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Chemical kinetics studies the rates of chemical reactions and their
dependencies.
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The most important unit operation in a chemical process is generally
a chemical reactor. Chemical reactions are either exothermic (release energy) or endothermic
(require energy input) and therefore require that energy either be removed or added to the
reactor for a constant temperature to be maintained. Exothermic reactions are the most
interesting systems to study because of potential safety problems (rapid increases in
temperature, sometimes called "ignition" behavior) and the possibility of exotic behavior
such as multiple steady-states (for the same value of the input variable there may be
several possible values of the output variable). In this module we consider a perfectly
mixed, continuously stirred tank reactor (CSTR).
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In this module, simple differential equations are
used to study the effects of the "drag" force which slows
the motion of a body moving through a fluid (in this case: air) and
is responsible for the safe landing of the skydiver.
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Flux and Surface
Integration
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Through the use of interactive materials, involving
practical examples, notions of flux and the associated concept of surface
integration are presented.
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To develop the mathematical description of a physical process in
which the gradient plays a central role. To formulate problems in
steady state one-dimensional heat conduction which provide practice
in solution of ordinary differential equations, physical interpretation,
and interaction via manipulation of parameters. To derive the partial
differential equations for heat conduction in two dimensions and solve
the equation governing steady states under various boundary conditions.
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This
module on lake pollution is about using differential equations
to model lake pollution. To model lake pollution can be complicated,
because there are many different factors which can be taken
into account. We will use a simplified model, and consider
only a few basic factors.
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There are many instances in biology and in
the environment where mass transport is an important phenomenon.
Everything from cellular osmosis to glucose uptake to pollution
in lakes and ponds can be related to mass transport. The Mass
Transport module introduces the ideas of concentration and
concentration difference and formalizes how these concepts
are responsible for many common phenomena. The module contains
a series of related demonstrations and exercises that build
on one another, allowing students an incremental understanding
of the subject through increasing levels of complexity.
Authors: Jonathan
Newell, Russell
Manson, Donald
Drew, Jason Hylan, Elisa Barney Smith |
Keywords:
concentration, differential equations, diffusion,
dilution, mass transport, semi-permeable membrane,
solute, solvent |
Learning Level: college |
Platform: Project
Links base technical requirements |
Applets: Single Chamber,
Two Sources
to Single Chamber, Washout
Dilution, Chamber
and Sink, Two Chamber,
Two
Chambers Plus Sink, N
Chamber (N=10), N Chamber
(N=10) Plus Sink |
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Linear systems of ODEs are introduced via
the chemical reactions leading to the chlorination of benzene.
One of the goals is to maximize the output of certain chlorinated
benzene products.
Authors: Gilberto
Schleiniger, Andrew Zydney, L. P. Cook, B.
Lenhoff |
Keywords:
differential equations, linear systems, ODE,
eigenvalues, eigenvectors, order reactions, initial
value problems, kinetics |
Learning Level: college |
Platform: Project
Links base technical requirements |
Applets: |
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The gradient, its interrelations with other math concepts, and its
applications to science and engineering. Rapid-change vector; normal
vector to level surface. The gradient and gradient operator in Cartesian
and other coordinate systems. The gradient as related to differentiability
and the directional derivative.
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