MAT 325: Differential Equations

Instructor

• Name: Steven Wilkinson
• Office: MEP 480
• Phone: (859)572-5775
• Email: wilkinson@nku.edu
• Online course information: http://www.nku.edu/~wilkinson and Canvas
• Office hours:
  • TR 11:00–12:00 in MEP 480
  • F 10:00–11:00 in MEP 480
  • Other times by appointment

Course Information

• Course description

  Ordinary differential equations with application.

• Credits

  3 credit hours.

• Prerequisites

  C- or better in either MAT 228 or MAT 229.

• Course specific outcomes

  • Become familiar with differential equations and systems of differential equations.
  • Be able to analyze certain types of differential equations.
  • Be able to model certain situations with differential equations and from the analysis of those equation gain information about the underlying situations.

• Resources

  • Ordinary Differential Equations: From Calculus to Dynamical Systems by Virginia W. Noonburg.
  • The material covered:
    • Chapter 1: Introduction to Differential Equations
    • Chapter 2: First-order Differential Equations
    • Chapter 3: Second-order Differential Equations
    • Chapter 4: Linear Systems of First-order Differential Equations
    • Chapter 5: Geometry of Autonomous Systems
  • Online materials will be provided on Canvas as the course progresses.

• Tentative weekly schedule

  Week	Topics
  Week 1: 1/9 - 1/15	Basic terminology Families of solutions Modeling
  Week 2: 1/16 - 1/22	Separable equations Slope fields Linear first order equations Deadline to add or drop with 100% tuition adjustment: Tue, Jan 17
  Week 3: 1/23 - 1/29	Existence and uniqueness Analytic methods
  Week 4: 1/30 - 2/5	Numerical methods Autonomous equations Deadline to drop with no grade and 50% tuition adjustment: Mon, Jan 30
  Week 5: 2/6 - 2/12	Homogeneous linear equations Constant coefficients
  Week 6: 2/13 - 2/19	Spring-mass equation Nonhomogeneous linear equations
  Week 7: 2/20 - 2/26	Forced spring-mass equation Autonomous second-order equations Review for exam 1
  Week 8: 2/27 - 3/5	Exam 1 Introduction to systems
  Spring Break Week: 3/6 - 3/12	No classes
  Week 9: 3/13 - 3/19	Matrix algebra Eigenvalues and eigenvectors
  Week 10: 3/20 - 3/26	Analytic solutions Deadline to drop with grade of W: Mon, Mar 20
  Week 11: 3/27 - 4/2	Phase plane Geometric behavior of linear systems
  Week 12: 4/3 - 4/9	Geometric behavior of nonlinear systems
  Week 13: 4/10 - 4/16	Bifurcations for systems Review for Exam 2
  Week 14: 4/17 - 4/23	Exam 2 Laplace transforms
  Week 15: 4/24 - 4/30	Inverse Laplace transform Review for final exam
  Final Exam Week: 5/1 - 5/5	Final exam on Tuesday, 5/2 (12:20 to 2:20)

• Other rescourses

  • Fuel NKU: On-campus food security resource
  • Health, Counciling, and Student Wellness: Suppport of the well-being of the community
  • Information Technology: Support for technology issues

Assessment

• Final Exam

  A final exam worth 50 points.
• Your final exam is a comprehensive two-hour exam.
• Taken in class during Finals Week on Tuesday, May 2, 12:20–2:20 p.m.

• Midterm Exams

  • There will be 2 exams during the semester, each worth 50 points. These will all be taken in class.
  • You can choose to retake a different version of any midterm exam. Any retake score will replace the original exam score, even if the original score is higher.

• Homework

  • Daily homework assignments worth 2 points each.
  • Weekly assignments worth worth 6 points each.

• Grading Scale

  Letter grade	A	A-	B+	B	B-	C+	C	C-	D+	D	F
  % greater than or equal to	92	90	88	82	80	78	72	70	68	60	--

• Midterm Grades

  Midterm grades will be posted in myNKU by the deadline established in the NKU’s academic calendar.

