Instructor: Christopher Sadowski
Email: csadowski at ursinus dot edu
Office: Pfahler Hall 101A
Office Hours: Monday, Tuesday, Thursday, Friday: 11:00-12:00
Tuesday and Thursday: 3:00-4:00
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:
Learning Goals: This course will meet the following departmental learning goals:
Location: Pfahler Hall 012
Meeting times: Tuesday and Thursday, 1:30-2:45
Grading:
-10% Homework
-10% Quizzes
-5% Maple Labs
-20% Midterm 1
-20% Midterm 2
-35% 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 will be on Thursday, 2/25/16.
Exam 2 will be on Thursday, 4/7/16.
Quizzes: We'll have a quiz each week on Thursday. The quiz will cover the material from the homework due that week.
Homework: There will be weekly homework assigned each Thursday, to be completed by the following Thursday. Late assignments will NOT be accepted, but the lowest assignment will be dropped.
Quizzes: We will have a quiz on Thursday of each week on the material covered in the previous week. The quiz will be on the homework material due that week. The lowest quiz grade 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: (1/18, 1/19, 1/21, 1/22)
Section 1.1: Definitions and Terminology
Section 1.2: Initial Value Problems
Section 1.3: Differential Equations as Mathematical Models
Week 2: (1/25, 1/26, 1/28, 1/29)
Section 2.1: Solution Curves without a solution
Section 2.2: Separable Equations
Week 3: (2/1, 2/2, 2/4, 2/5)
Section 2.3: Linear Equations
Section 2.4: Exact Equations
Week 4: (2/8, 2/9, 2/10, 2/11)
Section 2.5: Solutions by substitution
Section 2.6, 9.1, 9.2: Numerical Methods
Week 5: (2/15, 2/16, 2/18, 2/19)
Section 3.1: Linear Models
Section 3.2: Nonlinear Models
Week 6: (2/22, 2/23, 2/24, 2/25)
Section 3.3: Modeling with Systems of first order DEs.
Section 4.1: Higher order equations - preliminary theory
Week 7: (2/29, 3/1, 3/3, 3/4)
Section 4.2: Reduction of Order
Section 4.3: Homogeneous linear equations with constant coefficients
Week 8: (3/7, 3/8, 3/9, 3/10)
Section 4.4: Undetermined Coefficients - Superposition Approach
Section 4.5: Undetermined Coefficients - Annihilator Approach
Section 4.6: Variation of Parameters
SPRING BREAK
Week 9: (3/21, 3/22, 3/24, 3/25)
Section 7.1: Definition of the Laplace Transform
Section 7.2: Inverse Transforms and transforms of derivatives
Section 7.3: Operational properties
Week 10: (3/28, 3/29, 3/31, 4/1)
A crash course in linear algebra!
Week 11: (4/4, 4/5, 4/7, 4/8)
Section 8.1: Preliminary Theory - linear systems
Section 8.2: Homogeneous linear systems
Week 12: (4/11, 4/12, 4/14, 4/15)
Section 8.3: Nonhomogeneous linear systems
Section 10.1: Autonomous Systems
Week 13: (4/18, 4/19, 4/21, 4/22)
Section 10.2: Stability of Linear Systems
Section 10.3: Linearization and Local Stability
Week 14: (4/25, 4/26, 4/28, 4/29)
Section 10.4: Autonomous Systems as Mathematical Models
Week 15: (5/2)
Review