Mathematical Methods using Python: Applications in Physics and Engineering

Ниже — практический обзор по теме «mathematical».

It provides a practical, pedagogical introduction to utilizing Python in Mathematical and Computational Methods courses. This advanced undergraduate textbook presents a new approach to teaching mathematical methods for scientists and engineers. Both analytical and computational examples are integrated from its start. The book places less emphasis on mathematical proofs, and more emphasis on how to use computers for both symbolic and numerical calculations. Each chapter concludes with a set of problems designed to help students hone their skills in mathematical techniques, computer programming, and numerical analysis. It contains 182 extensively documented coding examples, based on topics that students will encounter in their advanced courses in Mechanics, Electronics, Optics, Electromagnetism, Quantum Mechanics etc.

This is followed by chapters dedicated to differentiation, integration, vectors and multiple integration techniques. An introductory chapter gives students a crash course in Python programming and the most often used libraries (SymPy, NumPy, SciPy, Matplotlib). The next group of chapters covers complex numbers, matrices, vector analysis and vector spaces. The book is accompanied by a dedicated GitHub website, which contains all codes from the book in the form of ready to run Jupyter notebooks. Extensive chapters cover ordinary and partial differential equations, followed by chapters on nonlinear systems and on the analysis of experimental data using linear and nonlinear regression techniques, Fourier transforms, binomial and Gaussian distributions. A detailed solutions manual is also available for instructors using the textbook in their courses.

Key Features:A unique teaching approach which merges mathematical methods and the Python programming skills which physicists and engineering students need in their courses

Uses examples and models from physical and engineering systems, to motivate the mathematics being taught

Students learn to solve scientific problems in three different ways: traditional pen-and-paper methods, using scientific numerical techniques with NumPy and SciPy, and using Symbolic Python (SymPy).

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