Foundations of Analysis II

Math 3220, Fall 2011 (http://www.math.utah.edu/~docampo/11fa-math3220)

Instructor — Roi Docampo Álvarez (docampo@math.utah.edu)

Meeting — MTWF 9:40-10:30, JTB 320.

Office Hours — MW 10:40-11:40 or by appointment, LCB 116.

Lecture Notes — "Foundations of Analysis", v2.5, by J. Taylor. Available for download at the author's website (http://www.math.utah.edu/~taylor/foundations.html).

Course Description — We will cover chapters 7 to 10 of the notes. Main topics: Advanced multivariable calculus. Continuity, compactness, differentiation and affine approximation, chain rule, Taylor series, extremization, error estimation, inverse and implicit function theorems, Riemann integration, Fubini's Theorem, change of variables formula. The emphasis is on further developing the student's ability to understand more abstract concepts and to write an effective and rigorous mathematical argument. A tentative schedule can be found hereat http://www.math.utah.edu/~docampo/math3220/syllabus.html.

Grading — There will be weekly homework assignments, weekly quizzes, two in-class midterms, and a comprehensive final exam. The homework will count for 20% of the grade, the quizzes for 20%, each of the midterms for 15%, and the final exam for 30%. Grades will be posted regularly on WebCT (http://webct.utah.edu).

Midterms and Final — Exams take place in JTB 320.

First midtermOct. 4, 9:40am to 10:30am
Second midtermNov. 21, 9:40am to 10:30am
FinalDec. 12, 8:00am to 10:00am

Quizzes — Every Friday there will be a 10-minute quiz at the beginning of class (except when there is a Midterm). It will contain questions related to the material covered in class during the corresponding week. For the quizzes, I usually give definitions a big emphasis.

Homework Assignments — Weekly assignments and their due dates will be posted on the website. Homework must be turned in at the beginning of class. Late homework is not accepted.

Due Date Assignment
Aug. 29 Section 7.1: 1, 2, 4, 5, 6, 7, 12
Section 7.2: 1, 2, 3, 4, 6, 9, 12, 13
Sept. 6 Section 7.3: 1, 2, 3, 4, 5, 6, 7, 8
9, 10, 11, 14, 15
Sept. 13 Section 7.4: 2, 4, 5, 7, 8, 9, 10, 12
13, 15
Sept. 20 Section 7.5: 1, 2, 4, 5, 7, 8, 9
10, 14
Sept. 27 Section 8.1: 1, 3, 5, 9
Section 8.2: 1, 3, 5, 6, 8
Oct. 5 Section 8.3: 1, 2, 3, 4, 5, 7, 8
Oct. 18 Section 8.4: 1, 2, 3, 5, 7, 8, 9, 10
14, 15
Section 8.5: 1, 2, 3, 5, 7, 8, 9, 10
Nov. 2 Section 9.1: 2, 4, 6, 8, 10
Section 9.2: 1, 2, 3, 4, 6, 9, 10, 12
Section 9.3: 2, 3, 5, 8
Nov. 9 Section 9.3: 9, 10, 11
Section 9.4: 1, 2, 3, 4, 8, 11, 12
13, 14
Nov. 21 Section 9.5: 1, 2, 5, 6, 7, 8
Section 9.6: 1, 2, 3, 4, 5, 10
Section 9.7: 1, 2, 4, 6, 7
Nov. 30 Section 10.1: 1, 3, 4, 5, 6, 10
Section 10.2: 2, 4, 6, 7

ADA Statement — The Americans with Disabilities Act requires that reasonable accommodations be provided for students with physical, cognitive, systemic, learning, and physical disabilities. Please contact me at the beginning of the semester to discuss any such accommodations you may require for this course.