MATH 409-503
Advanced Calculus I
Fall 2012
Instructor: David Kerr
Office: Milner 121
Office hours: week of December 3: Monday, Tuesday, Wednesday 10:00-11:30
Lectures: MWF 1:50-2:40, Blocker 164
Course description: Axioms of the real number system; point set theory of the real number line; compactness, completeness and connectedness; continuity and uniform continuity; sequences, series; theory of Riemann integration.
Textbook: William R. Wade. An Introduction to Analysis, fourth edition. Published by Prentice Hall.
Assignments
Assignment #1 (due September 5):  1.2: 0, 3, 4(a,c), 7(a,b), 10
Assignment #2 (due September 12):  1.3: 0(a,c), 1(a,e) (just state the answer), 4, 6, 7, 8
Assignment #3 (due September 19):  1.4: 2(b,d), 4(a,c); 1.5: 0(b,c,d), 2(a,b,c) (just state the answer), 5, 6
Assignment #4 (not to be handed in):  1.6: 0, 1, 3, 6
Assignment #5 (due October 3):  2.1: 0, 1(c,d), 2(a), 4, 7, 8
Assignment #6 (due October 10):  2.2: 0(a,b), 1(a,b), 2(b,c), 3(b);  2.3: 0, 3, 7
Assignment #7 (due October 17):  2.4: 0, 3(b,c), 4;  3.1: 0(c,d), 1(a,d), 3(a), 6
Assignment #8 (due October 24):  3.2: 0(a,c), 1(b), 6;  3.3: 0(a,c), 1(a,b), 2(a), 4
Assignment #9 (due October 31):  3.3: 5, 6, 10;  3.4: 0(a,d), 1(b), 4
Assignment #10 (due Thursday November 15 at 5:00 p.m.):  4.1: 3, 6;  4.2: 0, 1, 2;   4.3: 0(a,b)
Assignment #11 (due November 21):  4.3: 4, 9;  4.4: 1, 3, 5(a,c);  4.5: 0(a,b), 1, 7
Assignment #12 (due Friday November 30):  5.1: 0(a), 2(b), 3, 4;  5.2: 0(b), 2(a,b), 6;  5.3: 0(a,b), 1(b,c)
Exams
In-class exam #1: September 26, covers 1.1-1.6   Solutions
Practice #1 | Practice #1 solutions  (ignore #2 and #5(c), which cover Chapter 2 material)
Practice #2 | Practice #2 solutions
Solutions to some assignment problems
In-class exam #2: November 7, covers 2.1-2.4, 3.1-3.4, 4.1
Definitions and theorems you may be asked to state: limit (for sequences and functions), continuity, uniform continuity, derivative, Bolzano-Weierstrass Theorem, Extreme Value Theorem, Intermediate Value Theorem
Practice #1 | Practice #1 solutions
Practice #2  Some solutions: 1(a) T, (b) F, (c) T, (d) T, (f) T, (g) F, (h) T; 3(b) f(x)=x for x in [0,1) and f(1) = 0; 4(b) 34.
Final exam: December 11, 3:30-5:30
Definitions and theorems you may be asked to state: limit (for sequences and functions), Cauchy sequence, continuity, uniform continuity, derivative, Bolzano-Weierstrass Theorem, Extreme Value Theorem, Intermediate Value Theorem, Mean Value Theorem, Riemann integrability, Fundamental Theorem of Calculus parts (1) and (2)
Practice #1  (ignore the problems on series, power series, and uniform convergence)
Practice #1 solutions
Practice #2 | Practice #2 solutions