Math 337: Methods of Applied Calculus

Fall 2018 Policy Information

Course Description
This course will build on your previous studies of differential and integral calculus as well as ordinary differential equations. In the class we'll cover material that most of your professors wish that they could have covered in M237 and M238 if only they had had the time. The vector calculus portion will focus on the deep relation between the average of a function on the boundary of some region in space with the average of its derivative over the interior of the region. We will also focus on transforming differential equations into algebraic equivalents in order to solve them. Both have many applications in the sciences.

Prerequisites
MATH 237 and (MATH 238 or MATH 336).

Textbooks
We'll use chapters of your calculus and differential equations books. You'll want to have your:

You might also be interested in the supplementary optional texts

Most importantly, though, just holding the notes or a text won't be enough. You've got to read the material. And think about it. And work out the details with pencil and paper. And ask questions. And then repeat until it makes sense.

Stucture
This course is going to require a significant investment of your time. Lectures are a great way for you to see and appreciate math, but they don't do such a great job at giving you the mastery of the material. Since mathematics is learned by practice, homework is really the core of this course. In general, the more work you put in, the better you will do.

On-line Material
Course material will be posted on Canvas.

Grading
Grades will be assigned on the 10 point scale:

90-100 A- to A range; 80-89: B- to B+ range; 70-79 C- to C+ range; 60-69 D to D+ range; 59 and below: F.

Homework will be worth 35% of your final grade (due every 1 to 2 weeks), each exam will be worth 15% (there will be three), and the final project 20% (a topic of your choice).

Homework
Mathematics is learned by practice. To encourage you to practice, homework will be assigned regularly. I expect you to do all of the assigned homework. In addition, each assignment will contain six problems designated for grading. Solutions to these six problems should be written up before the due date, and this is what I will be collecting. Half of your score will reflect completeness (i.e. a reasonable attempt of all problems) while a roll of a dice will determine which problem I'll grade in detail for the other half of your score. There will be cases where part of the homework grade will be determined based on an oral presentation of your work, either in class or during office hours.

Do the homework. Collaboration (but not copying!) is encouraged. The time you spend working on the homework will be invaluable. You'll need to write the solutions clearly, including the steps that you took to get your final answer. You should be writing up a solution, not just writing the answer.

Exams
Exams will be announced with at least one week notice and may or may not include a take-home, in-class, and oral portion. A missed exam will result in a zero for that exam. There will be three. Two exams will treat the vector calculus material, while the other will focus on differential equation/transform methods.

Final Presentation
You'll work individually or with a partner to explore a topic related to this course material. I'll keep track of your progress via weekly meetings that will begin mid November. During finals week, your group will present your work during a 30 minute presentation and also submit a written report and/or poster.

Need a little extra help?
I love office hours. Please use them, and don't be afraid to send an email or give me a call.

Honor code
Remember that JMU has a strict honor code. While you are strongly encouraged to work with others in this class, the work you submit must be your own. Copying someone else's work won't help you learn the material and might just get you expelled.

Nature of the Course Content
(from course catalogue)
MATH 337. Methods of Applied Calculus. 4 credits. Offered every third semester as of fall 2015. Laplace transforms, power series and their application to differential equations. Vector differential and integral calculus; parametric curves; coordinate systems; line, surface and volume integrals; and gradient, divergence and curl including the theorems of Green, Stokes and Gauss. Prerequisites: MATH 237; and MATH 238 or MATH 336.