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 1.11.21.3 
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 R^{n}. 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
1form 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 

3/21 
Review 


3/28 
Section 4.1 Defining the integral Section 4.3 What functions can be integrated? 
78  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, 5:30pm8:00pm in our usual classroom,
Harriman 112 
