MATH 410-500
Advanced Calculus II
Spring 2014
Instructor: David Kerr
Office: Blocker 525L
Office hours: M 10:30-11:30, T 10:00-11:30, or by appointment
Lectures: MWF 9:10-10:00, Blocker 164
Course description: Differential and integral calculus of functions defined on Rm including inverse and implicit function theorems and change of variable formulas for integration; uniform convergence.
Textbook: William R. Wade. An Introduction to Analysis, fourth edition. Published by Prentice Hall.
Assignments (due at the beginning of class)
Assignment #1 (due January 22):  7.1: 1, 2, 3, 4;  7.2: 1, 2, 3
Assignment #2 (due January 29):  7.2: 5, 7;  7.3: 1(a,b,c), 2(a,c), 4, 5
Assignment #3 (due February 5):  7.3: 6;  7.4: 1, 2(a,b,c), 3(a,b,c)
Assignment #4 (due February 19):  8.1: 1(a,b,c,d), 2(a,b), 4;  8.2: 4, 5(b,c), 10
Assignment #5 (due February 26):  8.3: 1, 2, 3, 4, 7, 9;  8.4: 1
Assignment #6 (due March 5):  8.4: 3, 4, 6, 7, 8, 11;  9.1: 1
Assignment #7 (due March 19):  9.1: 2, 3(a), 4, 5(b), 8;  9.2: 1, 4, 6
Assignment #8 (not to be handed in):  9.2: 7;  9.3: 1(a,c), 2, 3, 5, 6, 7, 8(a,c,d)
Assignment #9 (due April 2):  9.4: 3, 4, 5, 6, 7, 8
Assignment #10 (due April 9):  11.1: 1, 2, 3, 4, 5(a,b);  11.2: 1, 3
Assignment #11 (due April 16):  11.2: 5, 8, 9;  11.3: 1(b,c), 2(a,c);  11.4: 4, 5
Assignment #12 (due April 23):  11.4: 3, 6, 10, 11;  11.5: 1(a,b), 4, 8
Assignment #13 (not to be handed in):  11.5: 6(a), 7, 9, 12(a,b);  11.6: 1, 6
Exams
In-class exam #1: February 12, covers 7.1-7.4
Definitions you may be asked to state: pointwise and uniform convergence for a sequence of functions
Practice problems: 3, 9, and 10 from Practice #1, and 4, 6(h), and 9 from Practice #2
In-class exam #2: March 26, covers 8.1-8.4 and 9.1-9.3
Definitions and theorems you may be asked to state: interior, closure, and boundary of a subset of Rn, compactness, the Heine-Borel theorem, the notion of a limit for functions from Rn to Rm
Final exam: May 5, 8:00-10:00 am, covers 7.1-7.4, 8.1-8.4, 9.1-9.4, and 11.1-11.6 (but not the implicit function theorem)
Definitions and theorems you may be asked to state: pointwise and uniform convergence for a sequence of functions, interior, closure, and boundary of a subset of Rn, compactness, the Heine-Borel theorem, the notion of a limit for functions from Rn to Rm, differentiability and total derivative of a function from Rn to Rm, Taylor's formula on Rn