Hello All,
Here are the slides that I presented today to the MSU capstone committee on the work we did during the 3rd quarter of our calculus class. I hope that it honestly depicts the time and effort we all put into our online adventure. Thank you again for your commitment to the project. I hope that it benefited you as much as it did me.
Cheers and Thanx
Bru
Showing posts with label Bru. Show all posts
Showing posts with label Bru. Show all posts
Wednesday, June 30, 2010
Friday, May 28, 2010
Final Review Slides: May 31, 2010
Hello All,
Here is an overview of what we covered this year in Calculus. It can serve as an initial review for the final exam.
Cheers, Bru
Here is an overview of what we covered this year in Calculus. It can serve as an initial review for the final exam.
Cheers, Bru
Monday, May 24, 2010
Today's Slides: May 21, 2010
Hello All,
Here are the slides from our introduction into solids of revolution and using a definite integral to calculate their volume.
Cheers, Bru
Here are the slides from our introduction into solids of revolution and using a definite integral to calculate their volume.
Cheers, Bru
Monday, May 17, 2010
Today's Slides: May 17, 2010
Hello All,
Here are the slides from our Exploration into 2D apps of the definite integral. (3D apps coming soon!)
Cheers, Bru
Here are the slides from our Exploration into 2D apps of the definite integral. (3D apps coming soon!)
Cheers, Bru
Friday, May 14, 2010
Today's Slides: May 14, 2010
Hello All,
Here are today's slides on finding the area between curves.
Cheers, Bru
Here are today's slides on finding the area between curves.
Cheers, Bru
Thursday, May 13, 2010
Today's Slides: May 12, 2010
Hello All,
Here are the slides from our exploration of some properties of definite integrals.
Cheers, Bru
Here are the slides from our exploration of some properties of definite integrals.
Cheers, Bru
Thursday, May 6, 2010
Today's Slides: May 5, 2010
Hello All,
Here are today's slides from our discovery of the Fundamental Theorem of Calculus.
Cheers, Bru
Here are today's slides from our discovery of the Fundamental Theorem of Calculus.
Cheers, Bru
Monday, May 3, 2010
Today's Slides: May 3, 2010
Hello All,
Here are the slides from constructing some very special Riemann sums.
Here are the slides from constructing some very special Riemann sums.
CRMS Calculus May 3, 2010
Cheers, Bru
View more presentations from Colorado Rocky Mountain School.
Wednesday, April 21, 2010
Today's slides: April 21, 2010
Hello All,
Here are today's slides of our "road trip" to discover the Mean Value Theorem.
Cheers, Bru
Here are today's slides of our "road trip" to discover the Mean Value Theorem.
Cheers, Bru
Monday, April 19, 2010
Today's Slides: April 19, 2010
Hello All,
We have two sets of slides today. The first one is our review of the entire year of Calculus (to date) in just 7 minutes, all on a single slide!
The second set of slides is our recreation of Rolle's Theorem.
We have two sets of slides today. The first one is our review of the entire year of Calculus (to date) in just 7 minutes, all on a single slide!
The second set of slides is our recreation of Rolle's Theorem.
Rolle's Theorem
Cheers, Bru
View more presentations from Colorado Rocky Mountain School.
Tuesday, April 13, 2010
Today's Slides: April 13, 2010
Hello All,
Here are today's slides on the definition of the definite integral.
Cheers, Bru
Here are today's slides on the definition of the definite integral.
Cheers, Bru
Monday, April 12, 2010
Today's Slides: April 12, 2010
Hello All,
Here are the slides from today's class which introduced you to Riemann sums.
Cheers, Bru
Here are the slides from today's class which introduced you to Riemann sums.
Cheers, Bru
Thursday, April 8, 2010
Forum: A Tale of Two Integrals
We have been working with Auntie Derivative and her Family of Functions, also known as the indefinite integral. We have also worked with the definite integral. Which image below illustrates which type of integral?
Did you pick the correct one? The indefinite integral is a family of functions with a given derivative and the definite integral is the area under a curve. Incredibly, they are related to each other, as we will soon discover!
What method have we used to approximate the definite integral (starts with a "t")? This method uses a strategy developed by Archimedes, considered by many to have been the greatest applied mathematician of antiquity. His method for finding areas under curves laid the groundwork for the invention of calculus by Newton and Leibniz two thousand years later. Read this recent New York Times article by Steven Strogatz, a professor of applied mathematics at Cornell University. Professor Strogatz discusses Archimedes method of exhaustion and many of the ideas we have covered this year: Zeno's Paradox of Motion, infinity, linear approximations, and the underlying basis for calculus - the concept of a limit. Post a short comment on one "take-away" from the article.
Did you pick the correct one? The indefinite integral is a family of functions with a given derivative and the definite integral is the area under a curve. Incredibly, they are related to each other, as we will soon discover!
What method have we used to approximate the definite integral (starts with a "t")? This method uses a strategy developed by Archimedes, considered by many to have been the greatest applied mathematician of antiquity. His method for finding areas under curves laid the groundwork for the invention of calculus by Newton and Leibniz two thousand years later. Read this recent New York Times article by Steven Strogatz, a professor of applied mathematics at Cornell University. Professor Strogatz discusses Archimedes method of exhaustion and many of the ideas we have covered this year: Zeno's Paradox of Motion, infinity, linear approximations, and the underlying basis for calculus - the concept of a limit. Post a short comment on one "take-away" from the article.
