### Synopses & Reviews

This book is intended to provide a bridge from courses in general physics to the intermediate -level courses in classical mechanics, electrodynamics and quantum mechanics. It begins with a short review of some topics in physics that are then used throughout the book to provide the physical contexts for the mathematical methods that are developed: electrostatics, electric currents, magnetic flux, simple harmonic motion, and the rigid rotor. The next chapters treat vector algebra and vector calculus; the concept of magnetic flux serves to give physical meaning to the integral theorems. A short chapter on complex numbers provides the needed background for the remainder of the text. Ordinary differential equations arise in may physical contexts; the simple harmonic oscillator serves as the illustrative example. Examples from both classical and quantum physics illustrate the chapters on partial differential equations and eigenvalue problems: the quantum harmonic oscillator and a particle in a box, a conducting sphere in a uniform field and a vibrating drum head. The eigenvalue problem leads naturally to a discussion of orthogonal functions, which again use the quantum harmonic oscillator to provide the physical insight, and to matrices, where coupled oscillators and the principal axes of a rotating rigid body provide the physical context. The text concludes with a brief discussion of variational methods and the Euler-Lagrange equation. Problems at the end of each chapter give the student experience in applying mathematical methods to the solution of physical problems. Illustrative exercises throughout provide guidance. Many of the exercises call for graphical representations, and some are particularly amenable to the use of numerical methods.

#### Review

From the reviews: The book is written nicely and can be very helpful for the students of physics who need mathematical background tailored especially for their needs. --Zentralblatt Math "Here is a bridge from courses in general physics to the intermediate-level courses in classical mechanics, electrodynamics and quantum mechanics. The author bases the mathematical discussions on specific physical problems to provide a basis for developing mathematical intuition. The text concludes with a brief discussion of variational methods and the Euler-Lagrange equation." (Meteorology and Atmospheric Physics, Vol. 84 (1-2), 2003) "The purpose of this textbook is to collect under a single cover mathematics required for mastering intermediate-level courses in classical mechanics, electricity and magnetism, and quantum mechanics. ... A set of exercises is provided for each chapter giving the student an excellent opportunity to apply mathematical apparatus for the study of physical systems. ... The book is written nicely and can be very helpful for the students of physics who need mathematical background tailored especially for their needs." (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 986, 2002)

#### Review

From the reviews:

The book is written nicely and can be very helpful for the students of physics who need mathematical background tailored especially for their needs.

--Zentralblatt Math

"Here is a bridge from courses in general physics to the intermediate-level courses in classical mechanics, electrodynamics and quantum mechanics. The author bases the mathematical discussions on specific physical problems to provide a basis for developing mathematical intuition. The text concludes with a brief discussion of variational methods and the Euler-Lagrange equation." (Meteorology and Atmospheric Physics, Vol. 84 (1-2), 2003)

"The purpose of this textbook is to collect under a single cover mathematics required for mastering intermediate-level courses in classical mechanics, electricity and magnetism, and quantum mechanics. ... A set of exercises is provided for each chapter giving the student an excellent opportunity to apply mathematical apparatus for the study of physical systems. ... The book is written nicely and can be very helpful for the students of physics who need mathematical background tailored especially for their needs." (Yuri V. Rogovchenko, Zentralblatt MATH, Vol. 986, 2002)

#### Synopsis

This book is intended to provide a mathematical bridge from a general physics course to intermediate-level courses in classical mechanics, electricity and mag- netism, and quantum mechanics. The book begins with a short review of a few topics that should be familiar to the student from a general physics course. These examples will be used throughout the rest of the book to provide physical con- texts for introducing the mathematical applications. The next two chapters are devoted to making the student familiar with vector operations in algebra and cal- culus. Students will have already become acquainted with vectors in the general physics course. The notion of magnetic flux provides a physical connection with the integral theorems of vector calculus. A very short chapter on complex num- bers is sufficient to supply the needed background for the minor role played by complex numbers in the remainder of the text. Mathematical applications in in- termediate and advanced undergraduate courses in physics are often in the form of ordinary or partial differential equations. Ordinary differential equations are introduced in Chapter 5. The ubiquitous simple harmonic oscillator is used to il- lustrate the series method of solving an ordinary, linear, second-order differential equation. The one-dimensional, time-dependent SchrOdinger equation provides an illus- tration for solving a partial differential equation by the method of separation of variables in Chapter 6.

#### Synopsis

This book is intended to provide a bridge from courses in general physics to the intermediate -level courses in classical mechanics, electrodynamics and quantum mechanics. It begins with a short review of some topics in physics that are then used throughout the book to provide the physical contexts for the mathematical methods that are developed: electrostatics, electric currents, magnetic flux, simple harmonic motion, and the rigid rotor. The next chapters treat vector algebra and vector calculus; the concept of magnetic flux serves to give physical meaning to the integral theorems. A short chapter on complex numbers provides the needed background for the remainder of the text. Ordinary differential equations arise in may physical contexts; the simple harmonic oscillator serves as the illustrative example. Examples from both classical and quantum physics illustrate the chapters on partial differential equations and eigenvalue problems: the quantum harmonic oscillator and a particle in a box, a conducting sphere in a uniform field and a vibrating drum head. The eigenvalue problem leads naturally to a discussion of orthogonal functions, which again use the quantum harmonic oscillator to provide the physical insight, and to matrices, where coupled oscillators and the principal axes of a rotating rigid body provide the physical context. The text concludes with a brief discussion of variational methods and the Euler-Lagrange equation. Problems at the end of each chapter give the student experience in applying mathematical methods to the solution of physical problems. Illustrative exercises throughout provide guidance. Many of the exercises call for graphical representations, and some are particularly amenable to the use of numerical methods.

#### Synopsis

The book provides a bridge from courses in general physics to the intermediate-level courses in classical mechanics, electrodynamics and quantum mechanics. The author bases the mathematical discussions on specific physical problems to provide a basis for developing mathematical intuition.

### Table of Contents

1. A Review / 2. Vectors / 3. Vector Calculus / 4. Complex Numbers / 5. Differential Equations / 6. Partial Differential Equations / 7. Eigenvalue Problems / 8. Orthogonal Functions / 9. Matrix Formulation of the Eigenvalue Problem / 10. Variational Principles