Virginia Tech Math Course

Math 2214: Introduction to Differential Equations

Index 85477
MWF 12:20-1:10, WLH 330

Course Web Site:
The course web site has information on homework assignments, software and other resources for Math 2214.

There will be no class on Friday, December 8.

Solutions to homework problems:
Will be made available on Canvas after homework is due.

Solutions to tests:
Test 1. Test 2.

Sample tests:

  • First midterm
  • Second midterm
  • Final exam

    Instructor: Michael Renardy (
    Office: McBryde 406 (Phone: 1-8001)
    Office Hours: 3-4 pm MWF.

    Course Content:
    First order ordinary differential equations, second order linear equations, linear systems of ordinary differential equations, numerical methods (most of Chapters 1-4 and 6). The material in the text will be supplemented with the use of Matlab to facilitate numerical and graphical solutions to complement the analytical techniques.

    Elementary Differential Equations, by W. Kohler and L. Johnson, Addison Wesley, 2nd ed. 2006.

    Math 2114 or 1114 and Math 1226 or 1206.

    Final Exam Schedule:
    Friday, December 15, 7:00 pm - 9:00 pm. The first half of this is the common time final and the second half is your instructor's part of the final exam. Please note that common time finals are usually not in the same room as your class. For room assignments click here. The final exam for this section of the course is in Surge 109. Double time students should report to WLH 350 at 5 pm.

    It is the firmly held position of Virginia Tech that our final exam schedule, as announced in the timetable, takes precedence over all discretionary activities. For this purpose, a decision by a full time Virginia Tech student to take a course under a dual enrollment arrangement with another institution is considered discretionary.

    Dates of midterm exams:
    September 27. November 3.

    Educational Objectives:
    Differential equations are at the core of the mathematical description of natural phenomena and are one of the principal applications of the calculus. The course introduces important classes of differential equations and techniques for solving them. Familiarity with these techniques is basic for studying any discipline of science or engineering.

    Homework and Grade:
    Grades are determined as follows:

  • Two midterms: 20% each
  • Final exam: 20% (half of this is the common part)
  • Online quizzes: 20% (see below for specifics)
  • Homework: 20% (see below for specifics)

    The final grade is determined by averaging the five partial grades. For instance, if you have a B on both midterms, an A on the final, a D on the homework, and a C on the quizzes, your grade is computed as (3+3+4+1+2)/5=2.6, which is a B-. However, if three or more of the partial grades are F, your final grade will be F regardless of what the remaining grades are. Your instructor reserves the right to deviate from straight averaging (in either direction) in cases where the distribution of grades is very unusual. Scores on homework, quizzes and midterms will be posted on Canvas.

    Attendance records are taken only to satisfy a departmental requirement to keep such records. Attendance has no impact on grades.

    The final exam consists of two parts. The common time final is multiple choice. The second part is specifically for this section of the course and resembles the midterm exams. Please note that common time finals are usually not in the same room as your class. Rooms will be announced near the end of the semester.

    All in-class exams are closed book. Calculators are permitted on mid-term exams and my part of the final as long as they are used for numerical calculations only and have no capabilities of symbolic manipulation or electronic communication. No calculators are permitted on the common part of the final exam. The quizzes and the common part of the final exam are multiple choice questions. The midterms and my part of the final exam are problems in the style of the homework. Students who miss exams for valid reasons are expected to take a makeup exam as soon as possible. There are no makeups for quizzes, unless you are prevented from taking a quiz by a technical problem. Since students will have a full week to do a quiz, only unforeseen contingencies, such as illness, will be accepted as an excuse for missing a quiz. If you miss a quiz and have a valid excuse, you will be graded on the remaining quizzes rather than making it up. The same applies to homework.

    Valid reasons for missing a test include illness, pregnancy, family deaths or celebrations, active participation in scholarly or athletic events, court dates, incarceration, etc., but do not include sleeping, getting drunk, recreational activities or other tests during the same day.

    Online quizzes:

    There will be one quiz each week starting on Thursday, September 14. Each quiz will start on a Thursday and end on Wednesday. Each quiz will have ten questions from the database which is available in the practice quizzes. The questions are chosen randomly, so different students will have different questions.


  • Online practice quizzes (if you are using a pop-up blocker, you may need to turn it off)
  • Graded quizzes: Some instructors will use the practice quizzes as a database for graded quizzes, which will be unproctored and can be taken anywhere. You must start a graded quiz by 11 pm on the day of the deadline.
  • List of practice quizzes: a table listing how practice quizzes correspond to sections in the text.
  • WHAT NOT TO DO: a list of rules to follow to avoid technical problems when taking a graded quiz.

