Welcome to Math 105!

Greetings. I wanted to take a few minutes to introduce myself, the TAs, and give you an overview of the course. I've posted a brief welcome letter introducing myself, my family and my research interests here. There will be three TAs for the course:

Multivariable Calculus often serves as a transition course to advanced mathematics. While many of its results are straightforward generalizations of single variable calculus, there are some fundamentally new phenomena that arise in higher dimension. At the end of the course, in addition to learning the results you will also have some familiarity with proof techniques. Click here for a more detailed explanation of my objectives for the course.

At many colleges and universities, multivariable calculus is covered in 15 weeks, and even then it is a bit rushed to include all the material. In a twelve week course, we have no choice but to make decisions on what material to cover and what to exclude. Typically this means that in Math 105 we do not cover vector analysis (such as line integrals) and the big three theorems, Green's Theorem, Gauss' Theorem (also known as the Divergence Theorem) and Stokes' Theorem. These theorems are a wonderful generalization of the fundamental theorem of calculus, and are covered in Math 106 (one of the topics we cover that 106 does not is Taylor series). I will hold supplemental lectures to cover these topics outside of class; attendance is entirely voluntary, and will have no bearing on your grade. I will not be insulted if no one attends; I am providing this option for those who wish to see these results (which are mostly used in physics and engineering, though Green's theorem is very similar to key results in complex analysis). I will inquire after class begins and find who is interested and when would be a good meeting time. These supplemental lectures won't start for a few weeks, as we first need to learn some preliminary material.

One of the difficulties of first year college is that most of you come from different schools with different backgrounds; you all have areas where you are extremely well prepared, and other areas that your school did not emphasize. As a counterpoint to the supplemental lectures later in the semester, at the start of the semester I will have a few `free form' lectures (if I forget please remind me!!!), where I am happy to discuss any mathematical topic you've had trouble with. You can of course email me suggestions on what to present, and you should also feel free to ask questions on anything either in my office or at any review session.

As you can tell from the comments above, there is a lot of material for this course, both new material we will cover and old material you are expected to know. To get the most out of this course, you need to prepare for each lecture. This means spending one to two hours a day, every day, on the course. This ranges from skimming the material before class to working on the daily homework problems. I strongly urge you to work on the problems in small groups; however, everyone must hand in their own write-up. Unless you say otherwise, 5% of your grade is based on reading the book and/or my lecture notes before class; so long as you miss doing this no more than twice, you will receive a 100% for this component of your grade. Reading the notes does not mean you should be able to deliver the lecture, but rather that you are prepared for class and know roughly what will be covered and are familiar with the terminology that would be used. In business you never go to a meeting unprepared -- you should treat classes the same way.

To help you evaluate whether or not you have the right background for the course, I have prepared a set of review problems and detailed solutions; these are available here. I strongly urge you to read these problems and make sure you can do them; this will give you a quick check on your background. I know that it has been awhile (ranging from a semester to over a year) since some of you have taken a calculus class, and I do realize that many of you will be rusty. The time between the end of winter study and the start of classes is a good window to review and make sure Math 105 is the right level for you. I'm happy to meet with anyone to discuss the course; my schedule is online here, and of course feel free to swing by my office (Bronfman 202) any time.

Though I enjoy and encourage class participation, our two sections are large (almost 30 and almost 40) and that does affect how well I can get to know you in class. I hope you will swing by or meet me for lunch / dinner / snack at some point to introduce yourself and let me know why you are taking this class, what you hope to get out of it, and what topics (if possible) you would like to see. The more input and feedback you give, the more you will get out of the course. Additionally, if you think you will need a letter of recommendation, I can write a stronger, more detailed one if we discuss material outside of class. Remember office hours and review sessions are not just to go over material from class or homework problems (though obviously that is a major point of these), but also opportunities to explore the material in greater depth. If you are interested in trying a research project, let me know as I have some that are appropriate for multivariable calculus students.

Finally, if you have any concerns or suggestions for the course and would prefer to communicate them anonymously, you may email me by using the account ephsmath@gmail.com  (the password is the first eight Fibonacci numbers, 011235813).

Looking forward to meeting you all.   //Steve

 

PS: My wife teaches marketing at UMass Amherst, 80 to 90 minutes away. Thus for evening review sessions you'll often find my two children, Cam (he's almost 6) and Kayla (she's almost 4), the fourth and fifth TAs for the course.