Math 291 - Honors Calculus III
Description
Math 291 is a course covering multivariable calculus, as well as relevant techniques from linear algebra. Unlike the standard multivariable calculus course 251, 291 may involve writing proofs on homework assignments and sometimes on exams.
Topics covered
Topics covered in Math 291 usually include:
- Vectors in Euclidean space
- Vector-valued functions
- Continuity and differentiability
- Curvature, torsion, and the Frenet–Serret frame
- Speed and arc length
- Continuity of multivariable functions
- Relationship between continuity and topology of Euclidean space
- Differentiation of multivariable functions: gradients, Jacobians
- Linear functions and basic linear algebra
- Implicit function theorem
- Lagrange multipliers
- Quadratic forms and quadratic approximation/second order Taylor series
- Integration in multiple variables
- Vector calculus: divergence and curl, related theorems
Note that the exact list of topics may vary by instructor and semester.
Comments on prerequisites
Unofficial/suggested additional prerequisites: AP Calculus BC with a score of 5, or strong performance in Rutgers math courses such as 152.
Most students who take 291 are students in their first semester at Rutgers, freshly out of high school with a 5 on the AP Calculus BC exam. A number of students may even come in with some prior knowledge of multivariable calculus or linear algebra, which is helpful but not necessary for the course.
Miscellaneous information
With an A grade in 291, students receive “internal proficiency” for Math 250, Introduction to Linear Algebra. In this case, the Math 250 requirement for the math major is waived. Moreover, when registering for a course that has Math 250 as a prerequisite, a student can request a prerequisite override and mention that they took 291 in place of 250 to add the course to their schedule. See the page on registration for more information.
Internal proficiency has a history of being honored by other departments as well, notably the Computer Science department. The CS undergraduate program will allow for 291 to be used in place of 250 for the CS major requirement and prerequisite purposes.
In the case of finishing 291 with a B or B+ instead of A, it is still possible to receive internal proficiency. Students in this situation will have the option to sit for an exam to receive proficiency, or they can continue on to 292 and try again for an A grade.
Resources
Textbook
The usual textbook for the class is a set of course notes produced by Eric Carlen, available online at https://sites.math.rutgers.edu/~carlen/291F17/MVCalc2017.pdf. This text is known to have many typos.
Additional materials
Lecture notes from when the course was taught by Zheng-Chao Han in Fall 2022, which complement the Carlen notes, may be found online at https://sites.math.rutgers.edu/~zchan/current-preprint/291CourseNotes2022.pdf.
Previous course webpages from when the course was taught by Eric Carlen may be found online: Fall 2017 and Fall 2013.