## MATH 2270 Multivariable Calculus

**Level:**II

**Semester:**1

**Number of Credits:**3

**Prerequisites:**MATH 1142 and MATH 1151 or (MATH 1150)

#### Course Description

This is a one-semester, three-credit course at the intermediate level in multivariate calculus intended for students who have satisfactorily completed six credits in elementary differential and integral calculus. For this reason, MATH 1142 - Calculus I and MATH 1151 - Calculus II (or their equivalents) are listed as prerequisite courses.

In this course, vector notation is introduced and utilized for modelling and solving problems in multidimensional space. The first section of the course deals with the Calculus of functions of several real variables. The fundamental ideas of limits and continuity are introduced, followed by the technique of partial differentiation via the chain rule and its related applications. One key application covered is the use of the method of Lagrange multipliers for the determination of constrained extrema.

This is followed by the calculus of vectors and their description of curves and surfaces in space. Differentiation of vectors is more fully developed, extending elementary notions of differentiation to those involving multiple variables. Integration is developed to encompass double integrals and triple integrals.

Finally, line and surface and volume integrals are considered. The Green’s Theorem in a plane, Stokes’ Theorem and the Divergence Theorem are introduced and utilized for the calculation of line, surface and volume integrals.

This course includes proofs and discussions at a level of complexity suitable for those intending to specialize in mathematics, as well as many examples and applications of the theory for those more interested in being able to make use of the theory in their various fields of interest.

#### Assessment

*Coursework 50%*

*Final Examination - one 2-hour written paper 50%*