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8-002-TrigSumRepresentation-TechniqueNarrative

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

Keywords: estimation Trigonometry Trigonometric Functions sum of square errors finite sum Fourier series Fouriere sum spectrum approximatiopn

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Abstract

Resource Image Students discover how to represent functions as sums of trigonometric functions and the value of such representations in many fields. This is an introduction to the study of Fourier Series.

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Article Context

Resource Type
Differential Equation Type
Technique
Qualitative Analysis
Application Area
Course
Course Level
Lesson Length
Technology
Approach
Skills
Key Scientific Process Skills
Assessment Type
Pedagogical Approaches
Vision and Change Core Competencies - Ability
Principles of How People Learn
Bloom's Cognitive Level

Description

We are going to do something that might seem foolish, but in a moment we will ask you to consider the possibilities for such a goal.

GOAL: Represent the function f(x) = x on the interval [-pi, pi] as a sum of trigonometric functions of the form sin(n x), n = 1,2,3, . . .  .

We decided to shout it out so it is absolutely clear.

Why would anyone want to express a simple function like f(x) = x as a sum of sine waves?

In so doing, we can learn about representing other functions f(x) (or data!) as a sum of trigonometric functions -- an activity we show is worthy of our attention and study.

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Authors

Author(s): Brian Winkel

SIMIODE - Systemic Initiative for Modeling Investigations and Opportunities with Differential Equations

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