University of Michigan - Shanghai Jiao Tong University Joint Institute

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Vv 255:  Applied Calculus III


General information

Credits: No credits are counted towards graduation for those who have completed Vv285
Prerequisites: Vv156, Vv186 or permission of instructor
Background and Goals: The sequence Honors Calculus Vv156-255-256 is an introduction to basic calculus. It
differs from the Honors Mathematics sequence in that new concepts are often introduced and extended from
concrete examples, remaining closely aligned to applications. Most theorems are stated rigorously and motivated
from examples, but complicated proofs and abstract generalizations are often omitted. The emphasis is on applying
mathematical results to concrete problems. 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 (with an
emphasis on euclidean space), linear independence and bases; scalar products and Gram-Schmidt
orthonormalization; linear maps and matrices; determinants; analytic geometry of lines and planes; parametric
representation of curves and surfaces; partial derivatives and applications; line, surface and volume integrals;
vector fields the classical theorems of vector analysis in three dimensions (Green, Gauss and Stokes) and
applications.
Alternatives: Vv285 (Honors Mathematics III) is a more theoretical course, which covers much of the same
material.
Course profile
Syllabus