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Unified course in ordinary differential equations. First-order equations, second-and-higher-order constant coefficient linear equations, systems of first-order (non)linear equations, and numerical methods. Mathematical models describing motion and cooling, SIR-epidemiology models, mechanical vibrations, rates of chemical reactions, radioactive decay and quantitative and computational thinking to address relevant intercultural and global issues. A student can earn credit for at most one of 2214 and 2406H A student can earn credit for at most one of MATH 2214, MATH 2405H and CMDA 2006. 


MATH 2214 requires students to have passed MATH 1114 or MATH 2114 or MATH 2114H or MATH 2405H; and Math 1226. 


Required: Elementary Differential Equations, 2nd Edition by Kohler and Johnson


  • An Introduction to Ordinary Differential Equations by James C. Robinson
  • Elementary Differential Equations with Boundary Value Problems by William F. Trench

Download  the syllabus with suggested problem assignments. (PDF)

Section Topic
1.2 Examples of Differential Equations
1.3 Direction Fields
2.1 Classifying and Solutions of Differential Equations
2.2 First Order Linear Differential Equations
2.3 Inroduction to Mathematical Models
2.4 Population Dynamics and Radioactive Decay
2.5 First Order Nonlinear Differential Equations
2.6 Separable Differential Equations
2.9 Applications to Mechanics 
2.10 Euler's Method
Section Topic
3.1 Classifying and Solutions to Second Order Linear Differential Equations
3.2 General Solutions of Homogeneous Equations
3.3 Constant Coefficient Homogeneous Equations
3.4 Real Repeated Roots: Reduction of Order
3.5 Complex Roots
3.6  Unforced Mechanical Vibrations
3.7 The General Solution of a Linear Nonhomogeneous Equation
3.8 The Method of Undetermined Coefficients
3.9 The Method of Variation of Parameters
3.10 Forced Mechanical Vibrations
3.11 Higher Order Linear Homogeneous Differential Equations
3.12 Higher Order Homogeneous Constant Coefficient Differential Equations
Section Topic
4.1 Introduction to First Order Linear Systems
4.2  Existence & Uniquesness
4.3 Homogeneous Linear Systems
4.4 Constant Coefficient Homogeneous Systems; The Eigenvalue Problem 
4.5 Real Eigenvaluesand the Phase Plane
4.6 Complex Eigenvalues
4.7 Repeated Eigenvalues
4.8 Nonhomogeneous Linear Systems
4.9 Numerical Methods for Systems of Linear Differential Equations
6.2 Equilibrium Solutions and Direction Fields
6.4 Stability
6.5 Linearization and the Local Picture
6.6 Two-Dimensional LInear Systems

The final exam is a Common Time Exam and consists of two parts:

  1. Common Exam
    This test is a multiple choice exam taken by all sections of MATH 2214. Samples of Common Time Final Exams given in previous years are available (koofers).
  2. Free Response Exam 
    Your instructor will give you information on what to expect for the second portion of the exam.


  • Both portions of this exam will be administered in person. The exam is NOT scheduled in your regular classroom. Rooms for the exam will be announced near the end of the semester. 
  • The final exam time is fixed and will not be rescheduled for discretionary reasons, including conflicts with work schedules or exams for classes at other colleges. 
  • If there is a conflict with the final in another class, follow the procedures proposed by your college to reschedule an exam.  Exams of courses that have a common-time final have priority and the exam for the other course should be rescheduled.

Check the timetable or your instructor's Canvas course site for the date and time of your final exam.

See the Timetable of classes for information on current offerings of MATH 2214.

The Undergraduate Honor Code pledge that each member of the university community agrees to abide by states:

“As a Hokie, I will conduct myself with honor and integrity at all times. I will not lie, cheat, or steal, nor will I accept the actions of those who do.”

Students enrolled in this course are responsible for abiding by the Honor Code. A student who has doubts about how the Honor Code applies to any assignment is responsible for obtaining specific guidance from the course instructor before submitting the assignment for evaluation. Ignorance of the rules does not excuse any member of the University community from the requirements and expectations of the Honor Code.

For additional information about the Honor Code, please visit

If you need extra help with course materials:


If you are currently enrolled in MATH 2214, you can contact your instructor through your Canvas course website.

If you have any general questions or concerns about MATH 2214, you can email the course coordinators at