Taylor Series Expansions $($Gradient$,$ and Vectors$)-$ Project

You will offer some background information, list the information that is known or provided, clearly express the technical issue, describe and support a solution approach, put the solution into practice, and finally confirm that the underlying assumptions are met. You should anticipate doing supporting hand$-$analysis as well, but the main output of your project will be a report outlining your efforts$$and "code" for computer analysis.

Problem Selection

Selecting a project that is relevant to your study or thesis, hobbies, or professional goals is suggested. An perfect project brings you one step closer to completing your thesis and establishes the framework for an academic report. Vector analysis is a necessary component of every project; this can be interpreted in a variety of ways.

A project should potentially include the following:$$

$$ Identifying an analytical $($or design$)$ challenge derived from a physical system.

$$ Analyzing your problem by hand $($with a pencil and paper$)$ in order to draw generalizations.

$$ Changing or mathematically expressing the hand analysis to draw conclusions about your specific system.

Approach

Software implementations can be done in Excel, Matlab, or Python.

Part $1$: Problem Selection

You have to have chosen a system of interest, listed in$$the course subjects, and provided an overview of your knowledge of the system.

Deliverables: a brief paper $($one to two pages$)$ outlining the following:$$

$$ background information about your system

$$ an illustration or picture of it;$$

$$ course topics or themes you anticipate being covered in this project

$$ a synopsis of your system knowledge

$$ a preliminary sketch of your work's output $($initial ideas about the next stage$)$

Part $2$: Problem Statement

$$Clearly define the system's purpose and the desired analysis or design objectives.

Deliverables $-$ a brief$$problem statement, including:

$$ State the features to be obtained $($analysis$)$ or selected $($design$)-$ what will you know when the project is completed?

$$ a description of the system's obtainable information and operational state.

$$ Explain why you believe this knowledge is enough to produce the required features or attributes.

$$ some ideas about the mathematical tools or approaches you may employ.

Part $3$: Detail of Approach and Early Results

$$Include a brief $$statement outlining your methodology and first outcomes. By this step, you should have a "prototype" of the$$analytic or design technique ready to use.

The report should provide an explanation of the mathematical analytical approach used.

$$ An explanation of how you implemented it$.$

$$ Initial findings for system or test case characteristics$/$properties$.$

Rubric

Introduction

$$ Introduce your system, the issue, and any thoughts you may have about this issue or group of issues.

$$ Explain your issue and system.

$$ List the aspects of your issue that are intriguing from an analytical standpoint.

$$ List the aspects of your issue that you think make it difficult and provide an explanation.

Approach

$$ Describe the theoretical strategy used to address this issue. Determine any necessary equations and state any underlying assumptions in detail.

$$ Which properties need to be identified or created?

$$ Which technological strategy and why will you use?

$$ Create any necessary equations.

$$ What presumptions guide the strategy?

Execution

$$ Use a spreadsheet, computer code, or a clearly specified set of manual processes to implement a design or analytic tool.

$$ Specify any characteristics or configurations and providing analytical support for them

$$ Describe the organization of your answers $($why$,$ not what; for example, why it includes the steps it does, in the sequence it does$).$

$$ Describe any compromises, difficult choices, or estimates you have to make when creating and executing your solution.