math 202 vector calculus // fall 2017
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]