Differential Equations

Math 2420: Differential Equations

Go here for the Mathematica computer labs.

Fall 2018

SySynonym: 62618, Section: 002, Northridge 2245
Monday / Wednesday 7:35 pm - 9:20 pm

Course Content:

Course Description: 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 and/or Fourier) will be applied to appropriate differential equations. Systems of linear differential equations will be studied. Skills: S  Course Type: T

Instructional Methodology: This course is taught in the classroom primarily as a lecture/discussion course. The class will also have a computer lab component.

Course Rationale: 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. 


Please make sure you have the necessary prerequisites for this course. That means you need a C or better in Calculus II (or an equivalent course) or an acceptable grade on placement tests. If I feel you are not prepared for this course, I may choose to withdraw you. If you have any questions about your preparation for the course, please come and talk to me about it.

Course Materials:

Text: Differential Equations and Boundary Value Problems: Computing and Modeling, 5th edition, Edwards & Penney & Calvis,Pearson (ISBN # 9780321796981)

Technology:  The use of calculators or computers in order to perform routine computations is encouraged in order to give students more time on abstract concepts.  Mathematica software is available for student use.  You will be required to use Mathematica software for the course; you may choose to purchase this (there is a “student edition” and various time-limited versions available at a reduced price), but you are not required to do so.  This software is available in the classrooms and in the Learning Labs.


You should bring your homework to class every day.  It will be collected regularly.  There may also be in-class assignments or quizzes collected for a grade. There will be a penalty on late homework. Homework that is more than a week late might not receive any credit.  If you do not follow the instructions that will be announced in class about how to organize and submit your homework, you may not receive full (or any) credit for it.


Attendance is required in this course.  It is extremely important for you to attend class regularly.  I MAY drop you from the course for excessive absences, although I make no commitment to do so.


There will be 3 exams plus a final exam (part of which will be comprehensive).  In addition, you will be assigned several computer labs which will count for a substantial grade.  Grades will be weighted as follows:


Tests 1, 2, 3




Computer labs and assignments, quizzes



Final Exam






Sometime after Test 3, there will be a single make-up exam over the material on tests 1-3; the grade on this exam can be used to replace your lowest grade on the first three tests, up to a maximum grade of 90 if you make complete corrections for tests 1-3 or 75 without the completed corrections.
If you take any test late for any reason, there will be a penalty of 10 points off your test grade. However, no late tests will be allowed after I hand the graded tests back in class.  If you miss a test, you must try to take it during this “late” period.  If you do not take the test during that period, you will receive a 0 for that grade.  In that case, you will need to take the make-up exam to replace that 0. 
Grades will be assigned as follows:

A :

90% or better and a grade of at least 80% on the final

D :

60% - 69%

B :

80% - 89% and a grade of at least 70% on the final

F :

below 60%

C :

70% - 79% and a grade of at least 60% on the final


W :

Withdrawn by student or instructor prior to last withdrawal date on school calendar

I :

Incomplete grades (I) will be given only in very rare circumstances. Generally, to receive a grade of "I", a student must have taken all tests, be passing, and after the last date to withdraw, have a personal tragedy occur which prevents course completion. An incomplete grade cannot be carried beyond the established date in the following semester. The completion date is determined by the instructor but may not be later than the final deadline for withdrawal in the subsequent semester.


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 last day to withdraw, neither the student nor the instructor may initiate a withdrawal. It is the responsibility of each student to ensure that his or her name is removed from the roll should he or she decide to withdraw from the class.  The instructor does, however, reserve the right to drop a student should he or she feel it is necessary. The student is also strongly encouraged to retain a copy of the withdrawal form for their records.
Students who enroll for the third or subsequent time in a course taken since Fall, 2002, may be charged a higher tuition rate, for that course. State law permits students to withdraw from no more than six courses during their entire undergraduate career at Texas public colleges or universities.  With certain exceptions, all course withdrawals automatically count towards this limit.  Details regarding this policy can be found in the ACC college catalog.
The withdrawal deadline for Fall 2018 is November 26, 2018.

Classroom behavior:

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 on the web at: http://www.austincc.edu/handbook

Class participation:

All students are expected to actively participate in this class. This can include asking relevant questions in class, participating in class discussions and other in-class activities, helping other students, coming to office hours with questions, and doing other things that contribute to the class.

Keeping up:

Please, try to keep up with the homework and with the lecture in class. There just isn't much time to catch up. This means you have to be sure to allow yourself plenty of time to do the homework and to study.

Ask questions:

Please, please, please, if you don't understand something, or you aren't clear about something, or if you think I (or the book) have made a mistake (it has been known to happen), or if you have any other questions, please ask. Don't let confusion accumulate. If you don't want to ask in class, come to our office hours (or call) and ask. It is much easier to ask a question now than to miss it on the test.  I expect all students to participate in class discussions and other activities. Trust me, you will get much more out of the class if you become actively involved in it.

