## Math 121 -- Calculus III

Calculus III is the third semester of calculus, taken by first-year students who have sufficient calculus background from high school or by students who have taken Calculus II (Math 114 and either 115 or 116). It covers both differential and integral multivariable calculus, Informal geometric arguments take the place of formal mathematical reasoning, so students who desire a rigorous treatment of the subject should take Math 215-216 instead.

Math 121 includes a variety of applications in all disciplines, and is appropriate for first-year students who have not yet decided on a major. Depending on the instructor, the mix of applications may favor either the natural or social sciences, and students choosing this course should be sure to determine this emphasis.

Math 121 is accessible to students who have taken only a year of calculus in high school, yet it has a visual appeal and wealth of applications that far surpasses single variable calculus. It is excellent preparation for many 200-level electives in mathematics, as well as courses in chemistry and physics. It may substitute for Math 216 in the requirements for the math major and minor and as a prerequisite for Math 317 and Math 333, but Math 216 provides better preparation for these courses.

Prerequisites: Math 114 and either 115 or 116, or advanced placement

Who should take this course?
Students considering a major in the natural sciences, or anyone else looking for a thorough treatment of multivariable calculus
Students considering a major or minor in mathematics who want to take multivariable calculus before linear algebra
Students who have wish to build on their knowledge of single-variable calculus to enjoy the visual appeal and wealth of applications of functions whose graphs are in 3-space and beyond.

Topics covered:
Geometry of Euclidean space and parameterized curves
Functions of several variables and partial derivatives
Chain rule and Taylor approximations
Unconstrained and constrained optimization
Multiple integrals in rectangular, cylindrical and spherical coordinates
Line and Surface Integrals, including Green's Theorem, the Divergence Theorem, and Stokes Theorem
Applications