During the Fall 2021 term, MFE II is coordinated by Prof. Raoul Normand (rjn5@nyu.edu).
In this class we will continue the study of multivariable calculus introduced in MFE II. We will focus first on vector calculus, namely line integrals, Green’s theorem, surface integrals, and finally the Divergence theorem. These are essential in our Calculus III curriculum. Next, we will concentrate on studying sequences and series, which have numerous applications in Economics such as annuities, mortgage payments, internal rate of return, etc. We will conclude with the fundamental formulas of Taylor. This covers the major parts of our Calculus II curriculum and provides all necessary tools for higher level math courses such as real and complex analysis. This will especially benefit students who double major in mathematics and economics since those who take the three-part Math for Economics courses will have effectively taken the three-part Calculus curriculum.
By the end of the course, students will be able to:
- Study parametric curves in the plane.
- Compute line integrals using the definition, the fundamental theorem, or Green’s theorem.
- Calculate multiple integrals.
- Use the cross product to determine plane equations and volumes.
- Compute surface integrals using the definition or the divergence theorem.
- Determine the convergence of improper integrals.
- Determine the convergence of sequences and series.
- Analyze functions expressed as power series.
- Use Taylor series to approximate functions and compute limits.
- Understand, make, and critique mathematical arguments.