Description
Book Synopsis: Differential forms eat tangent vectors, spit out numbers and do this in an alternating multilinear fashion. These properties make differential forms an essential tool for doing calculus on manifolds and thus of great interest to mathematicians and physicists. This book is aimed at the general reader who is interested in tackling a relaxed but wide-ranging introduction to this fascinating subject. The only prerequisite is a reasonable foundation in advanced, school-level mathematics. The text includes numerous worked problems.
Topics covered include:
- An introduction to basic concepts.
- How differential forms eat tangent vectors and spit out numbers.
- Manipulating differential forms, including the wedge product, differentiation and integration.
- How differential forms provide an alternative means of understanding three-dimensional vector calculus.
- The generalised Stoke's theorem, which applies to manifolds of any dimension.
- Maxwell's equations in the language of differential forms.
- Using differential forms to prove three nice topological theorems, including the famous hairy ball theorem.
By the author of A Most Incomprehensible Thing: Notes Towards a Very Gentle Introduction to the Mathematics of Relativity (ISBN 9780957389465) and Movement of the Spheres: Basic Astronomical Calculations Explained With 29 Spreadsheets (ISBN 9780957389489).
Details
Are you interested in expanding your knowledge of advanced mathematics? Look no further than our Beginner's Guide to Differential Forms! This comprehensive book is designed to provide a relaxed yet wide-ranging introduction to this fascinating subject. Whether you're a mathematician or physicist, you'll find that differential forms are an essential tool for doing calculus on manifolds. With numerous worked problems included, you'll be able to strengthen your understanding of concepts such as manipulating differential forms, differentiation and integration, and the generalised Stoke's theorem.
One of the great advantages of this book is that it requires only a reasonable foundation in advanced, school-level mathematics. You don't need to be an expert to grasp the content. We've made sure to present everything in a clear and accessible manner, making it suitable for the general reader. Whether you're a beginner or someone looking to refresh their knowledge, this guide will take you from the basics to a deeper understanding of differential forms.
Additionally, the Beginner's Guide to Differential Forms covers various intriguing topics, including how differential forms eat tangent vectors and spit out numbers. You'll also learn about using differential forms to comprehend three-dimensional vector calculus, as well as proving three nice topological theorems, including the famous hairy ball theorem. This book truly offers a comprehensive exploration of differential forms and their application in mathematics and physics.
Don't miss out on the opportunity to enhance your mathematical skills with this invaluable resource. Click here to get your copy of the Beginner's Guide to Differential Forms and start mastering this essential subject today!
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