All numbers indicate sections from Kosmala Second Edition.
R is for the reading assignment
C is for exercises that are assigned and will be collected
NC is for exercises that are assigned but will not be collected
Monday |
Wednesday |
Friday |
Aug. 30 |
Sept. 1 |
Sept. 3 Lecture: Introduction to Advanced Calculus Algebraic Properties of the Real Numbers Homework: R 1.1,1.4,1.7 C 1.7: 1defg,2 (in part b change d to b) NC |
| Sept. 6 Labor Day |
Sept. 8 Lecture: Relations Ordered Fields Natural Numbers and Mathematical Induction Homework: R 1.2 (pg 8-10),1.3 C 1.1: 3 (Just prove the first statement in each part) C 1.7: 3,4 NC 1.1: 1,2,4,5 NC 1.9: 1,2,3 |
Sept. 10 Special Time: 10:20-11:00 Lecture: Properties of the Natural Numbers Mathematical Induction Homework: C 1.3: 2acdhm (put each section on a new piece of paper) C 1.3: 5a |
| Sept. 13 Lecture: More Props of Natural Numbers Well Ordered Principle Homework: C 1.4: 5,6(hint: use the well ordered principle),7 C additional problems NC 1.3: 2kln NC Your part of |
Sept. 15 Lecture: Functions Inverse Functions Homework Due: Homework assigned through and including Sept. 10 Homework: R 1.2 C 1.2: 13,18,19,20 NC 1.2: 11,21,22,23 |
Sept. 17 Lecture: Finite and Infinite Sets Homework: R 1.5,1.6 C 1.5: 10,11,12 C 1.6: 4 NC 1.5: 3 |
| Sept. 20 Lecture: More Finite and Infinite Sets Homework: R 1.7 (pg. 45-47) C 1.6: 7b C Two Problems from Class |
Sept. 22 Lecture: Infinite and Countable Sets (con't) Homework Due: Homework Assigned Through Sept. 17 Homework: C additional problems |
Sept. 24 Lecture: Complete Order Fields Homework: R 1.8 C 1.7: 7,8,10 NC 1.7: 11, 13 |
| Sept. 27 Lecture: Archimedean Fields Homework: C additional problems C Problem From Class |
Sept. 29 Lecture: Archimedean Fields Real Valued Functions Homework Due: Homework Assigned Through Sept. 24 Homework: C Problem From Class C 1.2: 9,12 NC 1.2: 4,6,8 |
Oct. 1 Lecture: Other Real Number Properties Homework: R 2.1 C 1.2: 9 C 1.8: 9,13 NC 1.8: 4,5 |
| Oct. 4 Lecture: Other Real Number Properties Sequences Homework: C 1.8: 1,12,20 NC 1.8: 2,14,17,18 |
Oct. 6 No Class |
Oct. 8 Lecture: Convergence of a Sequence Homework Due: Homework assigned through and including Oct. 4 Homework: R 2.2 C 2.1:2bjk,6 NC 2.1:2acdefghi,5 |
| Oct. 11 Lecture: More Convergence Limit Laws Homework: C 2.1:3,5,8 NC 2.1:11,12 |
Oct. 13 Lecture: Limit Laws Homework: C 2.1:16 |
Oct. 15 Lecture: More Limit Laws Homework: C 2.1: 18 NC 2.1: 19 |
| Oct. 18 Exam 1 Through Material Covered on Oct. 11 Homework Due: Homework Assigned Through Oct. 11 Homework: C 2.2: 1,2,3 NC 2.2: 4 |
Oct. 20 Lecture: More on Limit Laws Infinite Limits Guest Lecturer: Dr. Hoffoss Homework: R 2.3 C 2.2: 5,7(k=3) (hint:|a^3-b^3|=|a-b||a^2+ab+b^3| C 2.2: 11g NC 2.2:11fhk |
Oct. 22 Lecture: Infinite Limits Guest Lecturer: Dr. Hoffoss Homework: R 2.4 C 2.3:2ab,3ad,5 NC 2.2: 14 NC 2.3: 2c,4 |
| Oct. 25 Lecture: More Infinite Limits Ratio Test Homework: C 2.3: 7,15 NC 17,18,20 |
Oct. 27 Lecture: Monotone Sequences Homework: R 2.5 C 2.3: 16 C 2.4: 4acd NC 2.4: 3,5,8 |
Oct. 29 Lecture: Cauchy Sequences Bolzano-Weierstrass Theorem Homework Due: Homework Assigned Through Oct. 22 Homework: R 2.6 C 2.4: 11dl,15a C 2.5: 2c NC 2.4: 11abcefghijk,15bcde NC 2.5: 1,2abde,3 |
| Nov. 1 Lecture: Bolzano-Weierstrass Theorem More Cauchy Sequences Homework: C 2.5: 5,11 NC 6,7abef |
Nov. 3 Lecture: Even More Cauchy Sequences Subsequences Homework: C 2.5: 9 C 2.6: 1 |
Nov. 5 Lecture: Subsequences Limit Superior Homework: C 2.6: 2acd(for part c use r bigger than 1) NC 2.6: 2b |
| Nov. 8 Lecture: Limit Superior Subsequence Theorem Homework Due: Homework Assigned Through Nov. 1 Homework: C Problem from Class C 2.6: 3 NC 2.6:5 |
Nov. 10 Lecture: More Subsequences Homework: R 7.1 C 2.6: 9bc,10 NC 2.7: 25,34 |
Nov. 12 Lecture: Limit at Infinity of a function Homework: R 3.2 C 3.1:2a,3,5b NC 3.1:5acj |
| Nov. 15 Lecture: Limit at a Number Homework Due: Homework Assigned Through Nov. 10 Homework: C 3.1: 5di,6b NC 3.1: 6a,7,11 |
Nov. 17 Lecture: Limit at a Number Homework: R 3.3 C 3.2: 1d,9 NC 3.2: 14 |
Nov. 19 Lecture: More Limits Homework: C 3.2: 6 NC 3.2: 1ab,3 |
| Nov. 22 Lecture: Take Home Exam Given |
Nov. 24 No Class. Work on Take Home Exam |
Nov. 26 Thanksgiving Break |
| Nov. 29 Lecture: Sided Limits Take Home Exam Due Homework Due: Homework Assigned Through Nov. 19 Homework: R 4.1 C 3.3: 1,3 C Problem From Class NC 4ab,5acf |
Dec. 1 Lecture: Exponential Function Homework: C 3.3: 2 |
Dec. 3 Lecture: Continuous Functions Homework: R 4.1 C 4.1: 2,3aj NC 4.1: 3bl,6ab |
| Dec. 6 Lecture: Open and Closed Sets Cont. functions on Compact Sets Homework: R 4.3 C 4.1: 4,6egh NC 4.3:1 |
Dec. 8 Lecture: Cont. functions on Compact Sets Homework: R 4.4 C 2 Problems from Class NC 4.3: 9,10 |
Dec. 10 Lecture: Homework Due: Homework through Dec. 8 |
| Dec. 13 Lecture: Questions for Final |
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