AMATH 383, Summer 2016
University of Washington
Instructor: Jakob Kotas, firstname.lastname@example.org
Office hours: Wednesdays 4-6PM, Lewis 129 (not my office), or by appointment.
Webpage: The course webpage is on Canvas at https://canvas.uw.edu/courses/1048499.
Course description: Introductory survey of applied mathematics with emphasis on modeling of physical and biological problems in terms of differential equations. Formulation, solution, and interpretation of results. Topics covered include: ODE review, unit analysis, basics of models, algebraic models, models of exponential decay, models from the physical sciences, models of population, optimization of linear programs, and PDE models.
Prerequisites: Proficiency in ordinary differential equations at the level of AMATH 351 or MATH 307 is assumed. Some knowledge of Matlab, linear algebra, PDEs, and systems of differential equations is beneficial but not necessary.
Textbook: K.K. Tung: Topics in Mathematical Modeling. Recommended, but not required to pass.
Homeworks: 30%. 6 assignments worth about 5% each. Assignments are due weekly. Collection will take place in-class. A paper copy should be submitted, not electronically, unless told otherwise.
Project: 70%. This will be split into several intermediate deadlines: names of people in group (1%), abstract (9%), final submission (60%). Collection will take place online via Canvas. See "Project guidelines" document in the Files section of Canvas for more information.
Homework policy: Collaboration is encouraged, but every student must submit their own assignment consisting of their own work. Solutions will be posted immediately after class. Late assignments will not be accepted and will earn a score of zero. In the rare event of an emergency (such as a medical emergency or death or medical emergency of a close family member,) with well-documented evidence, a homework will be dropped and other homeworks will be re-weighted accordingly.
Assignments are demanding, and you are encouraged to start them as early as possible. Homeworks will be graded mostly on completion. You are still expected to complete all problems. All homeworks count towards your grade. The lowest homework score is not dropped.
Project policy: Late submissions of the intermediate deadline assignments will be accepted at the discretion of the instructor. Late submissions of the final project will not be accepted due to time constraints at the end of the course.
Computing policy: Some Matlab will be used in the course and a basic understanding of Matlab will be beneficial. However, computing is not a main focus of this course. Those interested in learning more about numerical methods should consider taking AMATH 301, Beginning Scientific Computing.
Honor code: Students shall abide by the University of Washington Academic Honesty policies, which are outlined at https://depts.washington.edu/grading/pdf/AcademicResponsibility.pdf.
Coverage of lectures:
Mon 6/20: Intro, Fermi problems
Wed 6/22: Falling raindrops and mixing tank problems
Fri 6/24: Review of ODEs
Mon 6/27: Matlab template files, Taylor series, units and nondimensionalization
Wed 6/29: Class canceled
Fri 7/01: Nondimensionalization and scaling laws (ch. 2)
Wed 7/06: Scaling laws (ch. 2)
Fri 7/08: Models using exponential decay (ch. 4)
Mon 7/11: Orbital dynamics (ch. 5)
Wed 7/13: Orbital dynamics (ch. 5) & single-species population models (ch. 6)
Fri 7/15: Single-species population models (ch. 6)
Mon 7/18: Review of systems of differential equations
Wed 7/20: Lotka-Volterra predator-prey model (ch. 9)
Fri 7/22: pplane & Discrete logistic model (ch. 7)
Mon 7/25: Competition model (ch. 9)
Wed 7/27: Abstract meetings, day 1
Fri 7/29: Abstract meetings, day 2
Mon 8/01-Fri 8/05: Guest lectures: Collapsing bridges (ch. 14), conflict
Mon 8/08: Linear programming, day 1
Wed 8/10: Linear programming, day 2