**MATH 31B-3-Integration and Infinite Series-Spring 2017-UCLA**

**Lecture:** MWF, 9:00am-9:50am, at Humants Room A51.

**Professor:** Wenhao Ou (wenhaoou-at-math.ucla.edu, MS 5346).

**Office Hours:** M 4:00pm-5:30pm, W 4:00pm-5:30pm, or e-mail me to make an appointment.

**Teaching assistant:** Qi Guo (qiguo-at-math.ucla.edu , MS 3905), Assaf Shani (assafshani-at-math.ucla.edu, MS 2344), John Susice (jpsusice-at-math.ucla.edu, MS2963).

**TA Office Hours:** TBA.

**Textbooks: **Jon Rogawski and Colin Adams, *Calculus: Single Variable. Third Edition*.

**Description. **This course provides an introduction to integrations of functions of one variable.

**Schedule.**This course consists of three parts and about 25 lectures. We will start by recalling some properties of derivatives. In the second part, we will focus on the study of integrations of continuous functions. The last part consists of summations of series, which can be regarded as integrations of "discontinuous but locally constant" functions.

Weeks |
Sections | Topics |

1 |
7.1, 7.2, 7.3 | Review of Derivatives |

2 |
7.7, 7.8, 7.9 | Inverse Trig and Hyperbolic Functions |

3 |
8.1 | Integration by Parts |

4 |
8.5, 8.9 | Midterm 1, Method of Partial Fractions, Numercial Integration |

5 |
9.1, 9.4 | Arc length and Surface Area,Taylor Polynomials |

6 |
8.7 | Improper Integrals |

7 |
11.1 | Midterm 2, Sequences |

8 |
11.2, 11.3 | Summing an Innite Series, Series with Positive Terms |

9 |
11.4, 11.5 | Absolute and Conditional Convergence, Ratio and Root Tests |

10 |
11.6, 11.7 | Power Series, Taylor Series |

**Holidays:**

- Memorial Day holiday, M May 29

**Homework.** Homework is assigned weekly and collected during the lecture every Wednesday. There is no make-up homework. The lowest score is dropped from the computation of your grade. Please click here for the homework list.

**Exam Dates:**

- Midterm 1: Monday of week 4 (April 24), during the regular class hour.

- Midterm 2: Monday of week 7 (May 15), during the regular class hour.

- Final Exam: Wednesday, Jun. 14, 2017, 8:00am-11:00am.

**Grading.** There are two possibilities for the final grade:

- 10% Homework + 30% Best of the two midterms + 60%Final Exam.

- 10% Homework + 25% Midterm 1 + 25% Midterm 2 + 40% Final Exam.

**Academic integrity.** Please review the regulations at the following website: http://www.deanofstudents.ucla.edu/Student-Conduct

**Notes.**

- Textbooks, Calculators, laptops and cell phones are prohibited during the Midterms and the Final Exam.

- There will be no make-up test. A missed test will count for a zero for that test.

- Students may work together to solve homework problems, but each student must write down his/her own solutions on separate copy. One should also write down the names of his/her collaborators.

- Exam grading complaint should be submitted to the instructor, no later than two weeks after the exam, and before the last lecture.