Mathematical Methods in Physics, Engineering, and Chemistry

1. Auflage 2019
ISBN: 978-1-119-57965-6
Verlag: Wiley

Buch, Englisch, 448 Seiten, Format (B × H): 201 mm x 259 mm, Gewicht: 1179 g

A concise and up-to-date introduction to mathematical methods for students in the physical sciences 

Mathematical Methods in Physics, Engineering and Chemistry offers an introduction to the most important methods of theoretical physics. Written by two physics professors with years of experience, the text puts the focus on the essential math topics that the majority of physical science students require in the course of their studies. This concise text also contains worked examples that clearly illustrate the mathematical concepts presented and shows how they apply to physical problems.

This targeted text covers a range of topics including linear algebra, partial differential equations, power series, Sturm-Liouville theory, Fourier series, special functions, complex analysis, the Green’s function method, integral equations, and tensor analysis. This important text:

- Provides a streamlined approach to the subject by putting the focus on the mathematical topics that physical science students really need
- Offers a text that is different from the often-found definition-theorem-proof scheme
- Includes more than 150 worked examples that help with an understanding of the problems presented
- Presents a guide with more than 200 exercises with different degrees of difficulty

Written for advanced undergraduate and graduate students of physics, materials science, and engineering, Mathematical Methods in Physics, Engineering and Chemistry includes the essential methods of theoretical physics. The text is streamlined to provide only the most important mathematical concepts that apply to physical problems.

Autoren/Hrsg.

Borden, Brett

Luscombe, James

Inhaltsverzeichnis

Preface xi

1 Vectors and linear operators 1

1.1 The linearity of physical phenomena 1

1.2 Vector spaces 2

1.2.1 A word on notation 4

1.2.2 Linear independence, bases, and dimensionality 5

1.2.3 Subspaces 7

1.2.4 Isomorphism of N-dimensional spaces 8

1.2.5 Dual spaces 8

1.3 Inner products and orthogonality 10

1.3.1 Inner products 10

1.3.2 The Schwarz inequality 11

1.3.3 Vector norms 12

1.3.4 Orthonormal bases and the Gram–Schmidt process 12

1.3.5 Complete sets of orthonormal vectors 15

1.4 Operators and matrices 16

1.4.1 Linear operators 17

1.4.2 Representing operators with matrices 18

1.4.3 Matrix algebra 20

1.4.4 Rank and nullity 22

1.4.5 Bounded operators 23

1.4.6 Inverses 24

1.4.7 Change of basis and the similarity transformation 25

1.4.8 Adjoints and Hermitian operators 27

1.4.9 Determinants and the matrix inverse 29

1.4.10 Unitary operators 33

1.4.11 The trace of a matrix 35

1.5 Eigenvectors and their role in representing operators 36

1.5.1 Eigenvectors and eigenvalues 36

1.5.2 The eigenproblem for Hermitian and unitary operators 39

1.5.3 Diagonalizing matrices 40

1.6 Hilbert space: Infinite-dimensional vector space 43

Exercises 47

2 Sturm–Liouville theory 51

2.1 Second-order differential equations 52

2.1.1 Uniqueness and linear independence 52

2.1.2 The adjoint operator 55

2.1.3 Self-adjoint operator 56

2.2 Sturm–Liouville systems 57

2.3 The Sturm–Liouville eigenproblem 60

2.4 The Dirac delta function 64

2.5 Completeness 66

2.6 Recap 68

Summary 68

Exercises 69

3 Partial differential equations 71

3.1 A survey of partial differential equations 71

3.1.1 The continuity equation 71

3.1.2 The diffusion equation 72

3.1.3 The free-particle Schrödi

Über Autor(innen)

BRETT BORDEN, PHD, joined the Faculty of the Naval Postgraduate School in Monterey, CA in 2002, where he is Emeritus Professor of Physics. He served on the editorial board of the journal Inverse Problems from 2002 to 2013. Dr. Borden is a Fellow of The Institute of Physics.
JAMES LUSCOMBE, PHD, is a Professor at the Naval Postgraduate School in Monterey, California. He teaches a variety of topics, including general relativity, statistical mechanics, mathematical methods, and quantum computation.