MATH 326: Differential Equations

Elementary Differential Equations, 6th edition, by Henry Edwards and D. Penney.

We may skip around a little, but we will do our best to cover most of the textbook. Topics are subject to change depending on the progress of the class, and various topics may be skipped due to time constraints.

Please note that we will work on developing your independent reading skills in Mathematics. I certainly won't be able to cover in class all the material you will be required to learn. As a result, you will be expected to do a lot of reading. You should read the sections of the textbook which correspond to the material covered during the lectures. The reading will enable you to answer my questions and ask your own focused questions during the lecture and help you to better understand the material.

We will probably make use of the TI-89 calculators. Therefore, it is probably in your best interest to have one (or something equivalent that can calculate integrals.)

It may be helpful to make use of mathematical programs such as MATLAB, Maple, or Mathematica periodically. These are available in most student computer labs throughout campus.

Topics covered: Topics include first-order differential equations, linear differential equations, power series solutions, Laplace transforms, linear systems of differential equations, and various applications. If time permits, we may be able to study some higher-order, nonlinear systems. We will take a multifaceted approach, including both analytical and numerical solution methods, as well as qualitative methods which enable us to discover properties of solutions without actually having a formula.

The material covered in this course relies heavily on material from Calculus I and II. You should review differentiation and integration techniques early. Besides demonstrating competence in learning definitions, theorems, and problem-solving techniques of elementary differential equations, you will also be required to demonstrate the ability to do simple proofs on homework and exams. We will find that matrix algebra will be a useful tool, and we will cover the parts of that subject which will be necessary for our use. The program MATLAB (or an equivalent program) may be an extremely helpful resource throughout the course, both as a computational tool and as a remarkable aid to visualization.

We are embarking on a systematic study of ordinary differential equations. This represents the completion of the calculus of functions in a single variable. This calculus is initiated by the study of derivatives in an attempt to solve the tangent problem and to determine the rate of change of some fluctuating quantity. One then moves on to the integral in an attempt to solve the area problem. Then these two seemingly unrelated notions are finally connected via the amazing Fundamental Theorem of Calculus. And now, finally, we begin the final chapter of this story. The use of differential equations will make available to us the full power of the calculus of single variable functions. Differential equations have a far reaching impact beyond the realm of mathematics. The notions of ordinary differential equations are fundamental in almost all areas of science, engineering, and economics. Differential equations are widely used to model phenomena that arise in these areas.

Your overall grade will be determined as follows:

• 25% - WeBWorK, Quizzes, and Class Participation
• 25% - Exam 1
• 25% - Exam 2
• 25% - Final Exam

Your overall grade for the course will reflect how well the class is doing, and will be high if everyone is working hard on the homework and doing well on the exams. Almost all the questions on the exams will be in the same spirit with the homework questions. Therefore understanding how to do all the homework questions will enable you to do well on the exams.

Homework: Most homework will be done through the internet-based homework system called WeBWorK. However, there may occasionally be problems you must write out and hand in to me. All assignments must be completed by the given due date. Moreover, while it is not required that you complete a handwritten version of WeBWorK assignments, it is strongly encouraged. Writing a problem out by hand, showing all calculation steps, and keeping them collected in a notebook will greatly assist you as you prepare for exams.

Exams: There will be two Midterm Exams and one Final Exam. Exams are closed book, closed notes, closed friends, and open brain. Cell phones, iPods, and other electronic devices will NOT be permitted in exams. Whether or not calculators are allowed on an exam will be determined at a later time.

Quizzes and Class Participation: There will be occasional, unannounced quizzes in class to make sure students are understanding and keeping up with the course material. Quizzes will be based on material from homework and previous lectures. It is also imperative that you keep up with reading the textbook. NO MAKE-UP QUIZZES WILL BE GIVEN. Class participation will be based on your willingness to ASK and ANSWER questions in class.

It is essential not to fall behind because each lecture is based on previous work. If you have trouble with some material, SEEK HELP IMMEDIATELY in the following ways: