A new element, the vector, a symbol encompassing numbers, puts in its appearance. Students will learn how to work with vectors in modelling and solving problems in multidimensional space. Following this, the calculus of vectors and their description of curves and surfaces in space is considered. 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 integrals are considered. Students will learn, with Green's Theorem, how to transform a surface integral into a line integral and vice versa. 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. Two semesters in differential and integral calculus, such as MATH 120 and 121. Students should have done well in these courses in order to succeed in this difficult course.