MATH 409-503
Advanced Calculus I
Fall 2015
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: 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), 7(a,b), 10
Assignment #2 (due September 16):  1.3: 0(a,c), 1(a,e) (just state the answer), 4, 6, 7, 8
Assignment #3 (due September 23):  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(a)
Assignment #5 (due October 7):  2.1: 0, 1(c,d), 2(a), 4, 7, 8; 2.2: 0(a,b)
Assignment #6 (due October 14):  2.2: 1(a,b), 2(b), 3(a,b); 2.3: 0, 3, 7
Assignment #7 (due October 21):  2.4: 0, 3(b,c), 4;  3.1: 0(c,d), 1(a,d), 3(a), 6
Assignment #8 (due October 28):  3.2: 0(a,c), 1(b), 6;  3.3: 0(a,c), 1(a,b), 2(a), 4
Assignment #9 (not to be handed in):  3.3: 3, 5, 10;  3.4: 0, 1, 4, 6
Assignment #10 (due November 11):  4.1: 3, 6;  4.2: 0, 1, 2
Assignment #11 (due November 18):  4.3: 0(a,b), 4, 9;  4.4: 1, 3, 5(a,c)
Assignment #12 (due December 2):  4.5: 0(a,b), 1, 7;  5.1: 0(a), 2(b), 3, 4;  5.2: 0(b)
Assignment #13 (not to be handed in):  5.3: 0(a,b), 1(b,c), 3; 5.4: 0(b,c), 1(b), 7
Exams
In-class exam #1: September 30, covers 1.1-1.6
Definitions and axioms you may be asked to state: completeness axiom, countable set, well-ordering principle, Archimedean principle
In-class exam #2: November 4, covers 2.1-2.4, 3.1-3.4
Definitions and axioms you may be asked to state: limit of a sequence, Bolzano-Weierstrass theorem, Cauchy sequence, continuity, extreme value theorem, intermediate value theorem, uniform continuity
Practice #1 | Practice #1 solutions (ignore the problems involving derivatives)
Practice #2 (ignore the problems involving derivatives)
Final exam: December 15, 8:00-10:00 am, covers 1.1-1.6, 2.1-2.4, 3.1-3.4, 4.1-4.5, 5.1-5.4, with emphasis on Chapters 4 and 5
Axioms, theorems, and definitions you may be asked to state: completeness axiom, well-ordering principle, limit of a sequence, Cauchy sequence, continuity, intermediate value theorem, extreme value theorem, uniform continuity, derivative, mean value theorem, integrability