| Week |
Topics |
Book Sections |
Homework |
Notes |
| Aug
27-29 |
Primitive concepts
(sets, elements, functions,
operations).
First 9 axioms of the reals. |
I 2.1 - I 3.4 |
|
|
|
| Sep
3-5 |
First 9 axioms
(cont'd).
Min, max, inf and sup. |
I 3.4, I 3.8 |
I 2.5 # 19,20
Prove Thms I.5,I.12,I.13 |
Monday,
Sep 3
Labor Day
|
|
| Sep
10-12 |
The completeness
axiom. Existence of roots.
Inductive
sets. Naturals, integers, rationals.
Mathematical induction. |
I 3.9-11, I 3.13
I 3.6
I 4.1-2 |
Prove Thms I.22, I.25
I 3.5 #10, I3.12 # 2,5 |
|
|
| Sep
17-19 |
More examples of
proofs by induction.
Sigma
notation. Absolute values. |
I 4.6-8 |
|
|
|
| Sep
24-26 |
Limits of sequences
(finite and infinite). |
10.2 |
|
|
|
| Oct
1-3 |
Monotonic sequences.
Review. |
10.3 |
|
Test 1, Oct 3
|
|
| Oct
8-10 |
Bolzano-Weierstrass
Theorem.
Limits of functions. |
3.1-2 |
|
Tuesday,
Oct 9
Monday Class Schedule
|
|
| Oct
15-17 |
Continuity. Composite
functions.
Trigonometric functions (unrigorous). |
3.3-5, 3.7
2.5, 2.7
|
|
|
|
| Oct
22-24 |
Continuity and
neighborhoods.
Exponential
(unrigorous). Continuity of n-th root.
The Intermediate Value
Theorem.
Limits involving infinity. |
3.9-10
7.14-15 (parts) |
|
|
|
| Oct
29-31 |
Extrema of a
continuous function.
Review. |
3.16 |
|
|
|
| Nov
5-7 |
Derivatives and basic
theorems.
Geometric interpretation.
Chain rule. |
4.1-5
4.7-8
4.10 |
|
Test 2, Nov 7 |
|
| Nov
12-14 |
Inverse functions and
their derivatives.
Logarithms.
Mean Value Theorem. First derivative test. |
3.12-13, 6.20
4.13-14, 4.16 |
|
|
|
| Nov
19-21 |
L'Hopital's Rule (no
proof).
Applications to exponentials, powers and logs.
Step functions. |
7.12, 7.14, 7.16
1.8-10 |
|
Nov 21
Thanksgiving Recess
|
|
| Nov
26-28 |
Integrals of step
functions.
Integrals of general
functions.
Integrability of monotonic functions.
Basic
properties of integrals.
Review. |
1.12-14
1.16-17
1.20-21
1.24 |
|
|
|
| Dec
3-5 |
Proof of basic
properties of integrals.
Primitives.
Fundamental Theorems of Calculus.
Substitution. |
1.27
5.1-3
5.6-7 |
|
|