Monday, April 5, 2010
Today's Slides: April 5, 2010
Hello All,
Here are the slides from today's introduction to slope fields.
Cheers, Bru
Here are the slides from today's introduction to slope fields.
Cheers, Bru
Wednesday, March 31, 2010
Today's Slides: March 31, 2010
Hello All,
Here are the slides from today's class on the rules of integration.
Cheers, Bru
Here are the slides from today's class on the rules of integration.
Cheers, Bru
Tuesday, March 30, 2010
Today's Slides: March 30, 2010
Hello All,
Here are the slides from Exploration 5.1 and our introduction to integrals and integration.
Cheers, Bru
Here are the slides from Exploration 5.1 and our introduction to integrals and integration.
Cheers, Bru
Tuesday, February 23, 2010
Final Project: Learning in Motion
We’ve discussed the learning paradigm of “Watch it, Do it, Teach it”. It is one thing to watch someone do something; still another to do it yourself; but quite another to teach it to someone else. Real learning comes from teaching. Learning also does not occur in a vacuum. We learn through our interactions with others and with our environment. Collaboration is an important life-skill for the 21st century global citizen.
The goal of this final project is to work together to teach a calculus concept
and by doing so learn at the same time.
Nowhere is it more evident that calculus is the mathematics of change than in related rates problems. When two quantities change over time, the rates of their change are often related to each other. That’s one of the differences between algebra and calculus. In algebra we study the relationship between quantities. In calculus we study the rates of change of those quantities. In this respect, an algebraic equation is a static snapshot of two quantities frozen in time, while a differential equation of calculus represents a dynamic video of those quantities set in motion.
Within each group, the final project consists of three tasks:
PRESENT a related rates problem. Select a scenario from the pool of classic related rates problems or create an original situation with similar parameters. Act out the scenario either by video or by stitching together a storyline of still photos. Be creative! Use toys, props, or other inventive ways to illustrate your scenario (puppets, claymation, etc.). Here are some examples to spark your imagination.
Filling a cylinder
Baseball runner
Moving sea creatures
Stone thrown in lake
Flying pig
Reeling in the big fish
Your related rates problem should be presented clearly and concisely; i.e. in a way that it could be used as a homework or test problem. Make sure that it is fully-specified, but not redundant (that is, there can’t be too little or too much information to solve the problem). Your problem should not be ridiculously difficult, nor should it be so simple that it is practically trivial. It must require calculus to solve.
SOLVE your related rates problem. The solution will include a written description of the problem. All variables used to model the scenario will be clearly defined. The solution will contain a graphic to illustrate a “snapshot” of the scenario; and each step of the solution will be properly annotated.
REFLECT on your work on this project.
Each member of the group will describe his/her contribution to the project.
Each member of the group will write a reflection on what he/she learned from working on the final project. This may include the use of a new Web 2.0 tool or computer skill, thoughts on collaborative group work, or insight into related rates problems.
The presentation of your problem will be posted to our blog. It will begin with an introduction which includes a statement of purpose, the nom de plume of each group member, and a brief description of the project scenario. After the presentation, provide a hyperlink to our wiki where you will post the solution and reflection portions of the project. Here is the rubric for the project.
The finished project is due by 3:00 pm on Friday, March 5. This final project will be a reflection of your learning, group effort, and commitment to excellence. I hope that you have fun teaching the concept of related rates to others who will benefit from your knowledge.
Cheers, Bru
Friday, February 19, 2010
Wednesday, February 17, 2010
Today's Slides: February 17, 2010
Hello All,
Here are the slides from our first look at related rate problems.
Cheers, Bru
Here are the slides from our first look at related rate problems.
Cheers, Bru
Sunday, February 14, 2010
Forum Question: Quantifying Humanity
In January, 2006 the cover story of BusinessWeek was about numbers. According to the article, "the world is moving into a new age of numbers," where the “mathematical modeling of humanity promises to be one of the great undertakings of the 21st century.”
This article is another sign of the need for a more quantitatively-literate society. As more of us live, work, and play online, the more our digital profiles are open to analysis and susceptible to exploitation. People have been using mathematics to extract hidden patterns from data for centuries. However the increased volume of data in modern times has elevated the knowledge of math and computer technology to a 21st century life skill. In order to be smart consumers and informed citizens we need the ability to sort through data to identify patterns and establish relationships. Giving over that authority to the software behind our computers does not relieve us from the responsibility to be critical thinkers. Companies like Google and Yahoo are charting these oceans of data navigated by quants and math geeks who are becoming the new elite of the global economy. In the information age of the 21st century the best job in the world is that of data miner.
This week's Forum Question is to read, or listen to (a podcast is available) the BusinessWeek cover story. Of particular interest to you will be the last page which contains the overviews, "How Much Math Do We Need to Know?" and “How Math Transforms Industries”. Write a short summary of the article and then share your “take-aways” from the story.
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