Mathematical Modeling

Lecture on Hyperbolic Functions Theory, Derivations, and Applications

Editor2 weeks ago2 weeks ago08 mins

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 ago3 months 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: Partial differential equations (PDEs) are used in machine learning (ML)—especially in advanced fields like: Physics-informed neural networks (PINNs): These use PDEs…

Mathematics in Operations Research: Concepts, Methods, and Examples

Editor10 months ago4 months ago015 mins

Operations Research (OR) is a multidisciplinary field that uses mathematical models, statistical analysis, and optimization techniques to solve complex decision-making problems in various industries such as manufacturing, transportation, healthcare, finance, and logistics.

An Overview of Mathematics in Classical Mechanics

Editor10 months ago5 days ago014 mins

Classical mechanics, developed primarily through the work of Sir Isaac Newton and subsequent physicists such as Euler, Lagrange, and Hamilton, provides the foundation for understanding the motion of physical systems under the influence of forces.

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

Editor10 months ago5 days 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.

Solving Ordinary Differential Equations (ODEs) – 1st Order

Editor10 months ago5 days ago010 mins

Ordinary Differential Equations (ODEs) are equations involving functions and their derivatives. First-order ODEs involve the first derivative of the unknown function and are crucial in modeling phenomena such as population dynamics, heat conduction, motion under forces, and electrical circuits.

Understanding Fourier Series: Breaking Down Functions into Sines and Cosines

Editor10 months ago8 months ago07 mins

Fourier series is a powerful concept in mathematics and engineering that allows us to express periodic functions (functions that repeat their values in regular intervals) as the sum of simple sine and cosine waves.