University of Michigan - Shanghai Jiao Tong University Joint Institute

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Vv 256: Applied Calculus IV


General information

Credits: No credits are counted towards graduation for those who have completed Vv286
Prerequisites: Vv255, Vv285 or permission of instructors
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 focuses on ordinary differential equations and their
applications.
Content: Ordinary differential equations (ODEs) of first order; Systems of first-order equations; eigenvalue
problems; diagonalization and the Jordan normal form; application to linear systems of first-order equations and
linear second-order equations; nonlinear systems of ODE and stability analysis; elements of complex analysis and
residue theory; the Laplace transform and its applications to ODEs; power series solutions of ODEs by the
Frobenius method; Bessel’s and Legendre’s differential equations; introduction to the classical partial differential
equations of physics and some basic solutions by separation of variables.
Alternatives: Vv286 (Honors Mathematics IV) is a more theoretical course, which covers much of the same
material.
Course Profile
Syllabus