First, you will learn the fundamental concepts and theorems of differential and integral calculus of functions from Rn to Rm. Second, you will apply these ideas to optimization and see some spectacular results from classical physics, such as Kepler's laws and Guass's theorem. Third, you will learn be introduced to differential forms and manifolds, the natural context for many problems in geometry and mechanics. At the end of the day, you will master powerful tools with a very broad range of applicability.
This course will also give you an introduction to abstraction and higher mathematics. We will be careful about definitions and will give careful arguments, i.e., proofs, justifying everything we do. You will increase your ability to write clear and precise explanations of mathematical facts.
First, because it is really useful. Mathematicians sometimes say that all of mathematics is calculus and linear algebra. This isn't completely true, but it's close. Multivariable calculus will be used (heavily) in many of your later courses and in many of your careers.
Second, you are a top student in Math, and this course is designed to challenge students like you.
Third and most importantly, because it is really interesting! You will see some of the deepest and most productive ideas produced by human culture.
Yes! This course is designed for students who have mastered basic linear algebra, as demonstrated for example by doing well in Math 1554 (earning an A) or 1564 (earning an A or B).
The TAs and I are commited to helping you learn this material and succeed in the course. Keep at it and you will do well.
See the last section below for more hints on how to succeed in this class and advanced math classes in general.
This is a challenging course in multivariable calculus for mathematically ambitious and well-prepared students. You will learn the fundamental algorithms and computational recipes as well as the theoretical underpinnings necessary for more advanced mathematics. Enrollment in the course is by invitation only and typically requires a grade of A in Math 1554 or an A or B in Math 1564. Success in this course will prepare you for other 2000-level courses in such as differential equations, discrete mathematics, and foundations of mathematical proof.
There will be two 80-minute lectures and two 50 minute recitations each week. Lecture time will also include clicker quizes and some discussion. Recitations will be devoted to active learning, i.e., working problems and discussing difficulties. There will be weekly homework, two mid-term exams, and a final exam.