3C, Tuesday, 3PM-350PM, MS 5118. Coley, I. A. http://www.math.ucla.edu/~iacoley
- 3D, Thursday, 3PM-350PM, MS 5118. Coley, I. A. http://www.math.ucla.edu/~iacoley
- 3E, Tuesday, 3PM-350PM, MS 5137. Barnicle, M. G. http://www.math.ucla.edu/~barnicle
- 3F, Thursday, 3PM-350PM, MS 5137. Barnicle, M. G. http://www.math.ucla.edu/~barnicle

- My email address for this course is heilman(@-symbol)ucla.edu
- It is your responsibility to make sure you are receiving emails from heilman(@-symbol)ucla.edu , and they are not being sent to your spam folder.
- Do NOT email me with questions that can be answered from the syllabus.
- Homework questions sent to me by email will be answered altogether in the form of a "digest." I will get to every question, but I cannot reply to every email. This digest will be sent out typically two days before the homework is due.

- Late homework is not accepted.
- You may not use the internet to try to find the answers to homework problems.
- The lowest two homework scores will be dropped. This policy is meant to account for illnesses, emergencies, etc.
- Do not submit homework via email.
- There will be 10 homework assignments, assigned weekly on Friday and turned
in at the
**beginning**of class on the following Friday. In the second and eighth week of the quarter, the homework will not be turned in, and instead there will be a quiz in the discussion section. - A random subset of the homework problems will be graded each week. However, it is strongly recommended that you try to complete the entire homework assignment.
- Collaboration on homeworks is allowed and encouraged.
- All homework assignments must be
**written by you**, i.e. you cannot copy someone else's solution verbatim. - Label your homework with the lecture number and the discussion section number.
- Homework solutions will be posted ... (time)
- Reading the syllabus counts as one homework grade. In order to receive credit for reading the syllabus, you must read the syllabus by April 3, noon, PST.

- There will be two quizzes, administered in the second and eigth weeks of class. In the second and eigth weeks of class, the homework will not be turned in, and instead, the quiz will count for the homework grade. The problems from the quiz will closely resemble or be identical to problems from the homework from that particular week.
- Quizzes will be administered in your discussion section, which is on either Tuesday or Thursday. Each quiz should last about 15 minutes.

- The final grade is weighted as the larger of the following two schemes. Scheme 1: homework (15%), the first midterm (20%), the second midterm (25%), and the final (40%). Scheme 2: homework (15%), largest midterm grade (35%), final (50%). The grade for the semester will be curved. However, anyone who exceeds my expectations in the class by showing A-level performance on the exams and homeworks will receive an A for the class.
- We will use the MyUCLA gradebook.
- If you cannot attend one of the exams, you must notify me within the first two weeks of the start of the quarter. Later requests for rescheduling will most likely be denied.
- You must attend the final exam to pass the course.

** Tentative Schedule**: (This schedule may change slightly during the
course.)

Week | Monday | Tuesday | Wednesday | Thursday | Friday |

1 | Mar 30: 7.1, Derivatives of exponential functions | Apr 1: 7.2, Inverse functions | Apr 3: Homework 1 due. 7.3, Logarithms and their derivatives | ||

2 | Apr 6: 7.4, Exponential growth and decay | Quiz in section | Apr 8: 7.5-7.6, Compound interest, logistic growth | Quiz in section | Apr 10: Homework 2 (ungraded). 7.7, L'Hopital's Rule |

3 | Apr 13: 8.1, Integration by parts | Apr 15: 8.2,8.3, Trigonometric integrals, trigonometric substitution | Apr 17: Homework 3 due. 8.5, Method of partial fractions | ||

4 | Apr 20: Midterm #1 | Apr 22: 8.6, Improper integrals | Apr 24: Homework 4 due. 8.8, Numerical integration | ||

5 | Apr 27: 8.8, Error bounds for numerical integral | Apr 29: 9.1, Arc length | May 1: Homework 5 due. 9.2, Fluid pressure and force | ||

6 | May 4: 9.4, Taylor polynomials | May 6: 9.4, Taylor's Theorem, error bounds | May 8: Homework 6 due, 11.1, Sequences and Infinite Series | ||

7 | May 11: Midterm #2 | May 13: 11.2, Infinite Series | May 15: Homework 7 due, 11.2, More Infinite Series | ||

8 | May 18: 11.3, Convergence of series with positive terms | Quiz in section | May 20: 11.4, Conditional Convergence | Quiz in section | May 22: Homework 8 (ungraded). 11.5, Ratio and root tests |

9 | May 25: No class | May 27: 11.6, Power Series | May 29: Homework 9 due. 11.6, More Power Series | ||

10 | Jun 1: 11.7, Taylor Series | Jun 3: 11.7, More Taylor Series | Jun 5: Homework 10 due. Review of course |

**Advice on succeeding in a math class:**

- Review the relevant course material
**before**you come to lecture. Consider reviewing course material a week or two before the semester starts. - When reading mathematics, use a pencil and paper to sketch the calculations that are performed by the author.
- Come to class with questions, so you can get more out of the
lecture. Also, finish your homework at
least
**two days**before it is due, to alleviate deadline stress. - Write a rough draft and a separate final draft for your homework. This procedure will help you catch mistakes.
- If you are having difficulty with the material or a particular homework problem, review Polya's Problem Solving Strategies, and come to office hours.

- (solutions removed)