Frederick Manners' academic website

Math 142B (Spring 2022)

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 may 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). The TA is Rusiru Gambheera (email rgambhee). [All emails are at ucsd.edu.]

Class, section and office hours

Lectures are held on Mondays, Wednesdays and Fridays, 1400–1450, in PETER–103.

Lectures will be held in-person (unless circumstances change dramatically) and will be podcasted. There will be in-class activities that contribute (a small amount) towards your grade. However, I will make sure there is some mechanism to complete these remotely if necessary.

Section will take place in-person at the advertized times and places.

See the calendar below for section times and office hours.

Exams

There is one midterm exam, in-person and in-class, on Monday April 25.

The final exam is on Friday June 10, at 1500–1800. It is also in-person (location TBD).

You should ensure at the start of the quarter that you can attend these exams. In general, alternative modalities, dates or times will not be offered.

Homework

Homework will be set every week, due by 2359 each Monday night. The first homework deadline is on Monday April 4; the last on Monday May 30. There will be some optional homework in week 10 as exam practice.

Midterm week and the first 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.

First, your lowest homework score is dropped. Then, take 28% homework + 2% in-class activities + 30% midterm + 40% final.

The letter grade cut-offs will be at least as generous as the following table (but may be more generous). Separately, exam scores may be curved to adjust for difficulty.

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.

Provisional schedule

The rough, provisional, subject-to-change course schedule is given below. Note Week 1 starts on Monday March 28, 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

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 AP&M 7343 Mondays 12:30pm – 13:30pm, Fridays 3:00pm – 4:00pm
Rusiru Gambheera AP&M 5712 Mondays 3:00pm – 5:00pm

Course calendar