Catalog Description. Credit 3. Linear ordinary differential equations, solutions in series, solutions using Laplace transforms, systems of differential equations. Prerequisite: Math 251 (third semester of calculus).
Textbook. Fundamentals of Differential Equations and Boundary Value Problems by Nagle and Saff. Most sections will also be using Solving ODEs with Maple V for the laboratory component of the course.
The goal of this component is to use the computer as a computational and graphical tool to solve problems that would be too difficult to solve by hand. In addition, some pedagogical points can be enhanced with the use of the computer. The above mentioned ODE manual contains the relevant Maple syntax together with applications and modeling problems where Maple is needed as part of the solution process. You will get experience in solving differential equations using the computer (both symbolically and numerically) and you will eventually be expected to solve a modeling or applications problem/project where the computer is needed to complete the solution.
Basic hand computational techniques are still covered in this course, but perhaps not with the same emphasis as in the past. There is a a common core that belongs in any DE course. This core includes the basic techniques for solving first and second order equations together with applications; Laplace transforms, and two-dimensional systems. There is room at the end of the syllabus for additional topics such as series solutions, numerical methods, higher-dimensional systems and dynamical systems. Not all of these optional topics can be covered and they are left to instructor discretion...my choices are series solutions and higher-dimensional systems. There will be weekly homework which will be graded. This will include Maple-base homework, and you will need to take diligent advantage of the Maple evening open hours and the help sessions. The staff is drawn from the best and brightest veterans of this course in past semesters. (Some have even taken the course from your current instructor). See the course home page for further details. Homework will count for 20% of your grade. A project incorporating Maple will count for a further 10%. The final will count for 25%, and the three hour exams will count for 15% each.
Week 1 pp. 1-24
Week 2 pp. 24-30, pp. 35-46
Week 3 pp. 46-65
Week 4 pp. 86-128
Week 5 pp. 128-137, pp. 150-169
Week 6 pp. 169-188
Week 7 pp. 188-207
Week 8 pp. 207-214, pp. 240-260
Week 9 pp. 261-299
Week 10 pp. 351-380
Week 11 pp. 380-428
Week 12 pp. 734-763
There will be three major exams and a final exam are given in this course.
Exam 1: In week three after the material in Chap. 2 is finished. Exam 2: In week eight after the material in Chap. 4. Exam 3: In week twelve after Laplace transforms.