Always show your work:

It is much more important that you understand the processes involved in solving problems than that you just give me the right answer. If I see from your work that you understand what you are doing, I will usually give partial credit for a problem, even if you made a mistake somewhere along the line. If you don't show your work (unless I believe you could reasonably do it in your head), I may not give you full credit, even if the answer is right. If you can really do something in your head, that's great, but when in doubt, write it down.  It is also very important that you write what you mean. I will correct your notation the first few times, but I will start counting it wrong if you continue to write things incorrectly. In addition, please write clearly and legibly. If I can't read it, I won't grade it.

Time required and outside help:

To do homework and study requires two or three times as much time outside of class as the time you spend in class in order to succeed in this course. If you need more out-of-class help than you can obtain in your instructor's office hours, free tutoring is available in any of ACC's Learning Labs.
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: http://www.austincc.edu/tutor


Differential Equations, MATH 2420, Learning Outcomes
STUDENT LEARNING OUTCOMES - A student who has taken this course should be able to:

  1. Identify and classify homogeneous and nonhomogeneous equations/systems, autonomous equations/systems, and linear and nonlinear equations/systems.
  2. Solve first order differential equations using standard methods, such as separation of variables, integrating factors, exact equations, and substitution methods; use these methods to solve analyze real-world problems in fields such as economics, engineering, and the sciences.
  3. Solve second and higher order equations using reduction of order, undetermined coefficients, and variation of parameters; use these methods to solve analyze real-world problems in fields such as economics, engineering, and the sciences.
  4. Solve systems of equations and use eigenvalues and eigenvectors to analyze the behavior and phase portrait of the system; use these methods to solve analyze real-world problems in fields such as economics, engineering, and the sciences.
  5. Use LaPlace transforms to solve initial value problems.
  6. Solve boundary value problems and relate the solution to the Fourier series; use these methods to solve analyze real-world problems in fields such as economics, engineering, and the sciences.

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.

ACC College Policies

Statement on Scholastic Dishonesty - A student attending ACC assumes responsibility for conduct compatible with the mission of the college as an educational institution.  Students have the responsibility to submit coursework that is the result of their own thought, research, or self-expression.  Students must follow all instructions given by faculty or designated college representatives when taking examinations, placement assessments, tests, quizzes, and evaluations.  Actions constituting scholastic dishonesty include, but are not limited to, plagiarism, cheating, fabrication, collusion, and falsifying documents.    Penalties for scholastic dishonesty will depend upon the nature of the violation and may range from lowering a grade on one assignment to an “F” in the course and/or expulsion from the college.  See the Student Standards of Conduct and Disciplinary Process and other policies at http://www.austincc.edu/current/needtoknow

Student Rights and Responsibilities - Students at the college have the rights accorded by the U.S. Constitution to freedom of speech, peaceful assembly, petition, and association. These rights carry with them the responsibility to accord the same rights to others in the college community and not to interfere with or disrupt the educational process. Opportunity for students to examine and question pertinent data and assumptions of a given discipline, guided by the evidence of scholarly research, is appropriate in a learning environment. This concept is accompanied by an equally demanding concept of responsibility on the part of the student. As willing partners in learning, students must comply with college rules and procedures.

Statement on Students with Disabilities - Each ACC campus offers support services for students with documented disabilities. Students with disabilities who need classroom, academic or other accommodations must request them through Student Accessibility Services (SAS, formerly OSD).  Students are encouraged to request accommodations when they register for courses or at least three weeks before the start of the semester, otherwise the provision of accommodations may be delayed.

Students who have received approval for accommodations from SAS for this course must provide the instructor with the ‘Notice of Approved Accommodations’ from SAS before accommodations will be provided.  Arrangements for academic accommodations can only be made after the instructor receives the ‘Notice of Approved Accommodations’ from the student.

Students with approved accommodations are encouraged to submit the ‘Notice of Approved Accommodations’ to the instructor at the beginning of the semester because a reasonable amount of time may be needed to prepare and arrange for the accommodations.  Additional information about Student Accessibility Services is available at  HYPERLINK "http://www.austincc.edu/support/osd/" http://www.austincc.edu/support/osd/

Safety Statement - Austin Community College is committed to providing a safe and healthy environment for study and work. You are expected to learn and comply with ACC environmental, health and safety procedures and agree to follow ACC safety policies. Additional information on these can be found at http://www.austincc.edu/ehs. Because some health and safety circumstances are beyond our control, we ask that you become familiar with the Emergency Procedures poster and Campus Safety Plan map in each classroom. Additional information about emergency procedures and how to sign up for ACC Emergency Alerts to be notified in the event of a serious emergency can be found at http://www.austincc.edu/emergency/.

Please note, you are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be dismissed from the day’s activity, may be withdrawn from the class, and/or barred from attending future activities.

