Centered Difference Method Theory | Numerical Methods

In this video, we explore the Centered Difference Method Theory, a crucial concept in numerical methods and computational mathematics.

Learn how the Centered Difference Method Theory approximates derivatives. Whether you're a student, researcher, or simply curious about numerical analysis, this video provides a comprehensive understanding of the theory and its practical applications.

Join us as we break down the Centered Difference Method Theory step by step, explaining the underlying principles and mathematical concepts involved. We'll showcase visual demonstrations and practical examples, making it easy for you to grasp the theory intuitively.

Discover the advantages and limitations of the Centered Difference Method, and see how it impacts fields like physics, engineering, and computer science. This video equips you with the knowledge to apply this powerful numerical technique to your own projects and research.

This timeline is meant to help you better understand the intuition of the centered difference method: 0:00 Introduction 0:18 What is Numerical Differentiation? 1:18 Review of Derivatives & Relationship with Numerical Differentiation 2:47 Review of Taylor Series Approximations 3:30 Taylor Series of e^x centered at 1 4:50 Developing Centered Difference Method 6:54 Why would you use forward or backward difference method if error is better with centered difference method? 7:53 Outro

Relevant Numerical Methods Playlists: Numerical Methods Playlist: https://www.youtube.com/watch?v=F2NWYEOHIkc&list=PLDea8VeK4MUTOBXLpvx_WKtVrMkojEh52 Numerical Methods Examples Playlist: https://www.youtube.com/watch?v=UA7bzwCwHMI&list=PLDea8VeK4MUTxZGOTG-VNnW4T3TYwlEc9

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This video is part of our Numerical Methods course. Numerical methods is about solving math problems through approximating the solution of problems that would be difficult or impossible to solve analytically. In this playlist we will cover topics such as solving systems of linear equations, solving systems of non-linear equations, numerical integration, numerical derivatives, etc.. #studysession #numericalanalysis #finitedifferences ... https://www.youtube.com/watch?v=RJhbUvyTBf0