Field Theory Handbook: Coordinate Systems & Differential Equations

In this review of Field Theory Handbook: Including Coordinate Systems, Differential Equations and Their Solutions the reviewer finds a dense, reference-focused compendium best suited to practicing physicists and engineers. The book's single biggest strength is its systematic tabulation of coordinate systems and separated forms of the Laplace and Helmholtz equations, making it a quick lookup for applied problems. This is not a classroom textbook; instead it is a practical reference that compiles separation equations and their solutions across many geometries for direct use in electrostatics, magnetostatics, heat flow, acoustics and related classical-field problems.

Key Features

• Comprehensive coordinate tables: The book tabulates properties of 40 coordinate systems so practitioners can locate the coordinate relations they need without scanning multiple sources.
• Equation coverage: It states the Laplace and Helmholtz equations in each coordinate system, which speeds up problem setup for separation of variables.
• Separation solutions: The text provides separation equations and their solutions so readers can follow the standard method for solving boundary-value problems.
• Wide application scope: Examples and tabulations are arranged for use across electrostatics, magnetostatics, heat flow, diffusion, optics and acoustics, supporting multidisciplinary work.
• Reference tone: Its compendium format focuses on ready access to formulas rather than pedagogical development, saving time for experienced users.

Who It's For

Field Theory Handbook is aimed at practicing scientists and engineers who regularly solve partial differential equations and need a compact reference of coordinate systems and separated forms of the Laplace and Helmholtz equations. Those working in classical electrodynamics, heat transfer, acoustics, gravitation or diffusion will find the compiled solutions directly applicable to boundary-value problems.

It is not intended for introductory learners or readers seeking a modern textbook treatment: the book does not teach relativity or quantum mechanics and does not serve as a step-by-step pedagogical course. Students new to separation of variables should pair it with a classroom text for conceptual grounding.

Pros & Cons

Pros

• Extensive listing of 40 coordinate systems makes it easy to find uncommon coordinate representations.
• Concise presentation of the Laplace and Helmholtz equations in each system saves derivation time.
• Includes separated equations and their solutions, which is useful for direct application to real problems.

Cons

• Not a textbook: limited pedagogical explanation means it can be terse for readers unfamiliar with separation methods.

Specifications

Title	Field Theory Handbook: Including Coordinate Systems, Differential Equations and Their Solutions
Authors	P. Moon, D. E. Spencer
Scope	Tabulation of coordinate systems and separated equations for classical fields
Equations covered	Laplace equation; Helmholtz equation
Coordinate systems	Properties of 40 coordinate systems
Applications	Electrostatics, magnetostatics, heat flow, diffusion, optics, acoustics, gravitation

Our Verdict

For professionals who need a compact, authoritative list of coordinate systems and the separated forms of Laplace and Helmholtz equations, this handbook is excellent value and a time-saver. It is best purchased as a reference companion to applied work; those seeking tutorial explanations or coverage of relativistic and quantum topics should look elsewhere.

Frequently Asked Questions

Does this book include solutions for separation of variables?
The book provides the separation equations and their solutions for each coordinate system covered.

Is this suitable as a classroom textbook?
No, the handbook is a compendium and not a textbook; it lacks pedagogical development and is intended as a reference.

What fields does this handbook support?
It is applicable to electrostatics, magnetostatics, electric currents, heat flow, diffusion, optics, acoustics and gravitation.