MATH 326: Differential Equations

There is no required text for this course. However, if you need or want a supplemental resource to study from, almost any differential equations textbook is sufficient. Here are a couple of suggestions:

Elementary Differential Equations, by William Trench (free online textbook)

Elementary Differential Equations With Boundary Value Problems, 6th edition, by Henry Edwards and D. Penney.

Please note that it is a good idea to work on developing your independent reading skills. It would be a good idea to read a textbook as a supplement to our in-class work. 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 lectures and help you to better understand the material. There may be slight differences in terminology and definitions between the textbook and what we learn in class. When this occurs, use the in-class terminology and definitions.

A calculator is NOT required for this course, and you will not be able to use one during exams. It may be helpful to make use of a calculator (or mathematical programs such as MATLAB, Maple, or Mathematica) on homework. However, our primary use of technology will be java applets and visualization tools freely available on the internet.

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 and will be taking calculus to a new and exciting level. This topic 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 stand on the frontier of human knowledge and 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, including populations, circuits, spread of disease, flames, springs, bird flight, ocean waves, and many, many more.

Upon successful completion of this course, a student will be able to:

• Solve differential equations of first order using graphical, numerical, and analytical methods,
• Solve and apply linear differential equations of second order (and higher),
• Solve linear differential equations using the Laplace transform technique,
• Find power series solutions of differential equations, and
• Develop the ability to apply differential equations to significant applied and/or theoretical problems.

Your overall grade will be determined as follows:

• 16% - WeBWorK, Quizzes, and Class Participation
• 28% - Exam 1
• 28% - Exam 2
• 28% - Final Exam

The letter grade you earn for the class will be based on the following breakdown of number grades:

A	...	93-100				B+	...	87-89				C+	...	77-79				D	...	60-69
A-	...	90-92				B	...	83-86				C	...	73-76				E	...	0-59
						B-	...	80-82				C-	...	70-72

Homework: 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. 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, calculators, and other electronic devices will NOT be permitted in exams.

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:

Accommodations: SUNY Geneseo is dedicated to providing an equitable and inclusive educational experience for all students. The Office of Accessibility (OAS) will coordinate reasonable accommodations for persons with disabilities to ensure equal access to academic programs, activities, and services at Geneseo.

Students with approved accommodations may submit a semester request to renew their academic accommodations. More information on the process for requesting academic accommodations is on the OAS website.

If you have questions, contact the OAS by email, phone, or in-person:

Office of Accessibility Services - Erwin Hall 22, (585)245-5112, access@geneseo.edu.