MAA4212, Spring 2012
Advanced Calculus II
Section 01B8 : MWF 7th hour, Little Hall, room 219
Lecturer: Prof. Mike Jury
Office: Little 484
e-mail: mjury at ufl dot edu
Office Hours: MWF 3
Text: Introduction to Analysis, by Maxwell Rosenlicht, Dover, 1968.
***************REMINDER: Class meets in LIT0113 on FRIDAY 3/30***************
Course Content
A continuation of the rigorous treatment of the foundations of Calculus begun in MAA4211. Topics for the second semester include Riemann integration, sequences and series of functions, applications to first order ordinary differential equaitons, functions from Rn to Rm, and the inverse and implicit function theorems. Other topics may be included as time permits. In addition to mastery of the couse content, course objectives include reading, writing, and discovering proofs and constructing proofs and counterexamples in analysis.
Current Lecture Notes [Last update: 4/16]
Fall semester Lecture Notes [Last update: 11/14]
Homework assignments
Homework will be collected and graded roughly once a week; for a total of about 10 to 15 problems. In addition several problems will be assigned each lecture (not to be turned in).
Homework 1 (due Fri. Jan. 13): Prove Corollary 1.8 (see current notes).
Homework 2 (due Fri. Jan. 20): Problems 1.4 and 1.12 (see current notes).
Homework 3 (due Fri. Jan. 27): Problem 1.8 (see current notes).
Homework 4 (due Fri. Feb. 3): Problems 2.2 and 2.4 (see current notes).
Exam 1 review problems: Any problems from sections 1 and 2 of the current lecture notes (excluding power series); especially 1.1, 1.2, 1.16, 1.18, 1.19, 2.1, 2.3, 2.5, 2.6
Homework 5 (due Fri. Feb 17): Problems 2.11 and 2.12 (see current notes).
Homework 6 (due Fri. Feb 24): Problem 3.2 (see current notes).
Homework 7 (due Fri. Mar. 2): Prove Proposition 4.22 (see current notes).
Exam 2 review problems: From current notes: problems 2.7, 2.9, 2.10, 3.1, 3.3, 4.4, 4.6, 4.7, 4.10, 4.12, 4.14--16.
Homework 8 (due Wed. Mar. 28): Prove proposition 5.21 (see current notes).
Grading policies
The course grade will consist of the homework average (25% of the final grade) and three midterm exams (25% each). Final grades are assigned according to the standard scale: 90-100 A, 80-89 B, 70-79 C etc.
Tentative exam dates are as follows:
Exam 1 Wednesday February 8
Exam 2 Wednesday March 21
Exam 3 Monday April 23
The final exam (Friday, May 4th, 12:30--1:30) will serve as a make-up.
No notes or books will be allowed during exams.
University policies and resources