| Day | Date | Topics | Homework due: |
| Monday | Mar 31 | [8.1](7.2){5.1}<5.2> Limits and Derivatives: Definition | 7.1,7.8,7.31. due Mon Apr 7. |
| Wednesday | Apr 2 | [8.2](7.3){5.2}<5.2> Diff and Cts: Top Sine | 7.11,7.13,7.14. due Mon Apr 14. |
| Friday | Apr 4 | [8.1](7.5){5.6}<5.1> Top Sine, Four Deriv Forms | 7.4,7.5,7.9. due Mon Apr 14. |
| Monday | Apr 7 | [8.3,4,5,8](7.4,6,7,8){5.7-5.11}<5.2-5.3>Chain Rule and Mean Value Thm | 7.17,7.21,7.30. due Mon Apr 14. |
| Wednesday | Apr 9 | [8.8](7.8)<5.3>{5.13} Darboux, L'Hospital | 7.18,7.22,7.25. due Mon Apr 21. |
| Friday | Apr 11 | [9.1,2](9.1,2) Function Convergence: Examples | 7.20, 7.23, 7.26 (this problem should end with '.. -{c}'. due Mon Apr 21. |
| Monday | Apr 14 | [9.3](9.2,3,4) Uniformly Cauchy | 9.3, 9.4, 9.12. due Mon Apr 21. |
| Wednesday | Apr 16 | [9.4](9.4) Un Conv pres Bounded, Cts | 9.6, 9.7, 9.14. due Mon Apr 28. |
| Friday | Apr 18 | [9.5](9.5) Un Conv pre deriv, not diff: Weierstrass Function | 9.24, 9.25, 9.27. due Mon Apr 28. |
| Monday | Apr 21 | [10.1-10.6](9.6-9.8) Power Series: real analytic and radius of conv. | 9.21, 9.23, Show 1/(1-x) is real analytic in (-∞,1). due Mon Apr 28- not on Midterm I. |
| Wednesday | Apr 23 | Review | |
| Friday | Apr 25 | Midterm I: Covers chapters [8],[9] | Practice Midterm I with answers. |
| 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.
Office: Wednesdays from 10:30 to 11:30 in 2109 Mathematical Sciences Building.
Sections:
A01: Chuong Nguyen on Tuesdays at 6:10 pm in 205 Wellman.
Office: Tuesdays from 11 to 12 and Thursdays from 10:30 to 12 in 2204 Mathematical Sciences Building.
A02: John Walker on Tuesdays at 7:10 pm in 1134 Bainer.
Office: Fridays from 5:30 to 6:30 pm in 419 Physics Building.
B01: Raymond Chan on Thursdays at 7:10 pm in 1283 Grove.
B02: Raymond Chan on Thursdays at 6:10 pm in 1283 Grove.
Office: Mondays from 11 to 12 and Thursdays from 10 to 11 in 3131 Mathematical Sciences Building.
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.