    You log in to the practice quiz system with your Virginia Tech PID and Password, and log off when you are finished practicing. This server has no connection to the testing server, which means that you will not risk losing any graded work if you forget to quit your browser. It also means that these practice problems will not be available when you view past tests. If you want to review your practice quiz problems later, you can mark up to 30 individual problems using the link below each graded practice problem. There is a link to your list of marked problems available anytime you are in the practice problem system.

    The following is a list of quizzes and their deadlines. All quizzes are cumulative. The practice quizzes covered in each quiz will be added as the date of the quiz approaches:

  • Quiz 1: 9/20, covers Practice Quizzes 1-8.
  • Quiz 2: 9/27, covers Practice Quizzes 1-10
  • Quiz 3: 10/4, covers Practice Quizzes 1-12
  • Quiz 4: 10/11, covers Practice Quizzes 1-14
  • Quiz 5: 10/18, covers Practice Quizzes 1-16
  • Quiz 6: 10/25, covers Practice Quizzes 1-17
  • Quiz 7: 11/1, covers Practice Quizzes 1-20
  • Quiz 8: 11/8, covers Practice Quizzes 1-21
  • Quiz 9: 11/15, covers Practice Quizzes 1-22
  • Quiz 10: 11/29, covers Practice Quizzes 1-24
  • Quiz 11: 12/6, covers Practice Quizzes 1-26
  • Quiz 12: 12/13, covers Practice Quizzes 1-27

    Homework policy:
    Only selected problems will be graded. These problems will not be known to students in advance. For graded problems, a maximum of five points per problem will be awarded. Except for problems selected for grading, homework will not be marked. It is the students' responsibility to check the correctness of their homework by comparing with the solutions posted. Students should not expect credit for correct answers if no work is shown. Your instructor is smart enough to know that the answers are in the back of the book!

    All homework must be handed in at the beginning of the class period when it is due. If you come in late, hand homework in immediately when you come in.

    Note: Graphical parts of homework (plotting solution curves, direction fields etc.) should be done using John Mc Graw's Matlab based software. You can link to the necessary resources through the course web page. Some hints about initial hurdles and common errors are here.

    The following is a list of dates when homework solutions are due. The problems for each section are those from the syllabus posted on the course web site.

  • 1.2 and 1.3: 9/1
  • 2.1: 9/6
  • 2.2: 9/8
  • 2.3: 9/11
  • 2.4 and 2.5: 9/13
  • 2.6: 9/15
  • 2.9: 9/20
  • 2.10: 9/22
  • 3.1 and 3.2: 9/25
  • 3.3: 9/29
  • 3.4: 10/2
  • 3.5: 10/4
  • 3.6: 10/6
  • 3.7: 10/9
  • 3.8: 10/16
  • 3.9: 10/18
  • 3.10: 10/23
  • 3.11: 10/25
  • 3.12: 10/27
  • 4.1 through 4.5: 11/13
  • 4.6: 11/15
  • 4.7: 11/29
  • 4.8: 11/29
  • 4.9: 12/1
  • 4.10: 12/4
  • 6.2: 12/6
  • 6.4: 12/11
  • 6.5: 12/13

    Virginia Tech Honor System Information
    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 exclude any member of the University community from the requirements and expectations of the Honor Code. For additional information about the Honor Code, please visit:

    Honor Code Pledge for Assignments
    The Virginia Tech honor code pledge for assignments is as follows: I have neither given nor received unauthorized assistance on this assignment. The pledge is to be written out on all graded assignments at the university and signed by the student. The honor pledge represents both an expression of the students support of the honor code and an unambiguous acknowledgment that the student has, on the assignment in question, abided by the obligation that the Honor Code entails. In the absence of a written honor pledge, the Honor Code still applies to an assignment.

    Please check your schedule which comes out after the last add date. If you are not registered for this course or if you are registered incorrectly, please find a wizard who will fix the problem. Your instructor is not a wizard. Students who are not registered cannot receive a grade. Students who are registered for credit and do not turn in any work will receive NG grades (which count as Fs), even if they did not intend to be registered for credit. If you are registered for a different section of this course, you are expected to attend that section.

    If you need adaptations or accommodations because of a disability (learning disability, attention deficit disorder, psychological, physical, etc.), if you have emergency medical information to share with me, or if you need special arrangements in case the building must be evacuated, please make an appointment with me as soon as possible. My office location and hours are as above.

    Mathematics Department
    Virginia Polytechnic Institute & State University