University of Michigan - Shanghai Jiao Tong University Joint Institute


Vv 285: Honors Mathematics III

Credits:  4 credits (No credits are counted towards graduation for those who have completed Vv255)
Prerequisites: Vv186 or permission of instructor
Background and Goals: The sequence Honors Mathematics Vv186-285-286 is an introduction to calculus at the honors level. It differs from the Honors Calculus sequence in that new concepts are often introduced in an abstract context, so that they can be applied in more general settings later. Most theorems are proven and new ideas are shown to evolve from previously established theory. Initially, there are fewer applications, as the emphasis is on first establishing a solid mathematical background before proceeding to the analysis of complex models. The present course includes an overview of linear algebra followed by the calculus of functions in multidimensional euclidean space.
Content: Linear systems of equations and the Gauss-Jordan algorithm; finite-dimensional vector spaces, linear independence and bases; scalar products and Gram-Schmidt orthonormalization; linear maps and matrices; determinants; topology of normed spaces; the derivative and applications; curves, potentials and vector fields; higher derivatives and applications; the Riemann integral in n-dimensional space; integration on curves and surfaces; the classical theorems of vector analysis in three dimensions (Green, Gauss and Stokes); the inverse and implicit function theorems (as time permits).
Alternatives: Vv255 (Honors Calculus III) is an applications-oriented course, which covers much of the same material.