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
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
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
Students looking for a half-semester course to follow the half-semester Math 114,
and with applied interests
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
Gradients and directional derivatives
Chain Rule in several variables
Taylor polynomials in several variables
Geometry underlying optimization: first and second derivative tests for local maxima and minima
Least squares fitting
Lagrange multipliers for constrained optimization
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