LTI Systems, Delta Distribution, and more

In summary, the conversation is about finding alternative books for the math methods 3 course, particularly for the Preliminaries section. The person had a hard time with the problem sets and is looking for resources to properly learn this section. They mention that Boas should work for the rest of the course, which includes Complex Analysis, Fourier Series and Transforms, ODEs, and PDEs. They also request for the title of the file to be changed to "Prerequisites for complex analysis and Fourier transforms" in hopes that more people will read it.
  • #1
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Hi,

For my math methods 3 course, I am not quite sure which books to use. The course is based on the math methods book by Riley, Hobson, and Bence, and I don't particularly like it.

Hence, I am looking for some alternatives. Especially for the Preliminaries section. I had a real hard time doing the problem sets for that part, and I didn't know where to find resources to properly learn this.

For the rest of the course, which is Complex Analysis, Fourier Series and Transforms, ODEs, and PDEs, I suspect Boas should work.

I've attached a file with the aforementioned Preliminaries section.

Thanks!
 

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  • #2
Could the title please be changed to "Prerequisites for complex analysis and Fourier transforms"?

Maybe more people would actually read it then?

Thanks.
 

Related to LTI Systems, Delta Distribution, and more

What is an LTI system?

An LTI (linear time-invariant) system is a type of mathematical model used to describe a wide range of physical systems, such as electronic circuits, mechanical systems, and more. It follows the principle of superposition, meaning that the output of the system is a linear combination of its inputs. Additionally, it is time-invariant, meaning that its behavior does not change over time.

What is the delta distribution?

The delta distribution, also known as the Dirac delta function, is a mathematical tool used to represent an impulse or spike in a signal. It is defined as having a value of zero everywhere except at t=0, where it has an infinite value. It is often used in conjunction with convolution to model the response of a system to an impulse input.

What is the difference between continuous-time and discrete-time systems?

A continuous-time system is one in which the input and output signals are continuous functions of time. In other words, the input and output are defined for all values of time within a given interval. On the other hand, a discrete-time system is one in which the input and output signals are only defined at specific points in time, usually at regular intervals. This distinction is important in the analysis and design of systems, as different mathematical tools and techniques are used for each type.

How are LTI systems represented mathematically?

LTI systems are often represented using the convolution integral, which expresses the output of the system as the integral of the input signal multiplied by the impulse response of the system. This representation can also be expressed in the frequency domain using the convolution theorem, which states that the Fourier transform of the output signal is equal to the product of the Fourier transforms of the input signal and the system's frequency response.

What are some real-world applications of LTI systems?

LTI systems are used in a wide range of fields, including signal processing, control systems, communication systems, and more. For example, in signal processing, LTI systems are used to filter and process signals in audio and image processing applications. In control systems, they are used to design feedback controllers for mechanical and electrical systems. In communication systems, LTI systems are used to model the transmission and reception of signals over different channels. Overall, LTI systems are a fundamental concept in many areas of science and engineering.

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