## john a. lind

Reed College

### math 202 vector calculus // spring 2017

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