## john a. lind

Reed College

### 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]