| Day | Date | Topics | Homework due: |
| Monday | Mar 31 | [8.1](7.1,2,5) Derivatives | 7.1,8,31. due Mon Apr 7 |
| Wednesday | Apr 2 | [8.2,3](7.3,4) Algebraic Properties | |
| Friday | Apr 4 | [8.4](7.6) Extreme Values | |
| Monday | Apr 7 | [8.5](7.7) Mean Value Thm | |
| Wednesday | Apr 9 | [8.8](7.8) L'Hospital's Rule | |
| Friday | Apr 11 | [9.1,2](9.1,2) Function Convergence | |
| Monday | Apr 14 | [9.3,4](9.2,3,4) Uniform Conv Properties | |
| Wednesday | Apr 16 | [9.5](9.5) Function Series | |
| Friday | Apr 18 | [10.1,2,3](9.6) Power Series | |
| Monday | Apr 21 | [10.4,5,6](9.7,8) Pow Ser Properties | |
| Wednesday | Apr 23 | Review | |
| Friday | Apr 25 | Midterm I | |
| Monday | Apr 28 | [11.1,2](8.1,2,3) Integration | |
| Wednesday | Apr 30 | [11.3](8.4,5) Cauchy's Criterion | |
| Friday | May 2 | [11.4](8.6) Int Cts and Mon Funs | |
| Monday | May 5 | [11.5](8.9) Properties of Int | |
| Wednesday | May 7 | [11.6](8.7,8) Integrability | |
| Friday | May 9 | [12.1](8.11) Fundamental Theorem of Calculus | |
| Monday | May 12 | [12.2] Using the FTC | |
| Wednesday | May 14 | [12.3](9.4) Int Convergence | |
| Friday | May 16 | [12.4] Improper Integrals | |
| Monday | May 19 | [12.5] Principal Values | |
| Wednesday | May 21 | Review | |
| Friday | May 23 | Midterm II | |
| Monday | May 26 | HOLIDAY: Memorial Day | |
| Wednesday | May 28 | [8.6](9.9) Taylor's Theorem | |
| Friday | May 30 | [10.7] Analytic Functions | |
| Monday | Jun 2 | [12.7](9.9,10) Taylor's Theorem | |
| Wednesday | Jun 4 | Review | |
| Friday | Jun 6 | Final: Section A, 3:30-5:30 pm | |
| Thursday | Jun 12 | Final: Section B, 8:00-10:00 am |
Lecture: Eric Babson, babson@math.ucdavis.edu.
Mondays, Wednesdays and Fridays in 168 Hoagland Hall at
9:00 am for A sections and
1:10 pm for B sections.
Sections:
A01: Chuong Nguyen on Tuesdays at 6:10 pm in 205 Wellman.
A02: John Walker on Tuesdays at 7:10 pm in 1134 Bainer.
B01: Raymond Chan on Thursdays at 7:10 pm in 1283 Grove.
B02: Raymond Chan on Thursdays at 6:10 pm in 1283 Grove.
Texts: Introduction to Analysis by John K. Hunter and
Real Analysis: A Long-Form Mathematics Textbook by Jay Cummings for exercises and jokes.
See also Principals of Mathematical Analysis by Walter Rudin for the template text
and Understanding Analysis by Stephen Abbott for the department syllabus text.
Exams: One sheet of notes (both sides) is allowed.
Grades: There will be 200 points for homework, 200 points for the final and 200 points between the two midterms. Double the largest of the three for a total of 800 possible points.
| D- | D | D+ | C- | C | C+ | B- | B | B+ | A- | A | A+ |
| 400 | 424 | 456 | 480 | 504 | 536 | 560 | 584 | 616 | 640 | 680 | 720 |
Homework: Problems are listed for each lecture and due at the end of the following week. Nobody has ever learned mathematics without working out a great many exercises. If a section seems opaque work more similar problems. The exercises are taken from Cummings' textbook (which is fun and inexpensive) Ch 7, Ch 8 and Ch 9.
Course Outline: Math 127B covers formal definitions of derivatives and integrals along with sequences of functions with particular emphasis on power series as per the department syllabus. The topics are similar to the Math 21 calculus series but the focus there is on computation involving the small family of functions which can be integrated algebraically while this course will focus on all functions which can be integrated even if the result is hard to express. This puts much more emphasis on proofs, counterintuitive examples probing the limits of what is possible and sequences of functions approximating the answer rather than computation.