Fourier Expansion for a One-Period Function with Period 2pi

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In summary, the first step in approaching a question scientifically is to clearly define the research question or problem. To gather information, you can conduct experiments, collect data, or review existing literature. A hypothesis guides the direction of research and provides a framework for interpreting the results. Data analysis involves organizing, summarizing, and interpreting the data to draw conclusions. To ensure validity and reliability, it is important to use appropriate research methods and techniques, minimize bias, and replicate the study. Peer review and replication by other researchers can also help to validate the findings.
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Kuma
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Homework Statement



Given this one period graph of a function with period 2pi,

YpNoh.png


find a Fourier expansion.

Homework Equations


The Attempt at a Solution



So I was wondering if i can split up the integrals into two parts to find the coefficients. It is an even function so ak = 0.

for bk can I split the integral as follows

1/pi[int 0 to pi (x cos kx dx) + int pi to 2pi ((-x+2pi) cos kx dx]

?
 
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  • #2
Yup, that's what you're supposed to do. Also, remember a0 isn't equal to 0.
 

Related to Fourier Expansion for a One-Period Function with Period 2pi

1. What is the first step in approaching a question scientifically?

The first step in approaching a question scientifically is to clearly define the research question or problem. This involves identifying what you want to study, why it is important, and what specific aspect you want to focus on.

2. How do you gather information to answer a research question?

To gather information, you can conduct experiments, collect data, or review existing literature. It is important to use reliable and valid sources of information to ensure the accuracy of your findings.

3. What is the role of hypothesis in scientific research?

A hypothesis is a proposed explanation for a phenomenon or a prediction of the outcome of an experiment. It guides the direction of research and provides a framework for interpreting the results.

4. How do you analyze and interpret the data collected?

Data analysis involves organizing, summarizing, and interpreting the data to draw conclusions. This can be done through statistical methods, visual representations, or other analytical techniques.

5. How do you ensure the validity and reliability of your research?

To ensure validity and reliability, it is important to use appropriate research methods and techniques, minimize bias, and replicate the study. Peer review and replication by other researchers can also help to validate the findings.

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