Course: MAT201

Instructor: Ketover

S 2015

### Description of Course Goals and Curriculum

MAT201 is an introduction to multivariable calculus designed for students who have already taken calculus either in high school or at Princeton. Math majors should consider MAT203 instead. A solid calculus background is important especially at the beginning of the course, when concepts such as functions, limits and integrals are redefined for multiple variables. The first week focuses on objects in space such as planes and quadric surfaces that will be used throughout the semester and having a very good understanding of these will make the rest of the semester much more manageable. The course then focuses on multivariable functions and their properties. Part of the material, like partial derivatives, relies heavily on knowledge from normal calculus while Lagrange multipliers, for example, are a completely new concept. After looking at double and triple integrals, the last few weeks are then dedicated to Green, Stokes and Gauss theorems. This is for many students the most challenging part of the course. The instructors focus mostly on mathematical concepts but pertinent application to physics is covered too. While it is not a requirement for PHY104, there is an overlap and both courses would benefit from being taken together.### Learning From Classroom Instruction

Classes meet three times a week in small groups. There is no common lecture but all students complete the same assignments and take the same tests. The instructors cover all the material needed for the tests during classes or will provide the name of the chapters that have to be covered by the student if there is not enough time to cover everything during precept. It is recommended to do the reading before class. However, I found the material complicated to understand without previous explanations and not all the material covered in the textbook was pertinent for the assignments and the tests (although all the material covered is in the textbook). I thus suggest skimming the textbook before class and then coming back after class to read the appropriate chapters in more details. Knowing about the general concepts before class was really helpful but it is not necessary to go over the examples or even the formulas. This can be done after precept, while doing the problem set for example. It is essential to take notes during precept, especially because some of the material is difficult to understand when explained the first time. I often had to read over my notes after class in order to get a good grasp of the material. Your notes will also be helpful to remember which parts of the chapters you should focus on when studying.### Learning For and From Assignments

I learned the most from the weekly problem sets. They generally covered the material from the preceding week but I sometimes had to read ahead of what we were doing in class in order to do some of the problems. The first problems usually test that you know the right formulas and when to apply them while the problems at the end of the problem set are often more difficult and test understanding rather than memorization. For example, the first problem might ask you to find the triple integral of a function while the last one asks you to find the volume of a solid. Mathematically, these two problems are very similar but you will need to actually understand what a triple integral is (instead of just knowing how to solve it) in order to solve the second one. The examples in the textbook are a wonderful resource both for the problem set and to study for the quizzes and the tests. Another alternative is to look at the odd problems just before or after the problem that is assigned for the problem test. They are often similar in type and the solutions are available at the back of the book. The quizzes were about the same difficulty as the more difficult problems of the problem set. In order to study for the quiz, I did practice problems from the textbook that were similar to the problems in the assignment. There are also a lot of practice quizzes available, which you can take while timing yourself. While the midterm and the final were challenging because of the problems themselves, the main difficulty for the quiz was the time limit. This is why it is important to be able to solve problems quickly by doing more practice problems outside of the problem set. The problems in the midterm and the final were more difficult than most of the problems in the book and I studied mostly by doing the practice tests. At the end of the course, I also found it important to take the time to go over Green, Stokes and Gauss theorems very slowly in the textbook. These theorems are crucial to multivariable calculus but there is little time to go over them in precept. They also look similar to each other, at least at the beginning, and it took me a long time to completely understand them and to be able to solve problems from previous finals on these topics. MAT201 can sometimes feel very computation-heavy, especially toward the middle of the semester but the grading takes into account the understanding of the material, not only the correctness of the final answer. For this reason and because it also helped organize the material in my mind, I tried to give a clear structure to my answers. For example, there are many tools you can use to solve multivariable limits and it is very helpful to go through a list (from the most common strategy to the most specialized) when solving these types of problems.Go over the practice tests multiple times. Sometimes, you will find that something you thought you understood after looking at the solution, you can't do anymore on the next day.

### External Resources

Office hours were a great opportunity to address difficulties but also to get over material that had not been covered in depth in precept. I mostly went to my instructor’s office hours but, if these do not fit in your schedule, it is also possible to go to the office hours of one of the many other instructors. McGraw also offers study halls and individual tutoring. Finally, some videos online can be helpful to better visualize some structures in 3D.### What Students Should Know About This Course For Purposes Of Course Selection

MAT201 is offered both in the fall and in the spring. It is a requirement for many science and engineering majors. Students interested in majoring in economics can take MAT175 instead. Math majors usually take MAT215 but might take MAT203 if they are interested in more applied math. MAT104 or BC Calculus are required before taking the class.Multivariable Calculus

Go over the practice tests multiple times. Sometimes, you will find that something you thought you understood after looking at the solution, you can’t do anymore on the next day.