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Through geometric experimentation, the students
grasp the principles of optimization of multivariable functions
with equality constraints.
Authors: Ashwani
Kapila, Bruce Buhler |
Keywords:
advanced calculus, optimization, constraints,
multivariable, level sets, maxima, minima, Lagrange
multiplier |
Learning Level: College |
Platform: Project
Links base technical requirements |
Applets: Budget
Optimization, Navigation
Chart, Navigation
Optimization |
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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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In
this module, you will:
- Visualize and explore superposition of waves to synthesize
wave forms.
- Introduce the concept of the spectrum of a function.
- Examine specific wave forms and their decomposition.
- Understand the error in truncating a series representation
of a periodic function.
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This module will help you learn what Ampere's
Law is and how to use it to calculate the magnetic field given
the distribution of electric current. After finishing
you will know how to choose an appropriate Amperian loop,
and know how to use Ampere's law physically and mathematically.
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In
this module you will learn many of the physical characteristics
of electric fields. By the end of the module you will
understand how electric field is defined by the electric force
on a charge, that electric field is a vector, an electric
field is produced by a charge or a distribution of charges,
and how the magnitude and direction of the field depend on
the geometry of the distribution of sources. You will
learn to display electric fields and examine their geometric
properties, understand how field lines represent the strength
and direction of the field. Given an electric field,
you will be able to deduce the presence and relative magnitudes
of hidden charges producing it.
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Once you have completed this module you will understand
that a changing magnetic field gives rise to an electric field, and
what magnetic flux is, how it is related to magnetic field, and how
it is different from magnetic field. Furthermore, you should understand
Faraday's Law of electromagnetic induction, and Lenz's Law and its importance
to induction. You will be able to determine the circulation of the electric
field (EMF), and understand its physical meaning
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After completing this module you will know
what Gauss's law is, including when and how to use it, how
to select a useful Gaussian surface, and be able to use Gauss's
law physically and mathematically
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