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. 

Prerequisites:

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 we feel you are not prepared for this course, we may choose to withdraw you. If you have any questions about your preparation for the course, please come and talk to one of us about it.

Course Materials:

Text: Differential Equations with Boundary Value Problems: An Introduction to Modern Methods and Applications, Second Edition by James R. Brannan, William E. Boyce.  ISBN  ISBN  9780470595350 © 2011, John Wiley & Sons, Inc. Publishing.
There is a CD included which contains:  ODE Architect software, ODE Architect Companion, Student Solutions Manual, and other materials.  (ODE Architect may or may not work on your computer; it doesn’t work well on current versions of Windows.)
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.

Homework:

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 (as part of your homework/quiz/lab 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.

Grading:

There will be 3 exams worth 100 points each, 100 points from computer labs and homework combined (computer labs are weighted most heavily), plus a comprehensive final worth 150 points during the term. 
If you take any test late for any reason, there will be a penalty of 10 points off your test grade, from the deadline for the test announced in class until the day graded tests are returned to the class. However, no late tests will be allowed after the graded tests are handed back in class, and the final exam may not e taken late without prior approval of the instructor.  There will generally be a 10% penalty for all late computer labs.
If you miss a test, you must try to take it during this “late” period. If you miss this deadline as well, we may consider allowing you to make-up the test or hand in corrections on all tests and replace part of the missed test with your grade on the final, but only in the case of serious illness or emergency. Make-ups of any sort are solely at the discretion of the instructors.  All tests and assignments must be turned in on or before the last class meeting.
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.

Attendance:

Attendance is required in this course.  It is extremely important for you to attend class regularly. Although we may not take regular attendance, we MAY drop you from the course for excessive absences, although we make no commitment to do so.

Withdrawal:

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 Summer 2012 is August 1, 2012.

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.

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

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

Dates

Instructor

Sections

Topics

1

5/28/12

Holiday – No class today

5/29/12

Clarence

1.1, 1.2

Introduction to differential equations – what do they mean and how do they show up in applications.  Slope fields, qualitative solutions, applications (falling objects, population models, Newton’s Law of Cooling)

5/30/12

1.2, 2.1

More applications (mixing/tank problems), solving a differential equation, checking a solution, solving using separation of variables, solving using integrating factors; recycling – using a simpler differential equation to help solve a harder one.

5/31/12

1.4

Classification of differential equations (order, linearity, ordinary/partial, etc.), examples of different types of DE’s (DE = differential equation from here on out), including partial differential equations.

2

6/4/12

2.3

Linear and nonlinear equations, existence and uniqueness of solutions for linear and nonlinear equations, domain of solutions, linearity and the superposition principle

6/5/12

2.2, 2.3

More modeling with DE’s. More on existence and uniqueness.

6/6/12

2.4

Autonomous equations, population dynamics, qualitative solutions and equilibrium points, classification of equilibrium points, the phase graph

6/7/12

2.1, 2.3

Substitution methods – Beroulli and Homogeneous equations;

3

6/11/12

2.2

Equations with discontinuous coefficients, linearity and the superposition principle, existence and uniqueness of solutions for linear and nonlinear equations, domain of solutions

6/12/12

2.5

Exact equations, integrating factors for exact equations

6/13/12

1.3, 2.6, 2.7

Numerical methods – Euler’s method, Runge-Kutta method, error types, global and local accuracy of numerical methods, efficiency of methods, limits of numerical methods, computer use

6/14/12

Ch. 1 and 2

Review for Test 1, discuss how to know which solution method to use, review classification of DE’s to aid in choosing solution method, review existence/uniqueness/domain of solutions

Test 1 – Dates to be announced in class

4

6/18/12

Marcus

3.1, 3.2

Systems of first-order DE’s – application example, converting second order DE’s into a first-order system, converting higher order DE’s into a first-order system, going backwards (from first-order system to second order equation by substitution)

6/19/12

3.1, 3.2

Review of matrices and solutions to independent vs. dependent linear systems of equations, linearity and superposition – how many “independent” solutions does a system have?  Wronskian and linear independence

6/20/12

3.3

The power of patterns – “guessing” a solution to a system; making it work – finding the right parameters for a real solution, eigenvalues and eigenvectors, solving homogeneous first order linear systems with constant coefficients

6/21/12

Mathematica

Introduction to using Mathematica to work with differential equations – graphing, solving algebraic equations, solving differential equations, manipulating matrices

5

6/25/12

3.3

Solutions and the phase plane – long-term equilibrium behavior of different types of system, dependence of the solution type on the eigenvalues and eigenvectors, sketching the phase plane by hand, sketching solution curves from the phase plane

6/26/12

3.4

Complex eigenvalues – solutions in conjugate pairs, real and imaginary parts of a solution

6/27/12

3.5

Repeated eigenvalues, systems with an unknown parameter, stability of solutions

6/28/12

6.1, (6.3, 6.4)

Higher dimensional systems, how solving higher dimensional systems relates to the 2-dimensinoal case

6

7/2/12

6.3, 6.4

More higher dimensional systems

7/3/12

6.6

Methods of solving non-homogeneous systems –variation of parameters

7/4/12

Holiday – No class today

7/5/12

Ch. 3 and 6

Review for Test 2, summarize the relationship between eigenvalues/eigenvectors, long-term stability, and shape of phase plane

Test 2 – Dates to be announced in class

7

7/9/12

7.1, 7.2

Nonlinear systems – Finding “local” behaviors near equilibrium points, “almost linear” solutions, using the Jacobian to find local behavior

7/10/12

7.3, 7.4

Population modeling examples – Predator/prey and competing species

7/11/12

4.1 – 4.3

Second order DE’s for fun and profit – New equations with old methods, now with 50% less work

7/12/12

4.5, 4.7

Non-homogeneous second order equations, the method of undetermined coefficients, the return of variation of parameters

8

7/16/12

4.5, 4.7

More non-homogeneous second order equations, D operator notation, the Exponential Input Theorem

7/17/12

4.4, 4.6

Applications of second order equations – springs, vibration, forced vibrations, and resonance

7/18/12

9.2

Fourier series and orthogonality

7/19/12

9.4

Even and odd extensions with Fourier series

9

7/23/12

9.1

One dimensional boundary value problems

7/24/12

9.5

Partial differential equations (solving the Heat Equation by separation of variables)

7/25/12

Ch. 7, 4, and 9

More on the Heat Equations, Review for Test 3

Test 3 – Dates to be announced in class

7/26/12

Clarence

5.1, 5.2

Operators vs. transforms – The Laplace transform and its properties

10

7/30/12

5.2

More Laplace transforms

7/31/12

5.3, 5.4

The inverse Laplace transform – transforming a calculus problem into an algebra problem to solve initial value problems

8/1/12

5.4

More on solving using Laplace transforms

8/2/12

5.5

The strength of the Laplace transform – step functions and translation

11

8/6/12

5.6

Solving differential equations with discontinuous forcing functions

8/7/12

5.6, 5.7

More on discontinuous functions and the impulse function

8/8/12

Ch. 5

More Laplace transform

8/9/12

8.1, 8.2

Series solutions

12

8/13/12

Ch. 5, 8, 9

Review for the final exam

8/14/12

Final Exam, Part 1 (in class)

8/15/12

Final Exam, Part 2 (in class)