Reed College

MWF 11:00-11:50 in Physics 240A

Office Hours: M 12:10-13:00, Th 15:00-16:30, F 12:10-13:00 in Library 390; also by appointment

Math Help Center: SuMTWTh 19:00-21:00, in Library 389

Syllabus

Solutions to the homework (available via Reed proxy).

*Week 1*- M 8/28: §2.2 Euclidean space and the inner product
- W 8/30: §2.2, 2.3 angles and sequences
- F 9/1: §2.3 sequences and continuous mappings

*Week 2*- W 9/6: §2.4 limit points and closed sets [
__HW #1__DUE] - F 9/8: §2.4 bounded sets, compact sets [deadline to add course]

*Week 3*- M 9/11: §2.4 compact sets and continuity
- W 9/13: §3.5, 3.6 the determinant and its universal characterization [
__HW #2__DUE] - F 9/15: §3.8, 3.9 the determinant, volume and orientation

*Week 4*- M 9/18: §3.10 the cross product, lines and planes in R^3
- W 9/20: §4.1, 4.2 what is the derivative? [
__HW #3__DUE] - F 9/22: §4.3 the derivative is the best linear approximation

*Week 5*- M 9/25: §4.3 more on the derivative
- W 9/27: §4.5 calculating the derivative [
__HW #4__DUE] - F 9/29: §4.4, 4.5 the chain rule and criteria for differentiability

*Week 6*- M 10/2: §4.5 more on the criteria for differentiability
- W 10/4: §4.6, 4.7 higher order partial derivatives and extreme values [
__HW #5__DUE] - F 10/6: §4.7 eigenvalues and the second derivative matrix

*Week 7*- M 10/9: §4.7 the second derivative test and extreme values
- W 10/11: §4.7, 4.8 more extreme values, directional derivatives and the gradient [
__HW #6__DUE] - F 10/13: § 4.8, 5.4, 5.5: Lagrange multipliers

*Fall Break*

*Week 8*- M 10/23: §6.1 boxes and partitions
- W 10/25: §6.2 the definition of the integral
- F 10/27: §6.3 continuous functions are integrable

*Week 9*- M 10/30: §6.5, 6.6 Volume, Fubini's theorem and calculations
- W 11/1: §6.6 Fubini's theorem and calculations [
__HW #7__DUE] - F 11/3: §6.6 yet more calculations

*Week 10*- M 11/6: §6.7 change of variables
- W 11/8: §6.7 change of variables, calculations [
__HW #8__DUE] - F 11/10: §6.7 change of variables, more calculations

*Week 11*- M 11/13: §6.7 yet more calculations
- W 11/15: §9.1, 9.3 integrating over parametrized k-surfaces, intro to differential forms in R^n [
__HW #9__DUE] - F 11/17: §9.2, 9.3, 9.4 1-forms and flow integrals

*Week 12*- M 11/20: §9.2, 9.5 2-forms and flux integrals
- W 11/22: §9.5, 9.6, 9.7 computations, the algebra of differential forms [
__HW #10__DUE] - (thanksgiving break)

*Week 13*- M 11/27: §9.5 the differential operator, orientations
- W 11/29: §9.8, 9.10 the geometric meaning of differential forms, the pullback of forms
- F 12/1: §9.9, 9.14, 9.16 the fundamental theorem of integral calculus, Stokes's theorem [
__HW #11__DUE]

*Week 14*- M 12/4: §9.9, 9.16 Green's theorem, Gauss's theorem, the pullback-determinant theorem
- W 12/6: §9.10, 9.12, 9.13, 9.14 change of variables for differential forms and the proof of the super FTC
- [
__HW #12__DUE F 12/8]