Instructor
Ernest Boyd, Wissink 273, 389-1452
Office Hours:
Textbook
No textbook is required. We will develop class notes during the course.
Course Content
Applications of discrete and continuous mathematics to deterministic problems in the natural sciences, computer science, engineering and economics. Mathematical topics from calculus of variations, graph theory, discrete optimization, control theory, and ordinary and partial differential equations. Familiarity with the computer algebra system Mathematica will also be developed.
Schedule
1:00 - 1:50 pm, MTRF, Wissink Academic Computer Center Room 116
Tests
Two hour test with dates to be determined
Final exam, Monday, May 5, 12:30 - 2:30 pm
Grading Policy
Each test will be graded on its own scale normalized to 100%. The final will also be graded on a scale normalized to 100%. All of the homework collected will be totaled and graded as one test. At the end of the semester the four grades will be averaged and compared to the average of the scales. Grading will reflect the mathematical correctness of the answer and the quality of the presentation in terms of completeness and organization. Late assignments will be penalized. Assignments over one week late will receive no credit. Active participation in the class discussions will also be factored into the evaluations. Make-up tests will be given only in special cases, when an excused absence has been prearranged. Incompletes will follow the university's policy as expressed in the student bulletins and the faculty handbook. No incomplete will be given to repeat the entire course.
Every attempt will be made to accommodate qualified students with disabilities. If you are a student with a documented disability, please see the instructor as early in the semester as possible to discuss the necessary accommodations, and/or contact the Disability Services Office at (507)389-2825 (V) or 1-800-627-3529 (MRS/TTY).
Modify the logistic equation to model seasonal variation in the
intrinsic growth rate as
r = (rmax + rmin)/2 + (rmax -
rmin)/2*sin(2*Pi*t).
Analyze the model for mutualism: x' = x(1 - x + ay), y' = ry(1 - y + bx).
Modify the mycelium's intrinsic growth rate in the reaction-diffusion equation so that the equilibrium is stable in the absence of diffusion and unstable with diffusion.
Homework 6, 7, 8 on Linear Programming.
Homework 9, 10 on Linear Programming.
Exercises 3 and 5 on the Out-of-Kilter Algorithm. Also explain Iterations 10 and 11 of the example.
Find the continuously differentiable curve y(x) on [0, 1] with y(0) = 5 and y(1) = 2 that minimizes the surface area of revolution about the x-axis.
Find the continuously differentiable curve y(x) on [0, 1] with y(0) = 5, y(1) = 2 and arc length of 5 that would give the shape of a freely hanging rope under the influence of a constant gravitational field in the negative y-direction.