Here is the course description offered by the math department: MATH 231 covers only the differential calculus portion of MATH 230. Topics include partial derivatives, gradients, divergence, and curl, multi-variable chain rule, coordinate system transformations, and differential equations, with applications to geometry and optimization. This course is completed by students in several programs in engineering, mathematics and the sciences and secondary education.
This is a great course description... if you are familiar with the material already. Since I am assuming you are not, I composed some answers to basic questions that you might have about this course.
What can you expect from Math 231? Math 231 goes over all the mathematics of mechanics. It seeks to extend the material from math 140 (Calculus I) into three dimensions. It also uses parametric equations from math 141 (Calculus II), so make sure you are comfortable with that material as well. What does this information mean? It means that by the end of the course, you'll be able to describe objects moving in three space dimensions and include time. This is the math that got us on the moon. It is amazing stuff.
Is Math 231 hard? Everything is hard until you know it. Think back on all the math you have ever learned; it was all hard until you worked to understand it. That being said, expect to take your time with the problems in this class. While we will use math you have seen before in other classes, they will come together in strange ways. Because we are working in three dimensions, you will need to take your time visualizing the problems. If you have taken art, sculpture, 3-D design, ceramics, or a similar class, you might find these visualizations easier. If you struggle with visualizing, remember that all it takes is some practice. I also recommend you look into 3-D graphing software like Grapher, a standard software on all Macs. Whatever software you get, play around with it. This will help develop your intuition.
Do I need to buy the book? I design my classes to be self-contained, so you do not need to buy the book (you will need to ask the instructor for other sections). I will be posting lecture notes which will be sufficient.
If you're someone who typically learns from a textbook, I highly recommend you buy the book. It is a classic for a reason. It won't be a waste of money because the examples in the notes are different than those in the book. It will make a great reference and some of the techniques presented in the book are different than mine.
How are you as a teacher? Because I, too, am a student, I know you care about this question. I'll give you some statistics. When I taught Math 231 over the summer, 100% of my students found the lectures helpful. When they took the midterm, 60% felt very prepared and 30% felt adequately prepared. When asked about the frequent homework assignments, 90% of students felt they were an important tool for learning. Here is a comment from a student: "The atmosphere provides one of the best learning environments I've had. I stay focused and involve myself in the material because it's presented in a less-than-boring way."
That being said, this is not an easy class.I ask you to do a lot of work. Seriously, this is a demanding class. There is really no other way to learn math. A good friend of mine said, "Math travels from the hand to the brain," and I love this statement! Learning math, like most subjects, requires that you practice. I make most of that practice a required component to this class (and all of my classes).
Will you make me do group work? I want you to work in groups; educational research has shown that it is a great way to learn. In fact, at the graduate level, those who talk and reflect more about the material typically do a better job at learning it. That being said, I don't want to make people work in groups. It can be stressful to have to form a group with strangers and it can be worse when assigned a group with another person you don't get along with. I want you to enjoy your education. So, I won't make you do group work, but some of your assignments will have a social component to them to get you talking about math.