Text: Elementary Differential Equations and Boundary Value Problems (10 th
edition) by. Boyce and DiPrima. Lessons and topics to be covered: 1-8: First-
order ...
FALL SEMESTER MATH 315 SYLLABUS Instructor: David J. Wollkind, Office: Neill 211, Office Hours: 9-11 MWF. Text: Elementary Differential Equations and Boundary Value Problems (10th edition) by Boyce and DiPrima. Lessons and topics to be covered: 1-8: First-order ordinary differential equations and applications (chap. 2). 9-21: Second-order linear ordinary differential equations and applications (chap. 3). 22: Higher-order linear ordinary differential equations (chap. 4). 23-27: Systems of first-order linear ordinary differential equations (chap. 7). 28-30: Series solutions of second-order linear ordinary differential equations (chap. 5). 31-35: Partial differential equations, boundary value problems, Fourier series, and Laplace transforms (chaps. 10, 11, & 6). 36-43: Nonlinear differential equations, stability, and numerical bifurcation methods (chaps. 9 & 8). Examinations: #1: In-class on topic 1, Friday of the 4th week, 100 points. #2: In-class on topic 2, Friday of the 9th week, 100 points. Final Exam: Take-home, made available after lesson 29 and due on the day the final examination is scheduled in the 16th week, 200 points. Total points: #1 + #2 + Final Exam (maximum of 400 points). Grades: Determined solely on the basis of the total points on the examinations as follows: A: 400-358; B: 357-318; C: 317-278; D: 277-238; F: 237-0. Homework problems: Assigned but not collected during the first 27 lessons with detailed solutions to all problems either presented as part of a future lesson or distributed in class. Slide shows: The last three lessons 41-43 will be slide shows highlighting research areas. These deal with the dynamical behavior of a ODE model for temperature-dependent predator-prey mite systems on fruit trees and the pattern formational aspects of PDE models involving the Navier-Stokes equations for thermal convection in aerosol gaseous layers and interaction-diffusion equations for ecological Turing instabilities in arid environments or on marine beds, respectively. The major emphasis here is on the comparison of theoretical predictions with field or experimental data.
