MATH 2420 – Differential Equations

For course specific time and place see opening page of web site

INSTRUCTOR: Clarence A. McGuff,  Professor of Mathematics

Office:  NRG 2150 (inside 2149)

Phone:  512-223-4786  


web page:

Office Hours:  See opening page of web site

Others by appointment. These may be made in person at class time, for that day, or by phone or e-mail for later days.


MATH 2420 DIFFERENTIAL EQUATIONS (4-4-0). A course in the standard types and solutions of linear and nonlinear ordinary differential equations, include Laplace transform techniques. Series methods (power or Fourier) will be applied to ordinary and partial linear differential equations. Systems of linear

differential equations will be studied. Prerequisites: MATH 2414 or its equivalent. (MTH 2164)

PREREQUISITES:  MATH 2414 with a C or better or its equivalent.

COMMON OBJECTIVES FOR MATH 2420 - Differential Equations

 The objectives of Differential Equations are for the students to understand the following topics and to be able to apply these concepts to solve application problems.

Differential Equations covers the following topics.

1.First order differential equations, slope fields, numerical solution methods and the basic analytical solution methods: separation of variables, solving exact equations, solving linear equations, and substitution methods.

2.Higher order linear differential equations, both homogeneous and nonhomogeneous with methods of reduction of order, undetermined coefficients, and variation of parameters.

3.Systems of linear differential equations, phase portraits, numerical solution methods and analytical solution methods: using eigenvalues and eigenvectors and using systematic elimination.

4.Use of the LaPlace transform and series methods for solving differential equations. Other topics will be explored as time permits.

 These can also be found at:


The required textbook for this course is:

Text: Elementary Differential Equations and Boundary Value Problems by Boyce & DiPrima, Eighth Edition, John Wiley & Sons, Inc. Publishing.

There is a CD included which contains:  ODE Architect software, ODE Architect Companion, Study and Review materials


The use of calculators or computers in order to perform routine computations is encouraged in order to give students more time on abstract concepts.  The software ODE Architect is available for student use. It is recommend that instructors include computer projects and/or assignments as part of the course curriculum.  The ODE Architect software is available during and outside class.


This course is taught in the classroom primarily as a lecture/discussion course.

The class will also have a computer lab component.


This is a traditional introductory course in the standard types and solutions of linear and nonlinear ordinary differential equations and systems of linear differential equations usually taken by mathematics, engineering and computer science students.


Grades in this course will be based on the following numeric averages:

  Below 60% “F” ,   60% up to 70% “D”  ,   70% up to 80% “C” ,  

80% up to 90% “B”, above 90% “A”

There will be 4 tests, each worth approximately 100 points. A quiz/HW (see below) grade of 100 points andapproximately 10 lab grades also worth a total of 100 pts. This means that the grade in this class will be based on 600 points.  Tests may be given in class or the testing center at the instructor’s desecration.  A test taken after the announced deadline is late (see below).

Homework will be collected but not be graded. This is to assure that HW is attempted. 

Corrections: For each test taken on time, except for the last test of the semester, corrections may be done for up to 5 bonus points. Corrections must be completed before the next test or they will not be accepted. 

Late tests: A test taken late will have the grade reduced by 10 points. No test, late or otherwise, may be taken after the original test is returned to the class.  After that the test has been missed, see below.

Retake/makeup: I no longer give a retake/makeup on each test. You will still be allowed to makeup or replace one grade (of test 1, 2, or 3) only by taking a special comprehensive tests that will be given.  The maximum score on this makeup will be in the mid 80’s.  The time and place will be announced after test 3 and before the last week of school.  If you miss one test then you must use this test as a makeup otherwise you may use this tests to replace one test grade from material covered by that test.  If you miss two tests you will receive a non-removable zero on the second test.

Lab requirements will be handed out on the first lab day along with the lab problems. 

Student participation in class  and lab activities is expected.  This includes but is not limited to questions and/or comments during lecture, problem solving and/or correction methods both in class and labs.  Please, however, keep in class talk between two class members on subject and not disruptive of the rest of the class. 

