Syllabus for Multivariable Calculus (Math 3355)
Rick's Office: 451 Vincent Hall, 626-8308 or 626-1324
Email: fjw@geom.umn.edu, WWW: http://www.geom.umn.edu/~math335x
Supplemental Text: Differential Equations by
Blanchard, Devaney, and Hall
Text for sale at the Special Projects Office, 115 VinH, 8:30-4:00pm.
TAs: Bob Hesse (Workshop Czar), hesse@math.umn.edu
Sec 1 Ernesto Schirmacher, schirmac@math.umn.edu
Sec 2 Gerry Naughton, naughton@math.umn.edu
Sec 3 Tim Brule, brule@math.umn.edu
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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URL: http://www.geom.umn.edu/~math335x/Syllabus2/Syllabus2.html
Copyright: 1996 by the Regents of the University of Minnesota.
Department of Mathematics. All rights reserved.
Comments to:
hesse@math.umn.edu
Last modified: Thur, Jan 17 1997
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