mathematical physics

Lecture on Hyperbolic Functions Theory, Derivations, and Applications

1. Introduction to Hyperbolic Functions Hyperbolic functions are analogs of trigonometric functions but are defined using exponential functions rather than the unit circle. They appear in various areas of mathematics, physics, and engineering, including: – Calculus (integration, differentiation, and differential equations) – Physics (relativity, heat transfer, and wave mechanics) – Engineering (catenary structures, transmission lines)…

Partial Differential Equations (PDEs), Their Canonical Forms wave, heat, and Laplace equations

Editor3 months ago2 weeks ago025 mins

Partial differential equations (PDEs) are classified into different types based on their characteristics, which determine the nature of their solutions and the appropriate solution methods. The three most important PDEs in mathematical physics are: Read: Introduction to Tensor Calculus a key Component in Machine Learning building Partial differential equations (PDEs) are used in machine learning…

A Comprehensive Guide to Vectors, Kernel, Green’s Theorem, Bulk Modulus, Gauss’s Theorem with Examples

Editor10 months ago3 weeks ago016 mins

In the study of mathematics and physics, concepts like vectors, kernel, Green’s theorem, bulk modulus, and Gauss’s theorem play vital roles in a variety of fields, ranging from fluid dynamics to material science.

Classification of Partial Differential Equations (PDEs)

Editor10 months ago9 months ago010 mins

Partial Differential Equations (PDEs) are equations involving functions of several variables and their partial derivatives. They arise in various fields such as physics, engineering, economics, and biology. To understand and solve PDEs, it is crucial to first classify them. The classification helps to determine the nature of the equation and the appropriate methods for finding…