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Objective:
Research about a Mathematical Equation that had a great impact on advancing Engineering
and technology.
Learning Outcomes:
1. Gaining the basic research skills to conduct research about a scientific topic,
2. Improving the scientific writing skills to enable students to write scientific papers or thesis,
Research Details:
1. The research topic will be assigned to each group by the instructor.
2. The report should have the following: title page, table of contents, introduction, main body,
conclusion, and references. Acknowledgment and dedication should not be included in this
report.
3. The introduction should be about the equation definition, the importance of the equation, in
which field of engineering it is used? Which type of problems it is solving?
4. The main body should present the mathematical history of the equation, its derivation, the
mathematical expression of the equation, and the parameters used in the equation. It may
include a detailed discussion of a specific practical application that utilizes this equation.
5. The conclusion may include the constraints or limitations of the equation, its relation to any
other mathematical equations, a summary of the report, and an outlook of its applications in
future.
6. Note that each figure or table in the report should have a caption, it has to be numbered, and it
has to be referenced appropriately, if taken from an external source.
7. The report including the cover page, table of contents, and references should be between 15
and 20 pages.
Evaluation Criteria:
1. Reports will be evaluated based on clarity, arrangement, accuracy, and completeness. Also, the
originality of the report will be checked to confirm avoiding any plagiarism violation.
2. Presentations will be evaluated based on clarity, arrangement, accuracy, and completeness.
3. Students will be evaluated after the presentation by questions about their project. The main
purpose of this discussion is to investigate the level of understanding of the student.
Make sure there is no plagiarism
🛑 Struggling with where to start this assignment? Follow this guide to tackle your assignment easily!
✅ Understanding the Assignment
This research project requires you to study a mathematical equation that significantly contributed to engineering and technology advancements. Your report should include:
✔ The definition and importance of the equation
✔ The engineering field where it is applied
✔ The problems it solves
✔ Its historical background, derivation, and parameters
✔ Real-world applications and future outlook
Your final report should be between 15 and 20 pages, including a title page, table of contents, introduction, main body, conclusion, and references (but no acknowledgment or dedication).
📌 Step 1: Choose a Mathematical Equation
You will be assigned a specific equation by your instructor. Some well-known equations used in engineering and technology include:
🔹 Fourier Transform – Used in signal processing, communications, and image processing
🔹 Navier-Stokes Equations – Essential in fluid mechanics and aerodynamics
🔹 Schrödinger Equation – Fundamental in quantum mechanics and nanotechnology
🔹 Maxwell’s Equations – Crucial in electromagnetism, telecommunications, and circuit design
🔹 Laplace’s Equation – Applied in electrostatics, heat conduction, and mechanical engineering
If you haven’t been assigned a topic yet, choose an equation relevant to your engineering interest.
📌 Step 2: Structure Your Research Report
Your report should follow a clear and logical scientific paper format:
1️⃣ Title Page:
✔ Include the title of the report, your name, course name, instructor’s name, and date of submission.
2️⃣ Table of Contents:
✔ List all sections and subsections with page numbers for easy navigation.
3️⃣ Introduction (2-3 Pages)
👉 Explain what the equation is and why it is important.
🔹 Define the equation and state its mathematical significance.
🔹 Identify which engineering field it is used in (e.g., electrical, mechanical, civil, aerospace).
🔹 Describe the types of problems it helps solve (e.g., predicting motion, fluid dynamics, structural stability).
📢 Example:
“Maxwell’s equations are fundamental to the field of electromagnetism. They describe how electric and magnetic fields interact and form the basis of modern wireless communication, power generation, and electronic circuits.”
4️⃣ Main Body (10-12 Pages)
The core of your research should cover:
📍 4.1 Historical Background of the Equation
🔹 Who discovered or developed the equation?
🔹 What problem were they trying to solve?
🔹 How did it influence scientific and technological advancements?
📍 4.2 Derivation and Mathematical Expression
🔹 Provide the mathematical derivation of the equation.
🔹 Clearly explain the variables and parameters involved.
🔹 If possible, use simple numerical examples to demonstrate its use.
📢 Example:
*”The Fourier Transform equation is expressed as:
F(w)=∫−∞∞f(t)e−jwtdtF(w) = \int_{-\infty}^{\infty} f(t) e^{-jwt} dt
where F(w)F(w) is the transformed function, f(t)f(t) is the time-domain function, and jj represents the imaginary unit.”*
📍 4.3 Practical Engineering Applications
🔹 Explain how engineers use this equation in real-world scenarios.
🔹 Provide case studies or examples of industries that benefit from the equation.
🔹 Include figures, diagrams, or tables (properly labeled and referenced).
📢 Example:
“Maxwell’s equations are the foundation of modern wireless communication. They enable engineers to design antennas, radar systems, and mobile networks. Without them, technologies like Wi-Fi, GPS, and 5G communication would not exist.”
5️⃣ Conclusion (2-3 Pages)
🔹 Summarize the key findings of your research.
🔹 Discuss the limitations of the equation (e.g., conditions where it doesn’t work well).
🔹 Mention any related equations that expand on its functionality.
🔹 Provide a future outlook on how the equation will continue to shape engineering.
📢 Example:
“Despite its complexity, the Navier-Stokes equation remains an essential tool in aerodynamics, enabling the design of efficient aircraft, drones, and even weather prediction models. Future research aims to develop numerical methods to solve it more efficiently in real-time applications.”
6️⃣ References (1-2 Pages)
✔ Use APA or IEEE citation format to list all sources used (books, journals, websites).
✔ Ensure that figures and tables are correctly referenced if taken from external sources.
✔ Avoid plagiarism by properly crediting authors.
📢 Example Reference in APA Format:
Maxwell, J. C. (1865). A dynamical theory of the electromagnetic field. Philosophical Transactions of the Royal Society, 155, 459-512.
📌 Step 3: Formatting and Plagiarism Check
🔹 Use 12-point font, Times New Roman, double-spaced text
🔹 Add proper headings and subheadings for clarity
🔹 Include numbered equations and labeled figures/tables
🔹 Check plagiarism using Turnitin or any plagiarism-checking tool
📌 Step 4: Prepare for the Presentation
🔹 Summarize key points into a PowerPoint presentation (10-15 slides).
🔹 Use bullet points, images, and equations to explain concepts clearly.
🔹 Anticipate possible questions from your instructor and be prepared to discuss:
✔ How the equation was derived
✔ Its importance in engineering
✔ Real-world applications
✔ Limitations and future potential
🎯 Final Tip: Make Your Research Engaging!
Don’t just list facts—explain them! Imagine you are teaching someone with no background in engineering. Use examples, simple explanations, and diagrams to make your paper more engaging and informative.
✅ Now you’re ready to write an outstanding research report! 🎉
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