DISCLAIMER: The future is subject to change!
MONTH
or WEEK
| DAY
| Topic, Event
| Section;
Assigned
Problems
|
| AUGUST
|
| Chapter 1: The Real Numbers |
| |
| WEEK 1
| 23-27 August
|
|
|
|
| Mon 23
| Course Introduction
Policies, Objectives
|
|
| Wed 25
| Fields
| §1.1
|
|
|
| Fri 27
| Ordered Fields, Induction
| §1.2 #19
|
| WEEK 2
| 30 August -
3 September
|
|
|
|
| Mon 30
| Completeness, Archimedean Property
|
|
| SEPTEMBER
|
|
| Wed 1
| Set Algebra, Open and Closed sets
| §1.3 #7,8,17
|
|
| Fri 3
| Bolzano-Weierstrass Theorem
| §1.3
|
| Chapter 2: Differential Calculus of Functions of One Variable |
| |
| WEEK 3
| 7-10 September
|
|
|
|
| Mon 6
|
LABOR DAY HOLIDAY
No class meeting
|
|
| Wed 8
| Heine-Borel Theorem
Chapter 1 Homework Due
|
|
|
| Fri 10
| Functions and Limits
| §2.1 #8,25
|
| WEEK 4
| 13-17 September
|
|
|
|
| Mon 13
| Monotonic functions
|
|
|
| Wed 15
| Continuity
Intermediate Value Theorem 2.2.10
(M. Regennitter, O. Robinson, S. Wenke)
Maximum Theorem for Continuous Functions 2.2.9
(D. Pinkston, J. Staron)
| §2.2 #7,28
|
|
| Fri 17
| Uniform continuity, Theorem 2.2.12
(B. Kline, Y. Li, M. Sinnwell)
Strictly monotone functions
|
|
| WEEK 5
| 20-24 September
|
|
|
|
| Mon 20
| The Derivative, Differentiation Rules.
Read §§ 1-7, 9, 13-16, 21, 35 of
The Analyst by George Berkeley.
List three objections to differential calculus.
| §2.3 #8(a),24
|
|
| Wed 22
| The Chain Rule
J.Y. Min, H. Kunizawa
Extreme points
§§2.1-2 Homework Due
|
|
|
| Fri 24
| The Mean Value Theorem
Reference: On Avoiding the Mean Value Theorem
(P. Iverson, T. Anjonrin-Ohu)
|
|
| WEEK 6
| 27 September -
1 October
|
|
|
|
| Mon 27
| Lhospital's Rule
Reference: Lhospital's Rule Without
Mean Value Theorems
| §2.4 #41,45
|
|
| Wed 29
|
|
|
| OCTOBER
|
|
| Fri 1
| First Midterm Exam
Syllabus for Exam
|
|
| WEEK 7
| 4-8 October
|
|
|
| Chapter 3: Integral Calculus of Functions of One Variable |
| |
|
| Mon 4
| Definitions: Partition, refinement, Riemann sum, integrable
| §3.1 #3,10
|
|
| Wed 6
| Upper and Lower Sums, the Integral
§§2.3-4 Homework Due
|
|
|
| Fri 8
| Integrability Theorem
| §3.2 #5,7
|
| WEEK 8
| 11-15 October
|
|
|
|
| Mon 11
| Continuous functions are integrable (3.2.8)
M. Regennitter, O. Robinson
The integral is linear, monotone, additive on intervals
|
|
|
| Wed 13
| Monotone functions are integrable (3.2.9)
T. Anjonrin-Ohu, J. Staron
|
|
|
| Fri 15
| Fundamental Theorem of Calculus I (3.3.11)
Reference: [PostScript] [Acrobat]
B. Kline, M. Sinnwell
| §3.3 #12,13
Note: for #12 use the
Lipschitz condition.
|
| WEEK 9
| 18-22 October
|
|
|
|
| Mon 18
| Fundamental Theorem of Calculus II (3.3.12)
Reference: [PostScript] [Acrobat]
D. Pinkston, P. Iverson
|
|
|
| Wed 20
| Integration by Parts (3.3.15)
H. Kunizawa, J. Min
§§3.1-2 Homework Due
|
|
|
| Fri 22
| Taylor's Theorem [PostScript] [Acrobat]
| §2.5 #8(b), 10(a),(b)(iv).
|
| WEEK 10
| 25-29 October
|
|
|
|
| Mon 25
| Change of Variable (3.3.17-18)
|
|
|
| Wed 27
| Review
|
|
|
| Fri 29
| Second Midterm Exam
Syllabus for Exam
|
| NOVEMBER
|
| WEEK 11
| 1-5 November
|
|
|
|
| Mon 1
| Improper Integrals:
Nonnegative functions, comparison tests
| §3.4 #6,15
|
|
| Wed 3
| Absolutely integrable functions
|
|
|
|
| Fri 5
| Conditional convergence, Dirichlet's test
§§3.3,2.5 Homework Due
|
|
| WEEK 12
| 8-12 November
|
|
|
| Chapter 4: Infinite Sequences and Series |
| |
|
| Mon 8
| Sequences
| §4.1 #11,23
|
|
| Wed 10
| Limits superior and inferior
Cauchy's convergence criterion
Contraction mapping
|
|
|
| Fri 12
| Subsequence, limit point
Sequential continuity
| §4.2 #9(a),10
|
| WEEK 13
| 15-19 November
|
|
|
|
| Mon 15
| Series, Cauchy's criterion
Convergence tests
| §4.3 #9,14
|
|
| Wed 17
| Convergence tests
|
|
|
| Fri 19
| Absolute and conditional convergence
§§3.4, 4.1 and 4.2 Homework Due
|
|
THANKSGIVING BREAK
22-26 NOVEMBER |
| |
Fri 26 BUY NOTHING DAY
|
| WEEK 14
| 29 November
-3 December
|
|
|
|
| Mon 29
| Dirichlet's Test
|
|
| DECEMBER
|
|
| Wed 1
| Rearrangement of series
|
|
|
| Fri 3
| Products of series
|
|
| WEEK 15
| 6-10 December
|
|
|
|
| Mon 6
|
|
|
|
| Wed 8
|
|
|
|
| Fri 10
|
§§4.3 Homework Due
|
|
FINAL
EXAMS
| 13-17 December
|
|
|
|
| Thu 16
| Final Exam
9:45-11:45am, 260 Carver.
Final Exam Syllabus
|
|
