EAS439 Numerical Analysis SUSS Assignment Sample Singapore

EAS439 Numerical Analysis is a unique course that provides insight into the technology and math we use to solve computation problems. From root finding, interpolation, and approximation, the course dives deep into each topic to provide students with a comprehensive understanding of numerical algorithms and techniques.

Furthermore, what sets this course apart is its case-based approach using real-world examples to demonstrate how practitioners design and analyze models in complex scenarios. In taking this course, students will gain a strong foundation upon which they can apply their knowledge across different fields from aerospace engineering to financial economics.

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Below, we will outline the assignment tasks:

Assignment Task 1: Calculate approximate solutions to mathematical problems using fundamental numerical algorithms.

For those looking to accurately calculate approximate solutions to mathematical problems, mastering fundamental numerical algorithms can be an incredibly useful tool. Numerical algorithms are strategies and equations used to attempt to achieve an accurate answer, and if done correctly, they can make solving questions nearly effortless.

Knowing the basics of these algorithms can also aid in developing comprehension of more advanced concepts in mathematics as well. As a result, investing time into formally learning about numerical algorithms can not only provide individuals with a means for approximating solutions quickly but also give them a code base for tackling increasingly difficult math challenges in the future.

Assignment Task 2: Analyse a numerical algorithm’s accuracy, efficiency and convergence properties.

An accurate, efficient, and convergent numerical algorithm is essential for any application of numerical analysis. By leveraging complex mathematical methods and making use of computational power, one can analyze the accuracy, efficiency, and convergence properties of a numerical algorithm. Evaluating accuracy requires assessing the size of the errors made in comparison to the exact result.

Efficiency involves measuring the runtime required to obtain a given solution, while convergence looks at how quickly an algorithm converges upon a certain solution as it approaches zero error. All these components need to be considered holistically when evaluating a numerical algorithm’s performance.

Assignment Task 3: Design programming implementations for fundamental numerical algorithms.

Writing numerical algorithms is a critical skill for software engineers. Designing implementations that are sound and optimized necessitates an understanding and mastery of concepts such as truncation errors, integration, and discrete formulas. Numerical algorithms commonly rely on these fundamentals to leverage computing to solve real-world problems.

A skilled software engineer must use their expertise in analysis, problem-solving, and design to create a numerical algorithm implementation that meets stakeholder requirements while also ensuring optimal runtime performance. With modern tooling demonstrating mastery of fundamentals can be achieved easily and rapidly so that numerical programming implementations can be used effectively for mission-critical projects.

Assignment Task 4: Formulate numerical discretization procedures using the finite element method or finite difference method.

Numerical discretization procedures involving the finite element method (FEM) and the finite difference method (FDM) are an invaluable part of computational modeling. When combined with optimization algorithms, these procedures can be used to solve partial differential equations using a variety of mathematical models. Utilizing FEM and FDM can provide accurate approximations, information on boundary value problems, and a framework for robust and realistic simulations.

Moreover, they are often able to take into account non-linearity, which is useful in a variety of contexts. As such, formulating numerical discretization procedures using FEM or FDM can serve as an effective way to reduce errors that stem from a lack of precision or incorrect assumptions in digital simulations.

Assignment Task 5: Compose efficient, well-documented code and present numerical results in an informative way.

Developing efficient, clear, and well-documented code is essential for digital programming and data analysis. Good technical documentation allows others to understand what the code or analysis does, how it works, and how to modify it to suit new needs. It also helps ensure that the numerical results are presented clearly in an informative way that can be easily consumed by a non-technical audience.

Crafting well-organized and meaningful visual displays of numeric information, such as graphs and infographics, is beneficial in quickly communicating trends or observations from these metrics. All of this helps identify any insights from the data analysis more swiftly so that an organization can make more informed decisions for their business operations.

Assignment Task 6: Compute using simulation software for numerical analysis of aerospace engineering problems.

Simulation software provides immense advantages when used as part of the numerical analysis process for aerospace engineering problems. It can be used to learn more about complex phenomena such as fluid dynamics and thermodynamics and to test potential design solutions in a realistic environment without the expense of a physical prototype. It also allows for automated optimization analysis, helping engineers detect trade-offs between performance objectives like fuel efficiency and cost or weight.

Finally, simulation helps solve safety concerns by enabling testing of failure conditions in a virtual space before they arise in reality. Simulation has become an invaluable asset to help engineers optimize aerospace engineering projects across all domains.

Assignment Task 7: Appraise Verification and Validation (V&V) of engineering numerical simulations.

Verification and Validation (V&V) of engineering numerical simulations is a critical part of the development process, as it ensures that simulation results match the desired final product. V&V involves confirming the accuracy and reliability of design data, programming code, input modules, boundary conditions, physical models, equations, and output statement results. When properly executed, this verification helps eliminate costly errors such as bad assumptions or software bugs from cropping up during production.

To effectively perform V&V of engineering numerical simulation projects, organizations must adhere to care protocols with robust validation processes including relevant testing scenarios for both single scenarios and ensemble runs with intentionally-introduced errors to verify accuracy. Regular feedback from colleagues can also help surface potential problems early in the project lifecycle. Ultimately, V&V maintains an important role in ensuring successful engineering numerical simulation projects moving forward.