Projects for Calculus: The Language of Change


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Plant Modeling for Control Design. High Performance Computing. Each project begins with a brief review of a topic that has been presented in lecture.

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The student is then guided through a Maple exploration of the topic. Projects are rated as either Basic or Honors. Basic projects are mandatory for all students in the course. Honors projects are offered as extra credit or used for honors sections. All projects are in PDF format. Community Rating:.

MHS AP and Honors Calculus Student Projects on Related Rates of Change and Optimization

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  • Language as Calculus vs. Language as Universal Medium.
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Applied Research. Maplesoft E-Mail Lists. By inadvertently discovering this strange language, first in a corner of geometry and later in the code of the universe, then by learning to speak it fluently and decipher its idioms and nuances, and finally by harnessing its forecasting powers, humans have used calculus to remake the world. But Deep Thought was on the right track: the secret of the universe is indeed mathematical. What is calculus? How did humans figure out that God speaks it or, if you prefer, that the universe runs on it?

Finally, how can any of these stories and ideas be conveyed enjoyably and intelligibly to readers of goodwill like Herman Wouk, a very thoughtful, curious, knowledgeable person with little background in advanced math? His big novel ballooned into two big novels— Winds of War and War and Remembrance , each about a thousand pages. Once those were finally done, he tried to teach himself by reading books with titles like Calculus Made Easy —but no luck there.

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Finally, in desperation, he audited a high-school calculus class, but he fell too far behind and had to give up after a couple of months. The kids clapped for him on his way out. He said it was like sympathy applause for a pitiful showbiz act. A historian of mathematics would tell it differently. So would a pure mathematician. What fascinates me as an applied mathematician is the push and pull between the real world around us and the ideal world in our heads.

Phenomena out there guide the mathematical questions we ask; conversely, the math we imagine sometimes foreshadows what actually happens out there in reality. When it does, the effect is uncanny.


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To be an applied mathematician is to be outward-looking and intellectually promiscuous. To those in my field, math is not a pristine, hermetically sealed world of theorems and proofs echoing back on themselves. We embrace all kinds of subjects: philosophy, politics, science, history, medicine, all of it. This is a much broader view of calculus than usual. It encompasses the many cousins and spinoffs of calculus, both within mathematics and in the adjacent disciplines. Far from it. Science and technology were essential partners—and arguably the stars of the show.

My point is merely that calculus has also played a crucial role, albeit often a supporting one, in giving us the world we know today. Take the story of wireless communication.

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Without their observations and tinkering, the crucial facts about magnets, electrical currents, and their invisible force fields would have remained unknown, and the possibility of wireless communication would never have been realized. So, obviously, experimental physics was indispensable here.

But so was calculus. In the s, a Scottish mathematical physicist named James Clerk Maxwell recast the experimental laws of electricity and magnetism into a symbolic form that could be fed into the maw of calculus. Apparently something was missing in the physics. He tried patching it up by including a new term in his equation—a hypothetical current that would resolve the contradiction—and then let calculus churn again.

This time it spat out a sensible result, a simple, elegant wave equation much like the equation that describes the spread of ripples on a pond.

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AP Calculus Updates: Key Changes

A changing electric field would generate a changing magnetic field, which in turn would regenerate the electric field, and so on, each field bootstrapping the other forward, propagating together as a wave of traveling energy. And when Maxwell calculated the speed of this wave, he found—in what must have been one of the greatest Aha! So he used calculus not only to predict the existence of electromagnetic waves but also to solve an age-old mystery: What was the nature of light?

Light, he realized, was an electromagnetic wave. A decade later, Nikola Tesla built the first radio communication system, and five years after that, Guglielmo Marconi transmitted the first wireless messages across the Atlantic. Soon came television, cell phones, and all the rest.

Projects for Calculus: The Language of Change Projects for Calculus: The Language of Change
Projects for Calculus: The Language of Change Projects for Calculus: The Language of Change
Projects for Calculus: The Language of Change Projects for Calculus: The Language of Change
Projects for Calculus: The Language of Change Projects for Calculus: The Language of Change
Projects for Calculus: The Language of Change Projects for Calculus: The Language of Change
Projects for Calculus: The Language of Change Projects for Calculus: The Language of Change
Projects for Calculus: The Language of Change Projects for Calculus: The Language of Change

Related Projects for Calculus: The Language of Change



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