MATH 410-500
Advanced Calculus II
Spring 2017
Instructor: David Kerr
Office: Blocker 525L
Office hours: T 10:00-11:30 or by appointment
Lectures: MWF 10:20-11:10, BLOC 121
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. Errata.
Assignments (due at the beginning of class)
Assignment #1 (due January 25):  7.1: 1, 2, 3, 4;  7.2: 1, 2, 3
Assignment #2 (due February 1):  7.3: 1, 2(a,c), 3, 4, 5
Assignment #3 (due February 8):  7.4: 1(a,b), 2(a,b,c), 3(a,c);  8.1: 1(a,b,c,d)
Assignment #4 (due February 22):  8.2: 4, 5(b,c), 10;  8.3: 1, 2, 3, 4
Assignment #5 (due March 1):  8.3: 7, 9;  8.4: 1, 3, 4, 6, 7, 11
Assignment #6 (due March 8):  9.1: 1(a), 2(a), 4, 8;  9.2: 1, 4, 6, 7
Assignment #7 (not to be handed in):  9.3: 1(a,c), 2, 3, 5, 6, 7, 8(a,c,d);  9.4: 3, 4, 5
Assignment #8 (due March 29):  9.4: 6, 7, 8;  11.1: 1, 2, 3, 4, 5(a,b)
Assignment #9 (due April 5):  11.2: 1, 3, 4, 6;  11.3: 1(b,c), 2(a,c)
Assignment #10 (due April 12):  11.4: 3, 4, 5, 6, 10;  11.5: 1(a,b), 4
Assignment #11 (due April 19):  11.5: 6(a), 7, 9, 12(a,b);  11.6: 1, 6
Assignment #12 (due April 26):  12.1: 2, 4, 5, 6;  12.2: 3, 5
Exams
In-class exam #1: February 15, covers 7.1-7.4, 8.1
Definitions you may be asked to state: pointwise and uniform convergence for a sequence of functions
In-class exam #2: March 22, covers 8.2-8.4 and 9.1-9.4
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 continuity for functions from Rn to Rm
Final exam: May 8, 8:00-10:00 am
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, Jordan region, Riemann integrability for a bounded function on a Jordan region