Linear Algebra and Multivariable Calculus are two of the most widely used mathematical tools across all scientific disciplines. This course seeks to develop background in both and highlight the ways in which multivariable calculus can be naturally understood in terms of linear algebra.

Prerequisites, Other Courses, and Textbooks

This course assumes a strong understanding of differential calculus of one variable, as taught in the Math 41-42 series (or equivalent). For the linear algebra portion, we will start from the beginning and build up all concepts in lectures. However, this course is packed with information and moves very quickly. Students who are somewhat unsure of their mathematics background may want to consider courses in the 40 series. In particular, students missing the equivalent of Math 42 may find the portions of Math 51 that demand deeper conceptual understanding to be more difficult than those who have the experience of a full year of college-level calculus. (Students having quite a lot of experience with mathematical proof and who are looking for a more theoretical course may want to try Math 51H.)

The texts used in this course are Levandosky's Linear Algebra and Colley's Vector Calculus (3rd edition). The latter will not be used until the second half of the course. Both should be available at the campus bookstore. If you have problems finding either textbook at the campus bookstore, please contact your instructor.

Registering for the course

Students in Math 51 will attend a lecture three times per week and a discussion section twice per week. Students in Math 51A have an additional discussion section. Students register a lecture section on Axess.

Discussion sections are chosen from among options that correspond to each lecture section; for details, see the list of discussion section options.

Some hints for the course

Previous instructors of the course have compiled a list of "helpful hints," i.e, things you can do to enhance your performance in Math 51. Students are advised to look over the list and take the advice to heart.