You are expected to conduct yourself professionally with respect and courtesy to all. Anyone who thoughtlessly or intentionally jeopardizes the health or safety of another individual will be immediately dismissed from the day’s activity, may be withdrawn from the class, and/or barred from attending future activities.

Use of ACC email - All College e-mail communication to students will be sent solely to the student’s ACCmail account, with the expectation that such communications will be read in a timely fashion. ACC will send important information and will notify you of any college related emergencies using this account.  Students should only expect to receive email communication from their instructor using this account.  Likewise, students should use their ACCmail account when communicating with instructors and staff.  Instructions for activating an ACCmail account can be found at http://www.austincc.edu/accmail/index.php.

Testing Center Policy - Under certain circumstances, an instructor may have students take an examination in a testing center.  Students using the Academic Testing Center must govern themselves according to the Student Guide for Use of ACC Testing Centers and should read the entire guide before going to take the exam.  To request an exam, one must have:

·    ACC Photo ID
·    Course Abbreviation (e.g., ENGL)
·    Course Number (e.g.,1301)
·    Course Synonym (e.g., 10123)
·    Course Section (e.g., 005)
·    Instructor's Name

Do NOT bring cell phones to the Testing Center.  Having your cell phone in the testing room, regardless of whether it is on or off, will revoke your testing privileges for the remainder of the semester.  ACC Testing Center policies can be found at http://www.austincc.edu/testctr/

Student And Instructional Services - ACC strives to provide exemplary support to its students and offers a broad variety of opportunities and services.  Information on these services and support systems is available at:   http://www.austincc.edu/s4/ Links to many student services and other information can be found at: http://www.austincc.edu/current/ For help setting up your ACCeID, ACC Gmail, or ACC Blackboard, see a Learning Lab Technician at any ACC Learning Lab.

Concealed Handgun Policy - The Austin Community College District concealed handgun policy ensures compliance with Section 411.2031 of the Texas Government Code (also known as the Campus Carry Law), while maintaining ACC’s commitment to provide a safe environment for its students, faculty, staff, and visitors. Beginning August 1, 2017, individuals who are licensed to carry (LTC) may do so on campus premises except in locations and at activities prohibited by state or federal law, or the college’s concealed handgun policy. It is the responsibility of license holders to conceal their handguns at all times. Persons who see a handgun on campus are asked to contact the ACC Police Department by dialing 222 from a campus phone or 512-223-7999.Refer to the concealed handgun policy online at austincc.edu/campuscarry.

Student Support Services - Resources to support you are available at every campus.  Food pantries are available at all campus Student Life offices (https://sites.austincc.edu/sl/programs/foodpantry/).  Assistance paying for childcare or utility bills is available at any campus Support Center (http://www.austincc.edu/students/support-center).  For sudden, unexpected expenses that may cause you to withdraw from one or more of your courses, go to http://www.austincc.edu/SEF to request emergency assistance through the Student Emergency Fund.  Help with budgeting for college and family life is available through the Student Money Management Office (http://sites.austincc.edu/money/).  Counselors are available at any campus if you experience a personal or mental health concern (http://www.austincc.edu/students/counseling).  All services are free and confidential.


Course Outline and Approximate Calendar:
Please note:  schedule changes may occur during the semester.
Any changes will be announced in class.







1.1 - 1.2

Mathematical models, integrals as solutions



1.3 - 1.4

Slope fields, and separation of variables



Holiday - no class



1.5 - 1.6

Linear first order equations and substitution methods



1.6, 2.1

More substitution methods, exact equations, and population models



2.2 - 2.3

Equilibrium solutions and acceleration/velocity models



2.4 - 2.5

Numerical approximation methods




More numerical methods and review for Test 1

Test 1 – Dates to be announced in class




Intro to systems of equations, review of matrices,




The eigenvalue solution method




More on eigenvalue solutions




Phase portraits




Repeated eigenvalues




Non-homogeneous systems




Nonlinear systems




Ecological models and review for Test 2

Test 2 – Dates to be announced in class




Higher order linear equations, solving homogeneous equations with constant coefficients




 Non-homogeneous equations with undetermined coefficients



3.4, 3.7

Mechanical applications and electrical circuits



3.7, 3.8

More electrical circuits, reduction of order and basic boundary value problems with eigenvalues



7.1 – 7.2

Laplace transforms and initial value problems



7.3 - 7.4

Translations, derivatives, integrals, and products of transforms




Periodic and piecewise continuous functions and transforms




Impulse and delta functions and review for Test 3

Test 3 – Dates to be announced in class



8.1 - 8.2

Series and series solutions near ordinary points




Cauchy-Euler equations and series solutions near regular singular points



9.1 – 9.2

Fourier series and convergence




Even and odd extensions and Fourier Sine and Cosine series




Applications of Fourier series




Separation of variables and the heat equations



Final Exam, Part 1



Final Exam, Part 2


This webpage was created by Marcus McGuff.
It was last updated on August 26, 2018 .