Course Policies

• COVID

  • We will follow any NKU policies concerning the pandemic. NKU has a site devoted to its COVID policies and best practices.
  • Although masks are not required (unless the universities mandates them), I recommend wearing them in class since you will be working closely with your classmates.
  • If you need to quarantine because of COVID, let me know as soon as possible. I will work with you as best as I can to help you get through the course while you cannot be on campus. However, you will not be able to participate in the in-class assignments.
  • If I contract COVID, the course will switch to an online course until I test negative. If that happens, there will be no in-class assignments while we are online.

• Attendance

  • Attendance will not be recorded. However, you must be present to be given credit for a group assignment.
  • You are responsible for all material assigned or covered in class.

• Technology Requirements

  • To submit written assignments you can either scan them or take pictures of them. In the latter case you will need software that converts them to pdf files using something like the free phone app, Microsoft Lens.
  • For use in class and on homework, you may want access to a graphing calculator or an online app like Desmos available at https://www.desmos.com.
  • On some out-of-class work you may want to access Mathematica, a computer algebra system that you can freely download. NKU has directions for how to do so.

• Credit Hour Policy

  In accordance with federal policy, NKU defines a credit hour as the amount of work represented in the achievement of student learning outcomes (verified by evidence of student achievement) that reasonably approximates one hour (50 minutes) of classroom instruction and a minimum of two hours of out-of-class student work. For every course credit hour, a typical student should expect to spend at least three hours per week of concentrated attention on course-related work including, but not limited to, class meeting time, reading, reviewing, organizing notes, studying and completing assignments. At least an equivalent amount of time is expected for other academic activities such as online courses, laboratory work, internships, practica, studio work and other academic work leading to the award of credit hours.

Student Information

• Department Common Syllabus

  The Department of Mathematics has information relevant for all mathematics and statistics classes. The department syllabus is available online at https://inside.nku.edu/content/dam/math/docs/DepartmentSyllabus.pdf. Additional information concerning Secondary Education Students is available on that Departmental Syllabus.

• NKU Common Syllabus

  Northern Kentucky University has a common syllabus available at https://www.nku.edu/content/dam/academicaffairs/docs/docs/University%20Common%20Syllabus%202020.pdf.

• Academic Honesty

  All students should adhere to the highest degree of ethical integrity in academic conduct. Read Northern Kentucky University’s Code of Student Rights and Responsibilities for details of your responsibilities. In this class plagiarism, either copying from others or allowing others to copy from you, will result in a grade of 0 for the work in question.

• Accommodations Due to Disability

  Northern Kentucky University is committed to providing reasonable accommodations for all persons with disabilities. The syllabus is available in alternate formats upon request. Students with disabilities: If you are seeking classroom accommodations under the Americans with Disabilities Act, you are required to register with the Office for Student Accessibility (OSA) in SU 303. To receive academic accommodations for this class, please obtain the proper OSA forms and meet with me at the beginning of the semester. More information on OSA can be found at https://inside.nku.edu/osa.html.

• Communication

  Students should check their email and Canvas course sites regularly. Students may expect instructor responses to emails within 2 days.

• Names and Pronouns

  My gender pronouns are he, his, him. I will gladly honor your request to address you by an alternate name and/or gender pronouns from what is contained in NKU’s student records. Please advise me of these early in the semester so that I may make appropriate changes to my records.

Important Dates

• Monday, January 16: Martin Luther King Day, no classes
• Tuesday, January 17: Last day to drop with 100% tuition adjustment. Last day to add a class.
• Monday, January 30: Last day to drop with no grade appearing on transcript; last day to drop with 50% tuition adjustment.
• Monday, February 27: Midterm grades begin to be posted.
• March 6-12: Spring Break, no classes.
• Tuesday, March 14: Deadline for midterm grade submissions.
• Monday, March 30: Last day to drop a class with a W on your transcript.
• Friday, April 28: Last day of classes.