## Math 117 -- Calculus Applications: Multivariable Optimization

This half-semester course covers topics in differential multivariable calculus that are most useful in the social sciences, especially economics, but also form the basis of applications throughout the sciences. A deep understanding of multivariable calculus is achieved by seeing its techniques applied, and by using geometric intuition whenever possible. Constrained maximization and minimization is emphasized throughout the course. Some topics of interest to potential majors in the natural sciences have been omitted from the syllabus, but care has been taken to cover those topics in multivariable calculus most basic to the understanding of physical chemistry.

Students wishing a more complete treatment of multivariable calculus, including integration and vector calculus (which are important in the physical sciences) should take the full-semester course Math 121.

Math 117 is targeted primarily at two audiences. First, it is appropriate for students who enter Haverford with a substantial background in calculus, but not enough to place directly into multivariable calculus Math 121 (e.g., a strong performance in an AB calculus course in high school). Students in this category will naturally pair Math 117 with Math 116. Second, Math 117 may be taken as a follow-up to the half-semester integral calculus course Math 114. Math 117 is a particularly good follow-up to Math 114 for students interested in economics or chemistry, who do not plan to take the full multivariable calculus course Math 121. Arrangements can be made to take Math 121 after Math 117, but a full credit and a half will not be granted for this combination. Math 117 is adequate preparation for many 200-level math courses, including Math 203, 204, 210, 215, and 222.

Prerequisites: Math 114 or placement

Who should take this course?
Students with a good background in limits, derivatives, and integrals, but not placing into Math 121.
Students looking for a half-semester course to follow the half-semester Math 114, and with applied interests

Topics covered:
Vectors, dot products, equations of planes
Graphs and level curves of functions of two variables
Partial derivatives and their use in solving unconstrained optimization problems
Differentials