HARD problem on mathematical problem and fourier series

In summary, the conversation revolves around creating a mathematical model for hourly temperatures using Fourier series/transform. The person asking for suggestions to start the problem and the other person recommends looking into ARIMA or RNN methods for time series analysis.
  • #1
brad sue
281
0
HARD problem on mathematical model and Fourier series

Hi,
I have this problem about creating a mathematical model.
the context is Fourier series/transform.

It is about finding a mathematical model for hourly temperatures .
I have attached the file. I tried to search for Fourier model for temperatures but I had no sucess.
Can I have some suggestions so that I can start the problem please?
I tried but sorry I don't have anything to propose.

Please you can give you your ideas. Maybe it may help me.
thank you.
B
 

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  • #2
Besides the Fourier transforms, you could also investigate methods for time series analysis to model the temperature data. One approach would be to use an autoregressive integrated moving average (ARIMA) model. ARIMA is a statistical method used to analyze and forecast time series data. It can be used to model seasonal fluctuations, trend changes, and other patterns in the data. Another approach would be to try a recurrent neural network (RNN). RNNs are capable of learning complex temporal relationships and can be used to predict future values of a time series.
 
  • #3
ella

Hi Bella,

Creating a mathematical model for hourly temperatures using Fourier series/transform can definitely be a challenging problem. However, with the right approach and understanding of the concepts, it can be solved.

Firstly, it is important to understand the basics of Fourier series and transform. Fourier series is a mathematical representation of a periodic function as a sum of sine and cosine functions. On the other hand, Fourier transform is a mathematical tool used to analyze non-periodic functions in terms of frequency components.

In the context of hourly temperatures, we can consider the temperature data as a periodic function, repeating every 24 hours. This means we can use Fourier series to represent the temperature data. However, since temperature data is not strictly periodic, we can also incorporate Fourier transform to account for any non-periodic variations.

To start the problem, you can begin by collecting the hourly temperature data for a certain period of time, say a week or a month. Then, you can plot the data and observe any patterns or trends. This will give you an idea of the periodicity of the data and help you determine the appropriate frequency range for your Fourier series/transform.

Next, you can use the data to calculate the Fourier coefficients and construct the Fourier series representation of the temperature data. This will give you a mathematical model that can be used to predict future temperature values.

However, since temperature data can also have non-periodic variations, it is also important to incorporate Fourier transform in your model. This can be done by using a window function to isolate the periodic part of the data and then applying Fourier transform to the remaining non-periodic component. This will give you a more accurate and comprehensive model for hourly temperatures.

I hope this helps you get started on your problem. Good luck!
 

1. What is the "HARD problem" in mathematics?

The "HARD problem" refers to a term coined by philosopher David Chalmers, which refers to the subjective experience or consciousness that cannot be fully explained or reduced to physical processes. In mathematics, it is often used to describe the difficulty in understanding the relationship between the brain and consciousness, particularly in regards to solving mathematical problems.

2. What is a mathematical problem?

A mathematical problem is a question or situation that requires the application of mathematical concepts, theories, and methods to find a solution. It can range from simple arithmetic problems to complex equations and proofs.

3. What is a Fourier series?

A Fourier series is a mathematical tool used to represent a periodic function as a sum of trigonometric functions. It is named after French mathematician Joseph Fourier and is used in various fields, such as signal processing, image analysis, and solving differential equations.

4. How is the "HARD problem" related to Fourier series?

The "HARD problem" is often used in the context of understanding how the brain processes and solves mathematical problems, such as understanding how the brain can comprehend and manipulate abstract concepts and symbols. This can be related to the use of Fourier series, as it involves manipulating and representing abstract mathematical functions using trigonometric functions.

5. What are some potential applications of Fourier series in solving mathematical problems?

Fourier series has many applications in mathematics, physics, and engineering. It can be used to solve differential equations, analyze and filter signals, and approximate functions. It is also used in image and sound compression, as well as in the study of periodic phenomena in nature.

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