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

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
 Day Date Section(#s) covered Homework Wednesday September 22 Linear Algebra:1.1 1.1.1, 1.1.4. (Due Fri Oct 1). Friday September 24 Matrices: 1.2 1.2.1, 1.2.2, 1.2.4. (Due Fri Oct 1). Monday September 27 Inverses: 1.2 1.1.2, 1.2.6. (Due Fri Oct 8). Wednesday September 29 Topology: 1.3 1.3.1, 1.3.2. (Due Fri Oct 8). Friday October 1 Closure: 1.3 1.3.3, 1.3.4, 1.3.9. (Due Fri Oct 8.) Monday October 4 Continuity: 1.3 1.3.6, 1.3.7. (Due Mon Oct 18) Wednesday October 6 Continuity: 1.3 1.3.5, 1.3.8. (Due Mon Oct 18). Friday October 8 Compacta: 1.4 1.4.1.a, 1.4.2. (Due Mon Oct 18) Monday October 11 Derivatives: 2.5 2.5.2, 2.5.3. (Due Mon Oct 18) Wednesday October 13 Review Office Hours Today Friday October 15 Midterm I Answers and Practice Exam Answers Monday October 18 Continuously Differentiable: 2.6 2.5.4, 2.6.5 (Due Friday Oct 29). Wednesday October 20 Continuously Differentiable: 2.6 2.6.4, 2.6.6 (Due Friday Oct 29). Friday October 22 Multiple Derivatives 2.6 2.6.9, 2.6.10 (Due Friday Oct 29). Monday October 25 Chain Rule: 2.7 2.6.3, 2.6.7. (Due Friday Nov 5). Wednesday October 27 2.7.1 , 2.7.2, 2.7.3. (Due Friday Nov 5). Friday October 29 Inverse Function Thm: 2.8 2.8.1, 2.8.2. (Due Friday Nov 5). Monday November 1 Inverse Function Thm: 2.8 2.8.3, 2.8.4. (Due Monday Nov 15). Wednesday November 3 Inverse Function Thm: 2.8 2.8.5. (Due Monday Nov 15). Friday November 5 Riemann Integral: 3.10 Monday November 8 Lebesgue Condition: 3.11 3.10.5, 3.11.5 (Due Friday Nov 19). Wednesday November 10 Review Friday November 12 Midterm II Answers. Practice Exam and Answers Monday November 15 Fubini Thm: 3.12 3.12.1, 3.12.3 (Due Monday Nov 29). Wednesday November 17 Integration over Bounded Sets: 3.13 3.12.4, 3.13.1, 3.13.5 (Due Monday Nov 29). Friday November 19 Rectifiable Sets: 3.14 3.14.2, 3.14.6, 3.14.7 (Due Monday Nov 29). Monday November 22 Improper Integrals: 3.15 3.15.1, 3.15.2, 3.15.4. (Due Monday Nov 29) Wednesday November 24 Change of Variables: 4 4.17.3, 4.17.5 (Due Friday Dec 3). Friday November 26 No Class Monday November 29 Change of Variables: 4 Wednesday December 1 Change of Variables: 4 Friday December 3 Change of Variables: 4 Tuesday December 7 Final 1-3pm