Here is a worksheet for educational purposes on Sequences:

Calculus I Group Exploration 2, Sequences and Limits

Team member names: ________________________________________________________

The following exercise is designed to arrive at rules for determining long-term behavior directly from a sequence generator function without building a table.

1. Count off a,b,c,d,e,f.  All a’s group up and take sequence a, etc.

   1. an+1=1.05an, a0=543

   2. an+1=0.95an, a0=543

   3. an+1=1.05an, a0=-543

   4. an+1=0.95an, a0=-543

   5. an+1=-1.05an, a0=543

   6. an+1=-0.95an, a0=543

2. Have one person create a Google Spreadsheet.  Make your spreadsheet documents viewable to anyone with a link.  Invite your group members.

3. Make a table and a scatterplot of the data.  Use good axes labeling.  Infer the long term behavior/limit.

4. What is the general solution to the difference equation?  Check your answer using the spreadsheet.  

Add the link and your results (Your difference equation, the general solution, the limit, and the graph) to the class results page here. Please note you must be signed into Unity College Google Apps to edit the class results page.

Difference Equations are the basis for Discrete-Time dynamical systems Here is an Educational video on the topic

This video goes over 2 basic calculus concepts:

The blog posting tips are for how to write a reflective blog post in a mathematical setting: 

Tips for Creating Great Blog Posts in a Math Class

Judy Williams, Unity College

Note: Most of these ideas are for professional blogs, but can be used for reflectionary blog writing/journaling as well

• Use a short but effective title that hints at your controlling idea.

  • http://www.twelveskip.com/guide/blogging/1247/blog-post-title-templates-that-work

• Be creative about a hook to draw readers into your blog post.

  • http://beafreelanceblogger.com/blog-content-writing-hooks/

• Be sure you have a controlling idea and state it early in your blog post, maybe just after your hook.

• If there are multiple components to an assignment (e.g. an article to read, learning from your math class, and your own experience), do some prewriting on each separately and then look for connections.

• Clearly and concisely explain the similarities and differences for your readers.   Don’t presume they “get it.”

• Start with the mathematical concept you’re working on in class and show how the article illustrates that concept. Back this up with an example from your own life that also illustrates the concept.

• Use images, video, etc. to accompany text and break it up into accessible chunks. Make sure all images, etc., are visually appealing and have a clear connection to your topic.

  • https://blog.bufferapp.com/free-image-sources-list

• Use bullets, sub-headings, formatted text to make reading easy. Be concise! Avoid repetition!

  • http://writtent.com/blog/format-perfect-blog-post-10-tips/

• Return to your hook and central idea in closing.

  • http://www.copyblogger.com/closing-call-to-action/

• Invite comments. Consider including a call to action, if appropriate.

http://en.blog.wordpress.com/2012/04/12/how-to-get-more-comments/

A variety of graphs and calculations can come from the Christmas bird count It makes a good time series graph. 

Here is a link:

http://netapp.audubon.org/cbcobservation/

Nothing works better to check an answer then a software that can derive and intergrate almost anything 

Here is a link:

http://www.wolframalpha.com/

Khan Academy is great for learning mathematical based concepts.

Here is a link to it: 

https://www.khanacademy.org/

This link is to the hand out:

https://drive.google.com/a/unity.edu/file/d/0B2k1BmkveWWxZTQyZTQ0NzctYTBlNC00Y2RjLWIxYmYtMjg1NDkwMWMwMWU0/view

Colvin G. 2010. Talent is Overrated: What Really Separates World-Class Performers from Everybody Else. Penguin Publishing Group. 1-240.

This Book is about how practice makes perfect and can be directly applied to mathematics.

Here is a link to the book:

http://www.barnesandnoble.com/w/talent-is-overrated-geoff-colvin/1100833086

Smith R. 2008. Modeling Disease Ecology With Mathematics. New York: American Institute of Mathematical Sciences. 

Here is a link to the book:

https://www.amazon.com/Modelling-Mathematics-Differential-Equations-Dynamical/dp/1601330049

Ostebee A., and Zorn P. 1994. Calculus From Graphical and Symbolic Points of View. Saunders College Publishing.

Here is a link to the book:

https://books.google.com/books?id=d7ZGGM49tBkC&pg=PA41&lpg=PA41&dq=Ostebee+A.,+and+Zorn+P.+1994.+Calculus+From+Graphical+and+Symbolic+Points+of+View&source=bl&ots=Fe9CtxvuQ5&sig=lry6xEcZcEGy01jinJgpieKkbZI&hl=en&sa=X&ved=0ahUKEwjq7JnYjq3NAhVKdlIKHdeiBWIQ6AEIHjAA#v=onepage&q=Ostebee%20A.%2C%20and%20Zorn%20P.%201994.%20Calculus%20From%20Graphical%20and%20Symbolic%20Points%20of%20View&f=false

Neuhauser C. 2010. Calculus for Biology and medicine. Pearson Education. 

Here is a link to the book:

https://www.amazon.com/Calculus-Biology-Medicine-Life-Sciences/dp/0321644689

Ledder G. 2005. Differential Equations: A modeling Approach. McGraw-Hill Education.

Here is a link to the book:

https://www.amazon.com/Differential-Equations-Modeling-Glenn-Ledder/dp/0072422297

Greenwell R., Ritchey N., and Lial M. 2014. Calculus With Applications for the Life Sciences. Pearson Education. 

Here is a link to the book:

https://www.amazon.com/Calculus-Applications-Sciences-Raymond-Greenwell/dp/0201745828

Dick T., and Patton C. 1994. Calculus of a single Variable. PWS Publishing Company. 

Here is a link to the book:

https://www.amazon.com/Calculus-Single-Variable-Thomas-Dick/dp/0534939384/ref=sr_1_5?s=books&ie=UTF8&qid=1466097849&sr=1-5&refinements=p_27%3AThomas+P.%2C+Patton%2C+Charles+M.+Dick

Comar T. 2013 Undergraduate Mathematics for the Life Sciences: Models Processess & Directions (Eds.). Biocalculus at Benedictine University. Mathematical Association of America.

Here is a link to the book:

http://universitypublishingonline.org/maa/aaa/ebook.jsf?bid=CBO9781614443162

Bodine E., Lienhart S., and Gross L. 2014. Mathematics for the Life Sciences. Princeton University Press. 

Here is a link to the book:

http://press.princeton.edu/titles/10298.html

Bender E. 1978.  An Introduction to Mathematical Modeling. Wiley-Interscience. 1-46. 

Here is a link to the book:

https://books.google.com/books?hl=en&lr=&id=FvHDAgAAQBAJ&oi=fnd&pg=PA1&dq=Bender+E.+1978.+An+Introduction+to+Mathematical+Modeling.+Wiley-Interscience&ots=XkNyozGM_2&sig=XhXNb2xio_Wg3uoR1GAm8nIEXck#v=onepage&q&f=false

Alder F. 2012. Modeling the Dynamics of Life: Calculus and Probability for Life Scientists. Brooks Cole Publishing Co. 

Here is a link to the book 

http://www.cengage.com/search/productOverview.do?N=16+4294967225+4294947908&Ntk=P_EPI&Ntt=10192200511921727601168515210449811212&Ntx=mode%2Bmatchallpartial

Hughes-Hallet D., Gleason A., and Flath D. 2013. Calculus: Single and Multivariate. Wiley and Sons.

Here's a link to the book:

https://www.amazon.com/Calculus-Single-Multivariable-Deborah-Hughes-Hallett/dp/1118231147