**Syllabus for Multivariable Calculus (Math 3355)**

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Supplemental Text:

Text for sale at the Special Projects Office, 115 VinH, 8:30-4:00pm.

Sec 1 Ernesto Schirmacher,

Sec 2 Gerry Naughton,

Sec 3 Tim Brule,

This course will focus on the differential equations, coordinate transformations, and multivariable integration.

**Week 1**- (1/6-1/10) Linear Systems
- Read BDH §3.1, 3.2
- trace, determinant, eigenvalues, complex numbers
- Lab 8: Classification of planar phase portraits.
- Homework: (HW 11) Eigenvalues and the pitchfork diagram.

**Week 2**- (1/13-1/17) Explicit solutions to linear ODEs
- Read BDH §3.3, 3.4
- Solution of linear ODEs with real eigenvalues as linear combinations of straight-line solutions. Geometry of linear transformations.
- Lab 9: (GRADED) The geometry of eigenvalues, eigenvectors, and determinants.
- Homework: (HW 12) Analysis of a linear ODE: The shock absorber.

**Week 3**- (1/20-1/24) Bifurcations
- Read BDH §3.3, 3.4
- Solution of linear ODEs with complex eigenvalues; bifurcations
- Lab 10: (GRADED) Linear and nonlinear oscillators
- Homework: (HW 13) Analysis of linear ODE: Predator-prey

**GATEWAY I**- 1/28
**EXAM III**- 1/30. Covers first quarter, and weeks 1-3. (Takehome due 2/4)
**Week 4-5**- (2/4-2/7) Coordinate transformations
- Read: DF §6.5
- Polar coordinates, cylindrical and spherical coordinates.
- Lab 11: Cylindrical coordinates
- Homework: (HW 14) Study for exam. (HW 15) Nonrectangular coordinates.

**Weeks 6-7**- (2/10-2/21) Multiple Integrals
- Read DF §6.1, 6.2, 6.4
- Riemann sums, numerical integration, iterated integrals, volume integrals.
- Lab 12: (GRADED) Numerical integration and the metrodome (2 weeks)
- Homework: (HW 16) Numerical approximation: the Million Man March (HW 17) Multiple integrals

**GATEWAY II**- 2/25
**EXAM IV**- 2/27 Covers first quarter, weeks 1-6, with an emphasis on weeks
4-6. (Takehome due: 3/4)
**Weeks 8-9**- (2/24-3/7) Applications of integration
- Reading TBA
- Change of variables, integration in curvilinear coordinates, centroids
- Lab 13: The center of Minnesota
- Homework: (HW 18) Study for Exam (HW 19) Centroids

**Week 10**- (3/10-14) Line integrals
- Read DF §7.1, 7.2
- Path integrals, work, the gradient theorem
- Lab 14: The gradient theorem

**GATEWAY III**- 3/11
**FINAL EXAM**- 3/17, 1:30-4:30, TBA. The final exam covers material
from the entire course, with an emphasis on the second quarter, and
a slight emphasis on weeks 8-10.

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Last modified: Thur, Jan 17 1997

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