This schedule will be regularly updated. It is your responsibility to check it often.
Homework is due every Thursday. Underlined problems in should be handed in.
| When | Topics | # | Homework, Exams, Remarks. |
| 1/24 |
Administrative
stuff and general
information Chapter 1 - Sections 1.1-1.2-1.3 |
0 | Fill this
form. If you have the book: Read Chapter 0 and prepare a list questions to ask in class. |
| 1/31 |
Section 6.1 Discussion about differential forms. |
1 | Section 1.1: 4, 6, 9 Section 1.2: 2, 4, 8,10, 14, 16 |
| 2/7 |
Section 6.1 Discussion about differential forms. Snow |
2 | Section 6.1:1a, 1c, 2a, 6, 15 |
| 2/14 |
Discussion about integrating differential forms Section 1.5 (up to Subsection Convergence) and Section 3.1: Manifolds -Smooth Manifolds in Rn. -Parametrization of manifolds. |
3 | Following the procedure we discussed in class (that is,
dividing the curve in small arcs and considering vectors joining
consecutive the endpoints of these arcs), find the integral of the
1-form in R^2 2xdy+3y dx, against a curve
of your choice from the point (0,2) to the point (1,3). IMPORTANT:
Explain and justify every step. Extra credit: Try to find the integral along another curve with the same endpoints. Section 6.1: 12, 15 Interesting linkages Peaucellier linkage Watt's linkage Ellipse linkage Elliptical trainer. |
| 2/21 |
Section 2.10 The implicit and inverse function theorem (statements
only. We will discuss the proofs later). Section 3.1 Manifolds. |
4 | Section 1.5: 1, 2, 3, 5, 7. Section 3.1: 2, 3, 12, 13. |
| 2/28 |
Section 3.1 Manifolds. Review |
5 | Section 2.10: 1, 2, 5a, 5b, 6,8, 9, 10 (Prove only
that a continuous strictly monotonous function has an inverse. You
do not need to prove that the inverse is continuous... but of course
you can if you wish) Section 3.1: 5, 6, 7, 8. |
| 3/7 |
Section 3.2: Tangent spaces |
6 | Midterm 1: Tuesday 3/7 In class. Topics: Up to Section 3.
(including Section 3.1). No homework this week. |
| 3/14 |
Spring break |
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| 3/21 |
Review |
|
|
| 3/28 |
Section 4.1 Defining the integral Section 4.3 What functions can be integrated? |
7-8 | Section 3.2: 1, 2, 3, 4a,b,c,5a, 6, 7, 8, 12, |
| 4/4 |
Section 4.4 Measure zero Review |
9 | Section 4.1: 1, 2, 3. 5a,b,c,d, 6,
8, 9, 10, 14 Section 4.3: 1, 2, 3, 5. |
| 4/11 |
Midterm II Section 4.5 Fubbini's theorem Section 6.2 Integrating form fields |
10 | No homework this week but you should know how to solve the
following problems. Section 4.4: 1, 2, 5, 7. Section 4.5: 2, 3, 7,8 Midterm 2: Thursday 4/13 In class. Midterm Topics: Sections 3.2, 4.1, 4.3, 4.4. Sample problems for the midterm: Section 3.2: 4, 6, 8 Section 4.1: .9, 11, 14, 21 Section 4.3: 2, 3, 5, Section 4.4: 2, 7 |
| 4/18- |
Section 6.3 Orientation of manifolds Section 6.4. Integrating forms over manifolds |
11 | Section 4.4: 2, 7 Section 4.5: 3, 7, 8, 12, 15 |
| 4/25 |
Stokes theorem Section 6.6 Boundary orientation Section 6.7 The exterior derivative Section 6.9 The pullback |
12 | Section 6.2: 1a, 2a, 3b Section 6.3: 1, 2, 3, 4, 5, 12 6.4: 1, 4 |
| 5/2 |
Section 6.10 The generalized Stokes theorem Review |
13 |
Section 6.6: 2, 6a,b.
(In problem 2 and 6a, you only need to show that the boundary of
each region is a finite union of one dimensional manifolds. Section 6.7: 1, 2, 6, 7b. Secton 6.10: 2, 4, 5. Sample problems for the final |
| Final Exam: Wed. May 10, 5:30pm-8:00pm in our usual classroom,
Harriman 112 |
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