Reed College

MWF 9:00-9:50 in Library 204 [S01]

MWF 12:00-12:50 in Library 204 [S03]

Office Hours: M 15:00-16:30, T 10:30-11:30, F 11-11:50 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*- W 1/25: §2.2 Euclidean space and the inner product
- F 1/27: §2.3 sequences and continuous mappings

*Week 2*- M 1/30: §2.3, continued
- W 2/1: §2.4 compact sets and continuity
- F 2/3: §3.5, the universal characterization of the determinant
__HW #1__(due Wednesday 2/1):- §2.2: 2, 3, 9, 10, 15
- §2.3: 1, 2, 4, 7, 9

*Week 3*- M 2/6: §3.5, 3.6 properties of the determinant, the 2x2 case
- W 2/8: §3.8, 3.9 the determinant, volume and orientation
- F 2/10: §3.10 the cross product, lines and planes in R^3
__HW #2__(due Wednesday 2/8):- §2.4: 1, 2, 5, 8, 9, 10
- §3.5: 5

*Week 4*- M 2/13: §4.1, 4.2 a failed generalization, Bachmann-Landau notation
- W 2/15: §4.3 the multivariable derivative
- F 2/17: §4.4, 4.5 properties of the derivative
__HW #3__(due Wednesday 2/15):- §3.8: 2, 4, 6
- §3.9: 1, 2 [only the first part of the question], 3
- §3.10: 4, 10, 17

*Week 5*- M 2/20: §4.4, 4.5 the chain rule, calculating the derivative
- W 2/22: §4.5 calculating the derivative
- F 2/24: §4.6 higher order derivatives
__HW #4__(due Wednesday 2/22):- §4.3: 3, 4, 5, 6
- §4.4: 2, 5, 7
- §4.5: 7

*Week 6*- M 2/27: §4.7 extreme values
- W 3/1: §4.7, 4.8 more extreme values, directional derivatives and the gradient
- F 3/3: §4.8 directional derivatives and the gradient
__HW #5__(due Wednesday 3/1):- §4.5: 4, 5, 9
- §4.6: 3, 5
- §4.7: 1, 3, 4

*Week 7*- M 3/6: §6.1 boxes and partitions
- W 3/8: §6.2 the definition of the integral
- F 3/10: §6.3 integration and continuity
**TAKE-HOME MIDTERM EXAM DUE** __HW #6__(due Wednesday 3/8):- 4.7: 5, 9
- 4.8: 2, 6, 7

*Spring Break*

*Week 8*- M 3/20: §6.3, 6.6 continuous functions are integrable, calculations
- W 3/22: §6.6 Fubini's theorem and calculations
- F 3/24: §6.6 Fubini's theorem and calculations
__HW #7__(due Wednesday 3/22):- 6.2: 3, 4, 5
*Week 9*- M 3/27: §6.7 change of variables
- W 3/29: §6.7 change of variables, calculations
- F 3/31: §6.7 change of variables, more calculations
__HW #8__(due Wednesday 3/29):- 6.3: 4, 5 (both of these problems are optional)
- 6.5: 4, 9
- 6.6: 1, 3, 4, 5, 6
- 6.7: 1, 2
*Week 10*- M 4/3: §9.1 integrating over parametrized k-surfaces in R^n
- W 4/5: §9.2 flow and flux integrals
- F 4/7: §9.3, 9.4, 9.5 intro to differential forms, 1-forms and 2-forms
__HW #9__(due Wednesday 4/5):- 6.6: 7, 8, 9
- 6.7: 3, 5, 6, 7, 8, 9, 10
- 9.1: 3
*Week 11*- M 4/10: §9.6, 9.7 the algebra of differential forms
- W 4/12: §9.8 differentiation of differential forms
- F 4/14: §9.5, 9.8 the geometric meaning of integration of differential forms, and more on differentiation
__HW #10__(due Wednesday 4/12):- 6.7: 11, 12, 13 [please read, but do not turn-in 6.7.14; problem 6.7.18 is prep for Renn Fayre and may be turned in at any point before then for extra credit]
- 9.3: 1, 2
- 9.4: 1, 2, 3
*Week 12*- M 4/17: §9.9, 9.10 pullback of differential forms and change of variables
- W 4/19: §9.9, 9.14, 9.16 exact vs. closed forms, the fundamental theorem of integral calculus
- F 4/21: §9.12, 9.13, 9.16 Stokes's theorem, cubes, chains, and the boundary operator
__HW #11__(due Wednesday 4/19):- 9.5: 1, 2
- 9.7: 2
- 9.8: 2, 3, 4, 5
- 9.9: 2
*Week 13*- M 4/24: §9.14, 9.16 Green's theorem, Gauss's theorem
- W 4/26: §9.14, 9.16 more on the fundamental theorem of integral calculus
- F 4/28: Maxwell's equations
__HW #12__(due Wednesday 4/26):- 9.9: 3
- 9.13: 2, 3, 5, 6
- 9.16: 2, 3, 4

**FINAL EXAM:**1-5pm Tuesday 5/9, in Physics 123