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Interactive Learning Tools for Scientific Computing and Data Analysis Using R
Root-finding methods and numerical optimization techniques with applications in science, engineering, and data analysis
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Abstract
Scientific computing is the combination of mathematical models and computational techniques to solve problems in science and engineering. Data analysis interprets complex data and extracts relevant information to create informed decisions. Learning skills in scientific computing and data analysis, with data and models playing a prevalent role in fields such as physics, engineering, and medical research, will increase efficiency in decision making and modeling. A Jupyter Notebook is an open-source web application used to create and share documents that contain live code, visualizations and narrative text. In this project, Jupyter notebooks are used to introduce root-finding techniques including Newton-Raphson and Bisection, with implementations and examples comparing different approaches to solve root-finding problems, and sample applications in science and engineering showcased. Additionally, optimization methods are presented to find the maximum or minimum of a given function, and an application in curve fitting is shown. Optimization problems arise in a wide variety of applications in engineering design, parameter estimation, and machine learning. Students and researchers interested in fundamentals and applications of numerical analysis, physics, engineering design, optimization, scientific computing, and calculus can benefit from exploring the examples and methods explained and developed here.
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Sponsored by
National Science Foundation, Network for Computational Nanotechnology and Purdue University.
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