MATH 409-200
Advanced Calculus I
Fall 2013
Instructor: David Kerr
Office: Milner 121
Office hours: MT 2:00-3:30, or by appointment
Lectures: MWF 12:40-1:30, Zach 119D
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 (due at the beginning of class)
Assignment #1 (due September 9):  1.2: 0, 3, 4(a,c), 6, 7(a), 10
Assignment #2 (due September 13):  1.3: 0(a,b), 1(a,d) (just state the answer), 7, 8;  1.4: 2(b,d), 4(a,d)
Assignment #3 (due September 20):  1.5: 0(b,d), 2(a,c), 6, 7;  1.6: 0, 1, 3, 7;  2.1: 0, 2(a)
Assignment #4 (due October 4):  2.2: 2(b), 3(b);  2.3: 0(a,d), 3, 7;  2.4: 0, 4, 7;  3.1: 0(c,d)
Assignment #5 (due October 11):  3.1: 1(a,d), 3(a), 6;  3.2: 0(a,c), 1(b), 6;  3.3: 0(a,c)
Assignment #6 (due October 18):  3.3: 1(a), 2(a), 4, 10; 3.4: 0(d), 1(b), 4, 6; 4.1: 0, 1, 4
Assignment #7 (due October 25):  4.2: 0, 1, 2; 4.3: 0(a,b), 1(c), 2, 4, 9; 4.4: 1, 3, 5(a,d)
Assignment #8 (due November 1):  4.5: 0, 1, 7; 5.1: 0(a), 2(b), 3, 4;  5.2: 0(b)
Assignment #9 (due November 15):  5.3: 0(a,b), 1(b,c), 3; 5.4: 0(b,c), 1(b), 7; 6.1: 0(a,b)
Assignment #10 (due November 22):  6.1: 1(b,c), 2(d), 3(b), 8; 6.2: 0(d), 1(f), 2(c), 4; 6.3: 0(d), 1(b), 2(b,d)
Assignment #11 (not to be handed in):  6.3: 5, 6, 8, 10; 7.1: 1, 2, 3, 4, 5, 6 7.2: 1, 2, 3; 7.3: 1, 4, 5, 6;
Exams
In-class exam #1: September 25, covers 1.1-1.6 and 2.1-2.2
Axioms and definitions you may be asked to state: completeness axiom, well-ordering principle, definition of the limit of a sequence
Practice | Practice solutions
Exam #2: November 6, 7:00-8:30, Heldenfels 120, covers 2.3-2.4, 3.1-3.4, 4.1-4.5, 5.1-5.2
Theorems and definitions you may be asked to state: Bolzano-Weierstrass theorem, Cauchy sequence, continuity, extreme value theorem, intermediate value theorem, uniform continuity, derivative, mean value theorem, integrability
Practice #1 | Practice #1 solutions
Practice #2
Final exam: December 9, 10:30-12:30
Axioms, theorems, and definitions you may be asked to state: completeness axiom, well-ordering principle, limit of a sequence, Cauchy sequence, continuity, extreme value theorem, uniform continuity, derivative, mean value theorem, integrability, pointwise convergence, uniform convergence
Practice #1 | Practice #1 Solutions
Practice #2 | Practice #2 Solutions