Course Syllabus

Department of Mathematics and Computer Science, Lincoln University

COURSE NAME: Differential Equations


      Simmons, George. Differential Equations with Applications and Historical Notes Second Edition.


***To be provided for each section***


      Topics include solution methods and applications of first order differential equations, solution of higher order differential equations using the characteristic equation, the undetermined coefficients and variation of parameters methods, existence and uniqueness theorems for initial value problems, Laplace transforms, systems of linear differential equations.

PREREQUISITE:         MAT-221 (Calculus III)


    On completion of this course, the student should be able to:
  • Recognize and solve ordinary differential problems using the techniques of:
    • Direct integration
    • Separating the variables
    • Identifying homogeneous, exact, linear equations
    • Reduction of order
    • Homogeneous equations with constant coefficients
    • Methods of undetermined coefficients and variation of parameters
    • Operator methods for finding particular solutions
    • Laplace transforms methods
  • Be able to use these techniques to solve application problems in biology, business, chemistry, physics and engineering, e.g. growth, decay, chemical reactions, mixing, falling bodies and other motion problems.


Week 1-3
Chapter 1: The Nature of Differential Equations, Separable Equations.
Section 1: Introduction.
Section 2: General Remarks on Solutions.
Section 3: Families of Curves, Orthogonal Trajectories.
Section 4: Growth, Decays, Chemical Reactions, and Mixing.
Section 5: Falling Bodies and Other Motion Problems.

Week 4-7
Chapter 2: First Order Equations.
Section 7: Homogeneous Equations.
Section 8: Exact Equations.
Section 9: Integrating Factors.
Section 10: Linear Equations.
Section 11: Reduction of Orders.
Sections 12 and 13 are optionals

WEEK 8-12
Chapter 3: Second Order Linear Equations.
Section 14: Introduction.
Section 15: The General Solution of the Homogeneous Equation.
Section 16: The Use of a Known Solution to Find Another.
Section 17 The Homogeneous Eqution with Constant Coefficients.
Section18: The Method of Undetermined Coefficients.
Section 19: The Method of Variation of Parameters.
A topic taken from Chapter 20 or 21 (optional)

Week 13-16
Section 22: Higher Order Linear Equations.
Section 23: Operator Methods for Finding Particular Solutions

Chapter 9: Laplace Transform.
Section 48: Introduction.
Section 49: A few remarks on the Theory.
Section 50: Applications to Differential Equatons.
Sections 51 and 52 are optional.


  • Homework

            Daily homework will be given on material covered in class, reviewed the next day, and may be collected and graded on an unannounced basis. On all assignments, all work must be shown for credit.

             Students are encouraged to work cooperatively. The objective of group work is to develop individual skills while learning to work effectively as a team, to think and talk about problem solving and the underlying mathematical concepts, and to develop the ability to ask and answer questions as they arise. However, each student is responsible for all the assigned material, in other words, students can work together, but should not simply copy work from each other. Students are also encouraged to make regular visits during office hours, to meet in study groups, and to use the Math Lab or the Math Tutors from the School of Natural Sciences.

  • Quizzes, Tests and Final Exam

            Short quizzes will be given on an unannounced basis. One hour in- class exams will be announced at least a week in advance. A cumulative two hour Final Exam will be given as scheduled by the Registrar. ALL work must be shown for full credit.

  • Late Work And Make-Ups

    All graded assignments, quizzes and exams must be completed when scheduled. Late assignments or make-up tests or quizzes will only be allowed with official documentation and grades may be lowered. To qualify for a make-up, a student must have notified the professor and rescheduled in a timely manner.


        Participation+ 20%
        Tests 60%
        Final 20%
        (+Includes attendance, homework, classwork, projects, labs, quizzes, etc.)

The grading scale guideline: **
A       92-100%
A-       88-91%
B+      85-87%
B      82-84%
B-      78-81%
C+       75-77%
C       72-74%
C-      68-71%
D+      65-67%
D      58-64%
F      0-57%


1) Attendance:

Lincoln University uses the class method of teaching, which assumes that each student has something to contribute and something to gain by attending class. It further assumes that there is much more instruction absorbed in the classroom than can be tested on examinations. Therefore, students are expected to attend all regularly scheduled class meetings and should exhibit good faith in this regard. For the control of absences, the faculty adopted the following regulations:

  • Four absences may result in an automatic failure in the course.
  • Three tardy arrivals may be counted as one absence.
  • Absences will be counted starting with whatever day is specified by the instructor but not later than the deadline for adding or dropping courses.
  • In case of illness, death in the family, or other extenuating circumstances, the student must present documented evidence of inability to attend classes to the Vice President for Student Affairs and Enrollment Management. However, in such cases the student is responsible for all work missed during those absences.
  • Students representing the University in athletic events or other University sanctioned activities will be excused from class (es) with the responsibility of making up all work and examinations. The Registrar will issue the excused format to the faculty member in charge of the off- or on-campus activity for delivery by the student(s) to their instructors.
2) Statement on Academic Integrity:

Students are responsible for proper conduct and integrity in all of their scholastic work. They must follow a professor's instructions when completing tests, homework, and laboratory reports, and must ask for clarification if the instructions are not clear. In general, students should not give or receive aid when taking exams, or exceed the time limitations specified by the professor. In seeking the truth, in learning to think critically, and in preparing for a life of constructive service, honesty is imperative. Honesty in the classroom and in the preparation of papers is therefore expected of all students. Each student has the responsibility to submit work that is uniquely his or her own. All of this work must be done in accordance with established principles of academic integrity.

An act of academic dishonesty or plagiarism may result in failure for a project or in a course. Plagiarism involves representing another person's ideas or scholarship, including material from the Internet, as your own. Cheating or acts of academic dishonesty include (but are not limited to) fabricating data, tampering with grades, copying, and offering or receiving unauthorized assistance or information.

3) The Student Conduct Code:

Students will be held to the rules and regulations of the Student Conduct Code as described in the Lincoln University Student Handbook. In particular, excessive talking, leaving and reentering class, phones or pagers, or other means of disrupting the class will not be tolerated and students may be asked to leave. Students who constantly disrupt class may be asked to leave permanently and will receive an F.

4) The Core Curriculum Learner Competencies:

All courses offered through the Department of Mathematics and Computer Science require students to meet at least the following out of the 8 Core Curriculum Learner Competencies:

(1) Listen and effectively communicate ideas through written, spoken, and visual means;
(2) Think critically via classifying, analyzing, comparing, contrasting, hypothesizing, synthesizing, extrapolating, and evaluating ideas;

(6) Apply and evaluate quantitative reasoning through the disciplines of mathematics, computational science, laboratory science, selected social sciences and other like-minded approaches that require precision of thought;

(8) Demonstrate positive interpersonal skills by adhering to the principles of freedom, justice, equality, fairness, tolerance, open dialogue and concern for the common good.


* The instructor of a given section of the course may make some modifications to the evaluation as well as to the rest of the syllabi including but not limited to; the grade weights, number of tests, and test total points.

**The grading scale guideline includes a 2-point flexibility.

Please consult with the department chairperson for any program updates or corrections which may not be yet reflected on this page _ last updated 11/25/2007.

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