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# Category: Assignments(Page 1 of 3)

WeBWorK:  Assignment 16-LaplaceIVP  is due Tuesday, 5/24, at midnight.

WeBWorK: Assignment 14-InverseLaplaceTransforms  is due Tuesday, 5/16, at midnight.

OpenLab: None

WeBWorK: Assignments 12-Trench-EulerEquations  and 13-LaplaceTransforms-NoPiecewise  are due Tuesday, 5/9, at midnight.

OpenLab: None

WeBWorK: Assignment  11-Trench-SeriesSolutions  due Tuesday, 5/2, at midnight.

OpenLab: None

WeBWorK: Assignment  10-Trench-ReductionOfOrder  due Tuesday, 4/25, at midnight.

OpenLab: OpenLab #4: Flipping the class – Taylor Series is due Tuesday, 4/24, BEFORE class.

Hi everyone,

I wanted to share the scoring guide that I will use when grading your project – this is based on the Part 1 and Part 2 project assignments.  I also included my own solutions to the Project Example given in Part 2, if you’d like to compare.

## Project Scoring Guide

This project is worth 15 points towards the “OpenLab” portion of your grade, equivalent to three OpenLab assignments.  These points are assigned as follows:

• (5 points) A working numerical methods calculator using your choice of technology.
• 3 points – solution correctly implements each method (Euler’s Method, Improved Euler’s Method, Runge-Kutta Method)
• 1 point – solution displays intermediate points and other important values (k1, k2, etc.)
• 1 point – ease of implementation (can easily change initial condition, step size, target value)
• (5 points) Solutions to the Project Example
• 2 points – value of y(7.1) is approximated by each method
• 3 points – appropriate step size is chosen for each method
• (5 points) Writing Assignment
• 2 points – meet minimum length requirement (300 words)
• 1 point – Describe your project
• 1 point – Describe the process
• 1 point – Why do we need numerical methods? Why is this assignment included in the class?

## Project Example Solutions

The example given in the “Project Part 2” post was:

Project Example.  Given the differential equation $dy/dx = \frac{xy}{x-y}$ and initial condition $y(6)=0.8$, approximate the value of $y(7.1)$ using Euler’s Method, Improved Euler’s Method, and Runge-Kutta.

For each method, choose a step size that gives four correct digits following the decimal point.  How many steps are required to obtain this level of precision?

NOTE: The actual solution is $y(7.1)=3.700936$

In my own solution, implemented first in Google Sheets and later (when I needed more computing power) in Microsoft Excel, I obtained the following results:

Euler’s Method

To obtain four correct digits after the decimal point required:

• 275,000 steps
• step size h = 0.000004
• final approximation y(7.1) = 3.70090152430816

Improved Euler’s Method

To obtain four correct digits after the decimal point required:

• 390 steps
• step size h = 0.002820513
• final approximation y(7.1) = 3.70090010561837

Runge-Kutta Method

To obtain four correct digits after the decimal point required:

• 8 steps
• step size h = 0.1375
• final approximation y(7.1)=3.70091299278611

For your reference, here is the scoring guide I will be using for the EXAM 1 Special Offer

-Prof. Reitz

Name: ____________________

____ Includes Name, Date, Problem #s, original scores (up to 6 points deduction)

____ Presentation is neat, well-organized, readable (up to 4 points deduction)

____ Includes Original Exam

____ Max bonus (30 points for <50%, 20 points 50%-59%, 15 points 60%-69%, 10 points 70%-79%, 5 points 80%-89%)

First problem #:  ____

____ Original Score (out of 25)

____ Revised Score

____ (up to 5 points deduction if incomplete) Written explanation,  2 sentences,  what you did wrong OR how to solve the problem.

____ Bonus points earned for problem 1

Second problem #: ____

____ Original Score (out of 25)

____ Revised Score

____ (up to 5 points deduction if incomplete) Written explanation,  2 sentences,  what you did wrong OR how to solve the problem.

____ Bonus points earned for problem 2

 EXAM 1 SPECIAL OFFER BONUS POINTS:   _______ (Bonus points for problems 1 and 2, with maximum bonus based on original exam score, minus any deductions, ). EXAM 1 REVISED SCORE: ______

WeBWorK: Assignment  9-Nonhomogeneous  due Tuesday, 4/4, at midnight.

OpenLab: The deadline for OpenLab #3: Numerical Methods PROJECT was extended to this Tuesday, 3/28.

WeBWorK: Assignments  6-BasicSecondOrder,  7-SecondOrderRepeated,  and 8-SecondOrderComplex due Tuesday, 3/28, at midnight.

OpenLab: None

NOTE: On Tuesday, 3/14, classes were cancelled because of snow.

WeBWorK: None
OpenLab:  OpenLab #3: Numerical methods PROJECT  due March 23rd  (see the Project Part 1, Project Example Data, and Project Part 2 for details)

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