## Advanced Math Methods Modules

To find out more about what the version numbers mean, click on any of the indicators.

v 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 [ Full Metadata ] ## Flux and Surface Integration

v Through the use of interactive materials, involving practical examples, notions of flux and the associated concept of surface integration are presented.

Authors: Ashwani Kapila, Curt Breneman, Karen Cummings, Bruce Buhler Keywords: flux, surface integration, projected area, flow Learning Level: college Platform: Project Links base technical requirements Applets: Induction, Simple Uniform Flux, Simple Non-Uniform Flux, Wing [ Full Metadata ]

v 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.

Authors: Mike Malak, Joe Haus, Karen Cummings, Russ Dubisch Keywords: Learning Level: college Platform: Project Links base technical requirements Applets: Simple Fourier Synthesis, Fourier Synthesis with Continuously Variable Amplitudes, Fourier Synthesis with Variable Number of Components [ Full Metadata ]

## Electricity & Magnetism Series of Modules

A series of closely related modules addressing topics in electrostatics, currents and circuits, magnetism, electromagnetic induction, electrodynamics and optics.

v 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.

Authors: Mike Malak, Joe Haus Keywords: physics Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v 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.

Authors: Mike Malak, Joe Haus Keywords: physics Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v 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

Authors: Mike Malak, Joe Haus Keywords: physics Learning Level: College Platform: Project Links base technical requirements Applets: [ Full Metadata ]

v 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

Authors: Mike Malak, Kongki Min, Joe Haus Keywords: physics Learning Level: College Platform: Project Links base technical requirements Applets: Spherical Gauss's Law [ Full Metadata ]

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