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This guide provides a step-by-step approach to successfully completing the Approximating Non-Linear Systems By Linear Systems form. By following these detailed instructions, users will be able to navigate the components of the form effectively and efficiently.

Follow the steps to complete the form online.

1. Click ‘Get Form’ button to access the document and open it for editing.
2. Begin by entering the names of the team members in the designated sections. Ensure that all fields are filled out accurately to reflect the individuals involved.
3. Proceed to Part 1, where you will review and classify equilibrium points based on the provided differential equations. Use the space provided to draw phase lines and complete the conjecture statement regarding attracting and repelling points.
4. In the linear approximation section, follow the prompts to calculate the linear approximations based on the specified functions. Ensure to write the expressions clearly and check your sketches.
5. Complete all questions related to the system's equilibrium points in Part II. Make sure to graph both by hand and using computational tools as indicated, ensuring to label all relevant parts.
6. Continue to Part III, where you will calculate the derivative matrix of the non-linear map. Enter your calculations in the provided areas and check for accuracy against your previous findings.
7. Conclude your work by reviewing Parts IV and reinforcing your understanding of the commands needed for solving algebraic equations in Mathematica. Ensure that examples are followed closely, as the following will be relevant for future tasks.
8. Once all sections are filled, save your changes, and review your work for completeness before downloading, printing, or sharing the final document.

Begin completing your document online today to successfully understand and approximate non-linear systems!