Course Description:

Calculus is foundational not only to mathematics, but also to physical and biological sciences, engineering, economics, business, and more. Thus, it is a prerequisite to many courses in these fields. This course is a sequel to Math 3 and is appropriate for students who have successfully completed an AB calculus curriculum (or the equivalent) in secondary school.

The first third of the course is devoted to sequences and series (including Taylor series) in single-variable calculus. The remainder of the course studies scalar valued functions of several variables. This section starts with the study of vector geometry, equations of lines and planes, and space curves (velocity, acceleration, arc length). Then the focus turns to differential calculus of functions of several variables. Topics include limits and continuity, partial derivatives, tangent planes and differentials, the Chain Rule, directional derivatives and applications, and optimization problems including the use of Lagrange multipliers.

Required text: Stewart, James (2015). Calculus (Eighth edition). (ISBN: 9781285740621), OR Stewart, James (2015) Multivariable calculus (Eighth edition). (ISBN: 9781305266643) (These have the same content.)

Course Goals:

Students will learn the main concepts and techniques in sequences and series and differentiable multivariable calculus.
Students will improve their ability to sit with and analyze unfamiliar problems and craft solutions.
Students will identify areas in mathematics and other fields where calculus is useful.
Students will be prepared for more advanced courses in math and other departments that have Math 8 as a prerequisite.