# Books on complex valued functions and solution of PDE

• Applied
• jonjacson
In summary, the conversation discusses the study of different properties and distributions in mathematical science, particularly in the fields of geometry and mechanics. It also mentions the solutions of equations in classical and quantum mechanics, as well as the book "Lectures on Theoretical Physics vol. 6" by A. Sommerfeld as a recommended resource for understanding these concepts.
jonjacson
Hello folks,

1.- In geometry we study for example the conic sections, their exentricity and properties. I was wondering what part of the mathematical science studies the different properties of complex valued distributions. One example are the spherical armonics. I guess mathematicians have studied this.

Let's say this in other words, in Classical Mechanics the solution of the equations are the orbits, that are normally curves on the plane, but when you study quantum mechanics the solutions are distributions of complex valued functions. I know there are few analytical solutions, but I want to learn about other distributions that are analytical.

2.- When you study mechanics all the energies are allowed, but if you study membranes or chords only certain patterns are allowed. In Quantum mechanics the solutions of the differential equations are a set of discrete states. What part of math in general studies this particular differential equations that have a discrete set of functions as solutions?

Delta2
The best introductory book on these questions is

A. Sommerfeld, Lectures on Theoretical Physics vol. 6, Partial Differential Equations, Academic Press 1949

jonjacson

## 1. What are complex valued functions?

Complex valued functions are functions that take in complex numbers as inputs and output complex numbers. They can be represented as a combination of a real part and an imaginary part, where the imaginary part is multiplied by the imaginary unit, i.

## 2. How are complex valued functions used in solving PDEs?

Complex valued functions are used in solving PDEs because they allow for a more general and elegant solution compared to using only real valued functions. They also help in finding solutions to PDEs that have no real-valued solutions.

## 3. What are some common examples of PDEs that involve complex valued functions?

Some common examples include the heat equation, wave equation, and Laplace's equation. These PDEs involve complex valued functions because they model physical phenomena that have both real and imaginary components.

## 4. How can books on complex valued functions and PDEs be helpful for research in other fields?

Books on this topic can provide a deeper understanding of the fundamentals of complex valued functions and their applications in solving PDEs. This knowledge can then be applied to other fields such as physics, engineering, and mathematics to help solve complex problems.

## 5. Are there any recommended books on complex valued functions and PDEs?

Yes, there are many books on this topic that are highly recommended by experts in the field. Some popular ones include "Complex Variables and Applications" by James Ward Brown, "Partial Differential Equations: An Introduction" by Walter A. Strauss, and "Complex Analysis for Mathematics and Engineering" by John H. Mathews and Russell W. Howell.

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