Название: Mathematical Methods for Physics using Microsoft EXCEL
Автор: Shinil Cho
Издательство: CRC Press
Год: 2025
Страниц: 208
Язык: английский
Формат: epub (true)
Размер: 10.1 MB

In Mathematical Methods for Physics using Microsoft Excel, readers will investigate topics from classical to quantum mechanics, which are often omitted from the course work. Some of these topics include rocket propulsion, Rutherford scattering, precession and nutation of a top under gravity, parametric oscillation, relativistic Doppler effect, concepts of entropy, kinematics of wave packets, and boundary value problems and associated special functions as orthonormal bases. Recent topics such as the Lagrange point of the James Webb Space Telescope, a muon detector in relation to Cherenkov’s radiation, and information entropy and H-function are also discussed and analyzed. Additional interdisciplinary topics, such as self-avoiding random walks for polymer length and population dynamics, are also described.

This book will allow readers to reproduce and replicate the data and experiments often found in physics textbooks, with a stronger foundation of knowledge. While investigating these subjects, readers will follow a step-by-step introduction to computational algorithms for solving differential equations for which analytical solutions are often challenging to find. For computational analysis, features of Microsoft Excel including AutoFill, Iterative Calculation, and Visual Basic for Applications (VBA) are useful to conduct hands-on projects. For the visualization of computed outcomes, the Chart output feature can be readily used. There are several first-time attempts on various topics introduced in this book such as 3D-like graphics using Euler’s angle and the behavior of wave functions of harmonic oscillators and hydrogen atoms near the true eigenvalues.

There is a wide spectrum of topics covered by this book, from classical mechanics to quantum mechanics. Chapter 1 demonstrates graphical representations of the dynamics of a projectile with air resistance, rocket propulsion, and three-body problems including the Lagrange points, Rutherford scattering, and motions of a top. In Chapter 2, you analyze oscillations with external damping and driving forces, parametric oscillations, and coupled oscillation. Chapter 3 describes wave properties including the relativistic Doppler effect and foundation of wave optics such as the Fourier transform, Huygens’s principle, and diffractions. Chapter 4 describes electromagnetic potentials and EM waves derived from Maxwell’s equations. The main theme of Chapter 5 is entropy, from its thermodynamical definition to that of information. Chapter 6 guides special functions that we apply to boundary value problems. The concept of orthonormal basis is the main theme and shows series expansions using various special functions. Chapter 7 discusses the kinematics of wave packets and how eigenfunctions and eigenvalues are determined by the boundary condition of a particle in a box, a harmonic oscillator, and a hydrogen atom using a shooting method. In Chapter 8, we discuss polymer properties such as elasticity and length determined by self-avoiding walks. Several models of population dynamics are also introduced in this chapter to learn how to establish a model and visualize their outcomes.