MATH 127C Fall 2021



Teaching Assistant:
Chutong Wu, Email: ctwu@ucdavis.edu, Office: MSB 2129
Lecturer: Eric Babson, Office hour: Mondays 3:20-3:40, 4:20-4:40, 5:20-5:40 in Zoom: 7150588313.
Lectures: MWF 9:00-9:50am in Olson 250 except possibly for the final exam.
Discussions: T 5:10-6:00pm, 6:10-7:00pm in H Gym 290.
Grading: There will be 200 points for homework, 200 points for the final and 200 points between the two midterms. I will double the largest of the three for a total of 800 possible points. For final grades a score of at least 720 yields an A+, at least 680 an A, at least 640 a A-, at least 616 a B+, at least 584 a B, at least 560 an B-, at least 536 a C+, at least 504 a C, at least 480 an C-, at least 456 a D+, at least 424 a D and at least 400 a D-.


Course Outline: Following the department syllabus and department outline
from Analysis on Manifolds by James Munkres chapters 1-4 (sections 1-20).
This stack exchange thread discusses other good references.

More fun math: Directed Reading Program

Banach-Tarski Theorem: Why only some sets can get measures.

Dehn Theorem and Hilberrt's third problem: Why cube disections do not give all polyhedra.

This table is a rough and optimistic outline of when topics will be covered and will be edited as the term progresses. The exam scheduling will not change. Homework problems will be added.

Chain Rule: 2.7
DayDateSection(#s) coveredHomework
WednesdaySeptember 22Linear Algebra:1.1 1.1.1, 1.1.4. (Due Fri Oct 1).
FridaySeptember 24Matrices: 1.2 1.2.1, 1.2.2, 1.2.4. (Due Fri Oct 1).
MondaySeptember 27Inverses: 1.2 1.1.2, 1.2.6. (Due Fri Oct 8).
WednesdaySeptember 29Topology: 1.3 1.3.1, 1.3.2. (Due Fri Oct 8).
FridayOctober 1Closure: 1.3 1.3.3, 1.3.4, 1.3.9. (Due Fri Oct 8.)
MondayOctober 4Continuity: 1.31.3.6, 1.3.7. (Due Mon Oct 18)
WednesdayOctober 6Continuity: 1.3 1.3.5, 1.3.8. (Due Mon Oct 18).
FridayOctober 8Compacta: 1.4 1.4.1.a, 1.4.2. (Due Mon Oct 18)
MondayOctober 11Derivatives: 2.5 2.5.2, 2.5.3. (Due Mon Oct 18)
WednesdayOctober 13Review Office Hours Today
FridayOctober 15Midterm I Answers and Practice Exam Answers
MondayOctober 18Continuously Differentiable: 2.6 2.5.4, 2.6.5 (Due Friday Oct 29).
WednesdayOctober 20Continuously Differentiable: 2.6 2.6.4, 2.6.6 (Due Friday Oct 29).
FridayOctober 22Multiple Derivatives 2.6 2.6.9, 2.6.10 (Due Friday Oct 29).
MondayOctober 25Chain Rule: 2.7 2.6.3, 2.6.7. (Due Friday Nov 5).
WednesdayOctober 272.7.1 , 2.7.2, 2.7.3. (Due Friday Nov 5).
FridayOctober 29Inverse Function Thm: 2.8 2.8.1, 2.8.2. (Due Friday Nov 5).
MondayNovember 1Inverse Function Thm: 2.8 2.8.3, 2.8.4. (Due Monday Nov 15).
WednesdayNovember 3Inverse Function Thm: 2.8 2.8.5. (Due Monday Nov 15).
FridayNovember 5Riemann Integral: 3.10
MondayNovember 8Lebesgue Condition: 3.11 3.10.5, 3.11.5 (Due Friday Nov 19).
WednesdayNovember 10Review
FridayNovember 12Midterm II Answers. Practice Exam and Answers
MondayNovember 15Fubini Thm: 3.12 3.12.1, 3.12.3 (Due Monday Nov 29).
WednesdayNovember 17Integration over Bounded Sets: 3.13 3.12.4, 3.13.1, 3.13.5 (Due Monday Nov 29).
FridayNovember 19Rectifiable Sets: 3.14 3.14.2, 3.14.6, 3.14.7 (Due Monday Nov 29).
MondayNovember 22Improper Integrals: 3.15 3.15.1, 3.15.2, 3.15.4. (Due Monday Nov 29)
WednesdayNovember 24Change of Variables: 4 4.17.3, 4.17.5 (Due Friday Dec 3).
FridayNovember 26No Class
MondayNovember 29Change of Variables: 4
WednesdayDecember 1Change of Variables: 4
FridayDecember 3Change of Variables: 4
TuesdayDecember 7Final 1-3pm