MATH 261 - Elementary Differential Equations, Fall 2026
Course Syllabus

Instructor: Brian Leary
Email: Brian.Leary1@mail.wvu.edu
Office: Learning Resource Center, 323J
Office Hours: Mondays 2-3, Tuesdays 12-1, Wednesdays 2-3, Thursdays 11-1, Fridays 12-1

Class Room and Time: Innovation 303, Monday/Tuesday/Wednesday/Friday 11:00-11:50 am
Course Website: http://community.wvu.edu/~bal0018/math261F26.html

Course announcements and handouts may be posted on the website or the MyOpenMath page or sent via email. Please be sure to check the website regularly, and to regularly check the email address you have on record. You are responsible for any information posted on the course website.

Textbook: Trench, Elementary Differential Equations with Boundary-Value Problems, available to download for free at https://math.libretexts.org/Bookshelves/Differential_Equations/Elementary_Differential_Equations_with_Boundary_Value_Problems_(Trench)

Catalog Data: MATH 261 Elementary Differential Equations (4-0) Credits 4. Ordinary differential equations, Laplace transforms, partial differential equations, Fourier series, applications.
Prerequisite: MATH 251 or grade ``B" or better in MATH 315.

Course Material: This course is a study of differential equations. The majority of the course will be dedicated to ordinary differential equations (ODEs), and we will discuss both the classification of such differential equations and various different methods to solve them, as well as the many types of real-world problems that differential equations help model. Finally, we will discuss Fourier series as well as the classification and solution of certain partial differential equations (PDEs).  A rough schedule of the topics covered can be found at the end.

Course Objective: Upon completion of the course, the student should be able to classify and solve the types of ordinary differential equations covered in this course, be able to write and solve a differential equation for an applied problem, and be able to interpret the meaning of the solution for an applied problem.

Course Outcomes: Upon successful completion of the course, the student will be able to do the following:
  1. Solve first order differential equations.
  2. Solve ordinary differential equations using the methods of undetermined coefficients (annihilators) and the method of variation of parameters.
  3. Develop a system of linear differential equations to model a physical process.
  4. Find the Laplace transform of functions and use the Laplace transform to solve differential and integral equations.
  5. Find power series solutions of second order ordinary differential equations.
  6. Find the Fourier series of functions.
  7. Solve PDEs and boundary (initial) value problems using separation of variables.

Grading: Your final grade will be based on homework, quizzes, three exams during the semester, and the final exam.  Your final course score will be the maximum of the following two grading schemes:

Letter Grade Cutoffs:  A: 90%, B: 80%, C: 70%, D: 60%, F: below 60%

Homework: Homework will be completed online with MyOpenMath.com.  When you sign-up, you will use the Course ID and Enrollment Key given in class.  Homework assignments will be due at the beginning of class on most Fridays.  Note that most problems on the homework assignments may be resubmitted as often as needed until they are correct, so you should strive for a homework percentage near 100%!
A note about the homework: the only real point of the homework is for you to do it. The time you spend thinking, trying things, getting wrong answers, and (hopefully) getting right answers is the purpose of the homework.  The exams are where your course grade will really be decided, and the homework is your training for the exams.  Don't skip your training!

Quizzes: There will be a quiz given most weeks in which there is no exam.  This will be a very brief quiz given at the beginning of class, intended to test you with more immediacy than the exams and with less consequence.  The problems that appear on the quiz will be taken from the homework problems I assign.  Only your best 5 quizzes will count toward your grade, and there will be absolutely NO make-up quizzes.

Exams: There will be three exams, tentatively scheduled for Wednesday, September 9; Wednesday, October 7; and Wednesday, November 11. These will be 50 minute exams taken during the regular lecture time. The final exam time has been set by the university, and will be Wednesday, December 9 from 10:00-11:50.  Make-up exams will only be given to students with excused absences, and such make-up exams must be scheduled within 24 hours of the missed exam.

Getting Help: Always remember: asking for help when you need it is not a sign of weakness, but a sign of strength! Please feel free to attend my office hours or email me if you have questions about the course material.  If you are unable to make it to my regularly scheduled office hours, I am willing to make an appointment to meet at another time if possible.  Free tutoring is also available through the Student Success Center, located in the library on the second floor of LRC and online at https://studentsuccesscenter.wvutech.edu/tutoring. You should also find out if you qualify for TRIO SSS, located in Benedum 100 and online at https://triosss.wvutech.edu, which also provides tutoring services.  Additionally, for quick math questions, you can feel free to stop by the Math Department in LRC 323 and ask any math professor with an open door.  Finally, I would also encourage the formation of study groups, to learn from each other and help each other learn.

Class Policies:

Institutional Policies: Students are responsible for reviewing policies on inclusivity, academic integrity, incompletes, sale of course materials, sexual misconduct, adverse weather, student evaluation of instruction, and other statements. For these detailed policies of West Virginia University, please review: https://facultysenate.wvu.edu/resources/syllabus-policies-and-statements

Approximate Schedule of Topics:

Date Topic
18-Aug Syllabus, 1.2: Intro to Diff Eqs
19-Aug 1.2: Intro to Diff Eqs
21-Aug 2.2: Separable Equations
24-Aug 2.1: Linear First Order Equations
25-Aug 2.5: Exact Equations 
26-Aug 2.6: Integrating Factors
28-Aug 2.4: Bernoulli and Homogeneous Equations
31-Aug 4.1: Growth and Decay
1-Sep 4.2: Cooling and Mixing
2-Sep 4.2: Cooling and Mixing
4-Sep Catch-Up
8-Sep Review
9-Sep Exam 1
11-Sep 5.1: Homogeneous Linear Equations
14-Sep 5.2: SOLHECCs
15-Sep 5.2: SOLHECCs
16-Sep 5.3: Nonhomogeneous Linear Equations
18-Sep 5.4/5.5: Method of Undetermined Coefficients
21-Sep 5.4/5.5: Method of Undetermined Coefficients
22-Sep 5.6: Reduction of Order
23-Sep 5.7: Variation of Parameters
25-Sep Cauchy-Euler Equations
28-Sep 6.1: Spring Break
29-Sep 6.1: Spring Break
30-Sep 6.2: Spring Break
2-Oct 6.3: RLC Circuits
5-Oct Catch-Up
6-Oct Review
7-Oct Exam 2
12-Oct 7.2: Review of Power Series 
13-Oct 7.2: Review of Power Series 
14-Oct 7.3/7.4: Solutions about Ordinary Points
16-Oct 7.3/7.4: Solutions about Ordinary Points
19-Oct 7.5-7.7: Solutions about Singular Points
20-Oct 7.5-7.7: Solutions about Singular Points
21-Oct 8.1: Laplace Transform
23-Oct 8.2: Inverse Laplace Transform
26-Oct 8.3: Laplace Transform of IVP
27-Oct 8.4: Unit Step Function
28-Oct 8.5: Piecewise Continuous Forcing Functions
30-Oct 8.5: Piecewise Continuous Forcing Functions
2-Nov 8.6: Convolution
4-Nov 10.1/10.2: Systems of Differential Equations
6-Nov Catch-Up
9-Nov Catch-Up
10-Nov Review
11-Nov Exam 3
13-Nov 11.1: BVPs and Orthogonality of Trig Functions
16-Nov 11.2/11.3: Fourier Series
17-Nov 11.2/11.3: Fourier Series
18-Nov 12.1: The Heat Equation
20-Nov 12.1: The Heat Equation
30-Nov 12.2: The Wave Equation
1-Dec 12.3: Laplace's Equation
2-Dec Review
4-Dec Review