Numerical methods provide a way to compute (approximate) values of solutions to differential equations, even when we cannot solve the equations exactly. The drawback is the large number of numerical calculations required to obtain a desired value and level of precision. In this project, you will use technology to implement the various numerical methods and use your technological solution to solve differential equations problems.

**Assignment (Due Tuesday, April 4th).** Create a numerical methods calculator. You can choose your technology tool for this job – use any one of the following:

- a spreadsheet (Excel, Google Sheets, or other spreadsheet)
- if you choose to create a spreadsheet, you should have columns for , and so on, and each stage should appear in its own row

- a programming language (Java, Perl, or other programming language)
- if you choose to write code, your program should output the values of and so on at each stage

- mathematical software (MatLab, Maple, Mathematica, or other mathematical software)
- if you choose to use mathematical software, your program should output the values of and so on at each stage

**How to submit. **Part 2 of this project will talk about how to submit your project – you will be asked to upload your solution (spreadsheet, or code, or mathematical software document) and to write about what you did. For now, focus on getting your solution working.

**Requirements:**

- Your solution should allow you to solve problems of this type:

`Example. Given the differential equation and initial condition , approximate the value of using step size`

- Your solution must be able to carry out Euler’s Method, Improved Euler’s Method, and Runge-Kutta (you may implement these as three separate spreadsheets or programs if you wish).
- Your solution should display all the points found along the way, not just the final point.
- Your solution should also display other values found while carrying out each method:
- Euler’s Method: display the slope at each stage
- Improved Euler’s: display the values of at each stage
- Runge-Kutta: display the values of at each stage
- You can display other values as well, if you wish (for example, the intermediate y-value in the Improved Euler method that we refer to as ).

- Your solution may NOT use any built-in version of these methods (for example, most mathematical software contains a built-in command for Euler’s Method – you can use this to check your work, but you need to create your own solution).
- You should be able to relatively easily change the initial condition, step size, and target value.
- You should be able to relatively easily change the differential equation (it is ok if the equation is hard-coded into your program).

**Test your project**. Solution data for the above example using Euler, Improved Euler, and Runge-Kutta will be posted this weekend so you can test your project. You can also use examples from class to test your work, since you know what the solutions are.

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