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Introduction to boundary value problems and
eigenvalue problems for ODEs in the context of buckling,heat
conduction/diffusion,vibration problems. Intro to Fourier
method.
Authors: Richard Weinacht, George
Hsiao, B. Lenhoff, Andrew Zydney, Jack R. Vinson
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Keywords:
differential equations, heat transfer, diffusion,
strength of materials, buckling, heat conduction,
vibrating beam, vibrating string, BVP, eigenvalue |
Learning Level: College |
Platform: Project
Links base technical requirements |
Applets: |
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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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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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Mechanical Oscillations Series of Modules
A series of closely related modules addressing topics in mechanical
oscillations, simple harmonic motion, and dynamic system behavior.
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Observations of a forced oscillator, physical
and mathematical modeling of its dynamics, and comparisons
between predicted and actual behavior.
Authors: William
Siegmann, William
Boyce, Kevin Craig, Jessica Cavanaugh, Karen Leary, Celal Tufekci, Jeongmin Lee, Christine Goering |
Keywords:
differential equations, mechanical oscillations, spring, mass, damper, damping, forced, forcing |
Learning Level: college |
Platform: Project
Links base technical requirements |
Applets: Sine + Cosine, Beats, AF Plotter, Damped Forced Spring Mass, Undamped Forced Spring Mass |
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Observations of a linear pendulums, physical and mathematical
modeling of its dynamics, and comparisons between predicted
and actual behavior.
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Observations of systems with two masses and
three springs, physical and mathematical modeling of their
dynamics, comparisons between predicted and actual behavior,
and extensions to systems with more masses and springs.
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Observations of a non-linear pendulums, physical and mathematical
modeling of its dynamics, and comparisons between predicted
and actual behavior.
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Observations of a mass-spring system, physical
and mathematical modeling of its dynamics, and comparisons
between predicted and actual behavior.
Authors: William
Siegmann, William
Boyce, Kevin Craig, James Fairweather, Brian Griglak, Celal Tufekci, Karen Leary, Jessica Cavanaugh, Jeongmin Lee, Franklin Turner, Rahul Kulkarni, Laura Gross, Christine Goering, Sean Russell |
Keywords:
differential equations, mechanical oscillations,
spring, mass, damper, damping |
Learning Level: college |
Platform: Project
Links base technical requirements |
Applets: Undamped Spring Mass, Damped Spring Mass, Sine + Cosine |
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Observations of a spring pendulum system,
physical and mathematical modeling of its dynamics, and comparisons
between predicted and actual behavior.
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Interactive simulation of the vibrating string;
comparison with experimental data. Interactive derivation
of the solution of the wave equation for the vibrating string.
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This module will help you understand how a
circuit with an inductor and a capacitor undergoes an electromagnetic
oscillation, and how the period and frequency of an oscillation
depend on the inductance and capacitance. You should
also finish with an understanding of how the energy in a circuit
is conserved if there is no resistance.
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This module will help you understand what
electrical current and resistance are, the relationship between
voltage, current, and resistance. You will also be able to
calculate these quantities for resistors in a circuit, the
resistance of a network of resistors, and the resistance of
a resistor given its size and shape and the resistivity of
its material.
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