Instructor: Christopher Sadowski
Email: csadowski at ursinus dot edu
Office: Pfahler Hall 101A
Office Hours: Monday and Wednesday 1:30-3:00, Tuesday 9:00-10:00, Friday 1:30-2:30, and by appointment.
Text: Differential Equations with Boundary-Value Problems, 8th edition, by Dennis Zill and Warren Wright.
The following set of notes may also be helpful: Differential Equations by James Cook
Course Objectives: Students will learn the basic ideas and techniques of differential equations. Students will be required to know:
First order linear and nonlinear equations, and how to solve certain types. Included in this will be numerical methods and qualitative methods for describing solutions of differential equations
Modeling real world phenomena with differential equations
Techniques for solving higher order differential equations
How to solve linear systems of equations
How to linearize and determine the behavior of solutions to nonlinear systems
The Laplace transform
Learning Goals: This course will meet the following departmental learning goals:
Organize and synthesize evidence to identify patterns and formulate conjectures
Solve problems with mathematical components, and use standard software packages when appropriate
Communicate to technical and non-technical audiences
Work independently and in groups
Location: Pfahler Hall 109
Meeting times: MWF 11:00-11:50
Grading:
-20% Homework
-5% Maple Labs
-15% Midterm 1
-15% Midterm 2
-15% Midterm 3
-30% Final Exam
Exams:
Exams will be announced 2 weeks in advance. Make up exams will require documentation as proof of absence,
and will be assessed on a case-by-case basis. The following dates are tentative:
Exam 1: 2/24/17
Exam 2: 3/24/17
Exam 3: 4/28/17
Final Exam:
Homework: There will be weekly homework assigned each Friday, to be completed by the following Friday. Late assignments
will NOT be accepted, but the lowest assignment will be dropped.
Maple: There will be several Maple assignments throughout the semester to illustrate various important concepts and ideas.
Academic Honesty: Students may work together and discuss assignments with one another, but all work handed in must be solely
the student's. Any incident of cheating on a quiz or exam will results in a grade of 0 for the assignment, with no make-up allowed. A second incident of cheating will result in a failing grade for the course. All incidents of cheating will be reported to the Dean's Office. Please refer to the Student Handbook on Academic Honesty and the Statement on Plagiarism.
Attendance: Students are expected to attend all classes. If you are unable to attend class for a legitimate reason, please email me before class.
Inclement Weather Policy: Students will be emailed in the event that class is cancelled due to inclement weather.
Accommodations Policy: Students requiring accommodations should provide me with the appropriate paperwork from the Accommodations Office at the beginning of the semester.
SPTQ: Towards the end of the semester, students will be reminded to fill out SPTQ forms. These forms are invaluable to both the instructor and the department, since they provide valuable feedback to the instructor on how to improve the course, and provide evaluation information to the department chair. Honest constructive feedback (both positive and negative!) is appreciated.
Inclusive climate in the classroom: In this class we will work to promote an environment where everyone feels safe and welcome, even during uncomfortable conversations. Every voice in the classroom has something of value to contribute to class discussion. Because the class will represent a diversity of individual beliefs, backgrounds, and experiences, every member of this class must show respect for every other member of this class. You are encouraged to not only take advantage of opportunities to express your own ideas, but also, learn from the information and ideas shared by other students.
Syllabus (subject to change as the course progresses):
Week 1 (week of 1/16/17)
Section 1.1: Definitions and Terminology
Section 1.2: Initial Value Problems
Section 1.3: Differential Equations as Mathematical Models
Week 2: (week of 1/23/17)
Section 2.1: Solution Curves without a solution
Section 2.2: Separable Equations
Week 3: (week of 1/30/17)
Section 2.3: Linear Equations
Section 2.4: Exact Equations
Week 4: (week of 2/6/17)
Section 2.5: Solutions by substitution
Section 2.6, 9.1, 9.2: Numerical Methods
Week 5: (week of 2/13/17)
Section 3.1: Linear Models
Section 3.2: Nonlinear Models
Week 6: (week of 2/20/17)
Section 3.3: Modeling with Systems of first order DEs.
Section 4.1: Higher order equations - preliminary theory
Week 7: (week of 2/27/17)
Section 4.2: Reduction of Order
Section 4.3: Homogeneous linear equations with constant coefficients
SPRING BREAK
Week 8: (week of 3/13/17)
Section 4.4: Undetermined Coefficients - Superposition Approach
Section 4.5: Undetermined Coefficients - Annihilator Approach
Section 4.6: Variation of Parameters
Week 9: (week of 3/20/17)
Section 7.1: Definition of the Laplace Transform
Section 7.2: Inverse Transforms and transforms of derivatives
Section 7.3: Operational properties
Week 10: (week of 3/27/17)
A crash course in linear algebra!
Week 11: (week of 4/3/17)
Section 8.1: Preliminary Theory - linear systems
Section 8.2: Homogeneous linear systems
Week 12: (week of 4/10/17)
Section 8.3: Nonhomogeneous linear systems
Section 10.1: Autonomous Systems
Week 13: (week of 4/17/17)
Section 10.2: Stability of Linear Systems
Section 10.3: Linearization and Local Stability
Week 14: (week of 4/24/17)
Section 10.4: Autonomous Systems as Mathematical Models
Week 15: (week of 5/1/17)
Additional Topics
Last day of classes is 5/3/17