Grades will not be discussed on the phone or via e-mail.  The only exception to this will be for the final grade. I will send this grade via e-mail if certain requirements are met.

These requirements will be spelled out for you to sign and hand in with the final exam.   

Incomplete Grade Policy

Incomplete grades (I) will be given only in very rare circumstances.  Generally, to receive a grade of "I", a student must have taken all examinations, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion.                      

 Attendance/ Withdrawal Policy (withdrawal deadline is see opening page)

Attendance is required in this course.  Students who miss more than 4 classes may be withdrawn

It is the student's responsibility to initiate all withdrawals in this course.  The instructor may withdraw students for excessive absences (4) but makes no commitment to do this for the student. After the withdrawal date, neither the student nor the instructor may initiate a withdrawal.  I will only reinstate a student if I withdrew him in error and he is up to date course wise at the appropriate date.

MATH 2420



16-Week Semester












2; except 2.9



2 & 8.3;  TEST












9.1 – 9.5



9.1 – 9.5; TEST





















Review and Final Test


  Please note: schedule changes may and probably will, occur during the semester. Any changes will be announced in class.


ACC Testing Center policies can be found at:    

When a test is given in the testing center a deadline will be given and if a test is not taken by that deadline it will be considered as a missed test, see grading policy above.


The web address for student services is:

The ACC student handbook can be found at:




The web address is:

then click on “Campus Based Student Support Overview”.

Course-Specific Support Services

Sometimes sections of MATH 0197(1-0-2) are offered. The lab is designed for students currently registered in Differential Equations, MATH 2420. It offers individualized and group setting to provide additional practice and explanation. This course is not for college-level credit. Repeatable up to two credit hours.

Students should check the course schedule for possible offerings of the lab class.

ACC main campuses have Learning Labs which offer free first-come first-serve tutoring in mathematics courses. The locations, contact information and hours of availability of the Learning Labs are posted at:

Statement on Scholastic Dishonesty

"Acts prohibited by the college for which discipline may be administered include scholastic dishonesty, including but not limited to, cheating on an exam or quiz, plagiarizing, and unauthorized collaboration with another in preparing outside work.  Academic work submitted by students shall be the result of their thought, work, research or self-expression.  Academic work is defined as, but not limited to, tests, quizzes, whether taken electronically or on paper; projects, either individual or group; classroom presentations; and homework.”

Students who violate the rules concerning scholastic dishonesty will be assessed an academic penalty which the instructor determines is in keeping with the seriousness of the offense. This academic penalty may range from a grade penalty on the particular assignment to an overall grade penalty in the course, including possibly an F in the course. ACC's policy can be found in the Student Handbook page 33 or on the web at: 

Recommended Statement on Student Discipline

Classroom behavior should support and enhance learning. Behavior that disrupts the learning process will be dealt with appropriately, which may include having the student leave class for the rest of that day. In serious cases, disruptive behavior may lead to a student being withdrawn from the class. ACC's policy on student discipline can be found in the Student Handbook page 32 or on the web at:

Statement on Students with Disabilities

"Each ACC campus offers support services for students with documented physical or psychological disabilities.  Students with disabilities must request reasonable accommodations through the Office of Students with Disabilities on the campus where they expect to take the majority of their classes.  Students are encouraged to do this three weeks before the start of the semester.”

 Students who are requesting accommodation must provide the instructor with a letter of accommodation from the Office of Students with Disabilities (OSD) at the beginning of the semester.   Accommodations can only be made after the instructor receives the letter of accommodation from OSD.”

Statement on Academic Freedom

"Institutions of higher education are conducted for the common good.  The common good depends upon a search for truth and upon free expression.  In this course the professor and students shall strive to protect free inquiry and the open exchange of facts, ideas, and opinions.  Students are free to take exception to views offered in this course and to reserve judgment about debatable issues. Grades will not be affected by personal views.  With this freedom comes the responsibility of civility and a respect for a diversity of ideas and opinions.  This means that students must take turns speaking, listen to others speak without interruption, and refrain from name-calling or other personal attacks."