## Math 142B (Spring 2020)

### Summary

Math 142B is the second and final course in the *Introduction to Analysis* sequence. Topics include: power series; uniform convergence of functions; properties of the derivative; Riemann integration; Taylor series.

Using the groundwork of rigorous analysis developed in Math 142A, in Math 142B we give a proper treatment of differential and integral calculus, and applications.

There is no required textbook for the course. However, *Elementary Analysis: The Theory of Calculus* by Kenneth A. Ross is a good optional textbook. The course material covers roughly chapters IV–VI; **but** we may cover other topics not covered here. It is available free in electronic form from the UCSD library (you will need to VPN in). Please contact me if you have trouble accessing this textbook.

### Contacts

The instructor is Freddie Manners (email `fmanners`; office AP&M 7343, not that that matters). The TA is Eva Loeser (`ehloeser`). [All emails are at `ucsd.edu`.]

### Class, section and office hours

Lectures are held on Mondays, Wednesdays and Fridays, 0900–0950. For the foreseeable future, lectures will be held **via Zoom**.

Section will also take place **via Zoom**. For now assume this is at the advertize time (Monday evenings); this may be tweaked slightly going forward if circumstances allow.

See the calendar below for section times and office hours.

Virtual attendance in class is **mandatory**, and in-class activities carry credit. The only exception is if your timezone or circumstances make this logistically difficult. In that case, you may arrange to attend the lecture "doubly virtually" at a pre-arranged time. You *must contact the lecturer* to arrange this option, or discuss other logistical difficulties.

Section attendance is **also mandatory**, and credit is assigned to attending at least 80% of section. *However*, with the TA's approval you may leave before the end of section and still count as attending.

**Please note that all lectures, sections and office hours may be recorded in Zoom and reposted to the class.**

### Exams

There is **one midterm exam** on Monday April 27. Most likely this will be "in-class" but this will be confirmed soon (the other option being take-home).
The **final exam** is on Wednesday June 10, 0800—1100.

Given the remote set-up, some changes to the usual exam set-up will be made, and these have not all been decided. Meanwhile you should think of this set-up as being *as close to normality as possible*. In particular you must **ensure you are free on the dates and time**, or alternative times (for logistical reasons) negotiated in advance. Flexibility will *not* extend to alternative dates or make-up exams.

### Homework

Homework will be set every week, **due by 2359 each Tuesday night**. The first homework deadline is on Tuesday April 7; the last on Tuesday June 2. There will be some optional homework in week 10 as exam practice.

Midterm week will have reduced homework loads, but still some homework.

Please note: while discussing homework problems in groups is permitted (and encouraged), your final written-up solutions **must be written by you, by yourself, in your own words**. If your homework appears to have been copied directly from another student (or another source) that may constitute an academic integrity issue. You also may **not** post homework questions or solicit answers on the internet.

### Grading

Your **combined grade** for the course is calculated as follows.

A+ | A | A- | B+ | B | B- | C+ | C | C- | F |
---|---|---|---|---|---|---|---|---|---|

97 | 93 | 90 | 87 | 83 | 80 | 77 | 73 | 70 | < 70 |

### Resources

In addition to this website, the course has a Canvas page, a Gradescope page and a Piazza site. The sign-up codes for Gradescope and Piazza are listed on the Canvas home page.

You should find all Zoom links for the course on the course Canvas page under the "Zoom LTI" tab.

### Provisional schedule

The rough, provisional, subject-to-change course schedule is given below. Note Week 1 starts on Monday March 30, etc..

Week | Rough textbook sections | Topic |
---|---|---|

1 | 4.23, 4.24 | Power series; uniform convergence |

2 | 4.25, 4.26 | More uniform convergence; differentiating and integrating power series |

3 | 4.26, 5.28 | — first properties of the derivative |

4 | 5.28, 5.29 | — the Mean Value Theorem; review |

5 | [midterm], 5.30 | Midterm; L'Hopital's rule |

6 | 5.30, 5.31 | — Taylor's theorem |

7 | 6.32 | The Riemann integral |

8 | 6.33, 6.34 | More on the Riemann integral; the Fundamental Theorem of Calculus |

9 | [holiday], 6.34, [review] | Memorial Day; —; review |

### Homework assignments

Those assignments that have not been created yet link to a placeholder.

Week | Deadline | |
---|---|---|

1 | Tuesday April 7, 2359 | p1.pdf |

2 | Tuesday April 14, 2359 | p2.pdf |

3 | Tuesday April 21, 2359 | p3.pdf |

4 | Tuesday April 28, 2359 | p4.pdf |

5 | Tuesday May 5, 2359 | p5.pdf |

6 | Tuesday May 12, 2359 | p6.pdf |

7 | Tuesday May 19, 2359 | p7.pdf |

8 | Tuesday May 26, 2359 | p8.pdf |

9 | Tuesday June 2, 2359 | p9.pdf |

10 | Never (optional pset) | p10.pdf |

### Office hours

Regular office hours and locations are listed in the table below. However, please **check the calendar below** for any one-off changes or cancellations.

Instructor / TA | Location | Regular hours |
---|---|---|

Freddie Manners | Zoom | Mondays 2:30pm – 3:30pm, Fridays 11:30am – 12:30pm |

Eva Loeser | Zoom | Tuesdays 9:00am – 11:00am |