dan lasota's masters in education portfolio for online innovation and design

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Lesson Plan Revised

3 June 2012

First Order Differential Equations - a unit taught over three weeks

We will continue to post your work as noted below to the class blog. Part of your responsibility in posting will be to comment on your classmates published work. In order to facilitate this you'll be required to furnish comments to the post immediately above your post. The first student to post will comment on the section's sample problem and I will comment on the last student post for the section after the assignment posting period has closed. Your posts and comments are worth 20 pts and will be graded against the following rubric:

0 - 1 2 - 4 5
Timeliness post or comments are late or are made within the grace period post or comments are made on Wednesday or Thursday post or comments are made within the first three days of the week (Sunday, Monday, or Tuesday)
Accuracy of posted material resulting solution is incorrect or mostly wrong, there is no flow of thought from problem to solution or work is not shown solution has minor errors like incorrect sign or is missing a constant or has a mislabeled axis or wrong units, there is not a logical flow of steps from problem to solution solution is accurate, each important step in generating the solution is shown and the process is logical and legible
Accuracy of comments comments are mostly wrong or totally wrong comments contain some accurate material but also have errors comments are accurate
Comments identify solution method comments do not identify theorem of type of equation being solved for comments properly identify correct theorem and principle being applied

Learning Objectives

  • define and identify first-order linear differential equations
  • define and identify separable, exact, homogenous and Bernouli equations
  • apply algorithms to solve first order differential equations
  • construct falling body word problems from physics that simulate gravity environments on other planets using separable equations
  • critique solution methods to differential equations and explain the underlying justification for solution
  • use Mathematica programming and graphic methods to visualize differential equation solutions to first order linear differential equations

Week 1 - Separable and Linear Equations

Instructor Guide Notes introducing ordering of differential equations, identification of order of the equation.
Coverage of separable equations and linear equations.

Reading from Text
Sections 2.1 - Introduction: Motion of a Falling Body
2.2 - Separable Equations
2.3 - Linear Equations

Khan Academy Videos:
What is a differential equation
Separable Differential Equations
Separable differential equations 2

Assessment First half of each textbook homework due at end of week posted to blog under student's username.
Group work: split class into two designations: red and blue. Each member of the class will pick someone from the opposite designation and work with them, grading and critiquing their work on these problems. Work will be posted to class blog.

Excersises 2.2 (p. 43) 1-26 Blue # 28, 32, 36, 40. Red # 27, 31, 35, 39
Excersises 2.3 (p. 52) 1-23 Blue # 24, 28, 32, 36 Red # 26, 30, 34, 38

Use the Mathematica Equation Editor to demonstrate the steps in solving the function y = f(x) from the initial differential equation which you find on this week's assignment section. Post your results to the class blog feed.

Week 2 Exact Equations, Homogenous Equations, Bernouli Equations

Instructor Notes and Screencast and Comments putting focus on these new types of first order differential equations. On the class blog instructor will have responded to any unanswered questions and given comments where appropriate.

Reading from Text
2.4 - Exact Equations
2.6 - Substitutions leading to Homogenous and Bernouli Equations
Instructor Guide Notes (with video) covering exact equations, test for exactness, method for solving exact equations, and substitution method.

Khan Academy Videos:
Exact Equations Intuition 1 (proofy)
Exact Equations Intuition 2 (proofy)
Exact Equations Example 1
Exact Equations Example 2
Exact Equations Example 3
First order homegenous equations
First order homogenous equations 2

Assessment First half of each textbook homework due at end of week posted to blog under student's username. Group work (2nd half) split class into two designations: red and blue. (This week work with a different classmate) Each member of the class will pick someone from the opposite designation and work with them, grading and critiquing their work on these problems. Work will be posted to class blog.

Excersises 2.4 (p. 61) 1-26 Blue # 28, 32, 36, 40. Red # 27, 31, 35, 39
Excersises 2.6 (p. 74) 1-27 Blue # 41, 45 Red # 43, 47

Use the Mathematica to graph the solution function that satisfies the initial differential equation which you find on this week's assignment section. Post your results to the class blog feed.

Week 3 Lab and Quiz

Learning Activities Instructor Guide Notes including

  • screen cast of pertinent features of Mathematica that will be used in the lab
  • description of the University of Michigan Lab book exercises and the relevance of Lab #3 in engineering and physical sciences
  • reminders about testing procedures
  • pointers to additional online resources, resources from textbook, class blog and instructor office hours (via eLive, or email)
  • On class blog instructor will have posted any answers to requests for help that went unanswered by students, and will have commented on student responses where necessary.

Math Lab
At the bottom of this page is "lab 3" in PDF.
It is from a larger NSF funded resource created by a professor at the University of Michigan. The original full copy can be obtained at http://www.math.lsa.umich.edu/~glarose/courseinfo/diffeq/psfiles/labbook.ps

Follow the directions for Lab #3 in that manual and use your copy of Mathematica to complete the problems in your Mathematica journal. Journals must be posted to our class website by Wednesday of this week.

Assessment Quiz on Chapter 2. Follow procedures from course syllabus to complete and submit quiz. The quiz on chapter 2 will be available on the course website after Wednesday. You have until Sunday midnight to finish.

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