Mathematical physics.

*(English)*Zbl 0189.33501
Addison-Wesley Series in Advanced Physics. Reading, Mass. etc.: Addison- Wesley Publishing Company. xi, 735 p. (1968).

Compared to a number of works in this field one’s attention is especially attracted in this textbook by the author’s aim and conception. The book is written for undergraduate students of physics. It contains the following 16 chapters: 1. Vectors, Matrices, and Coordinates; 2. Functions of Complex Variable; 3. Linear Differential Equations of Second Order; 4. Fourier Series; 5. The Laplace Transformation; 6. Concepts of the Theory of Distributions; 7. Fourier Transforms; 8. Partial Differential Equations; 9. Special Functions; 10. Finite-Dimensional Linear Spaces; 11. Infinite-Dimensional Vector Spaces; 12. Green’s Functions; 13. Variational Methods; 14. Traveling Waves, Radiation, Scattering; 15. Perturbation Methods; 16. Tensors.

We should observe that the author is a physicist who shows that he has a good acquaintance with classical and modern mathematics. For this reason his selection of material is interesting. The inductive approach is used in each chapter throughout the book and stress is given to the pedagogical side. Most of the chapters start with an example or discussion, with subject matter that is probably familiar to the reader. This method achieved the greatest success in the presentation of the finite and infinite vector spaces.

The book is very readable and also well suited for independent study. The question of mathematical rigor is quite important in the subject treated here. However one can notice that some more complicated questions are insufficiently clarified. It is possible that the reader may obtain the impression that these questions are easy, e.g. the branch, branch line and branch point of a multivalued function. This simplification is not easy to avoid in such a textbook. The author gives a number of cross-references which can help the reader. Perhaps the list could contain some source books on treated problems. This is undoubtedly a good book which will be most suitable for students and all who are interested in physics.

We should observe that the author is a physicist who shows that he has a good acquaintance with classical and modern mathematics. For this reason his selection of material is interesting. The inductive approach is used in each chapter throughout the book and stress is given to the pedagogical side. Most of the chapters start with an example or discussion, with subject matter that is probably familiar to the reader. This method achieved the greatest success in the presentation of the finite and infinite vector spaces.

The book is very readable and also well suited for independent study. The question of mathematical rigor is quite important in the subject treated here. However one can notice that some more complicated questions are insufficiently clarified. It is possible that the reader may obtain the impression that these questions are easy, e.g. the branch, branch line and branch point of a multivalued function. This simplification is not easy to avoid in such a textbook. The author gives a number of cross-references which can help the reader. Perhaps the list could contain some source books on treated problems. This is undoubtedly a good book which will be most suitable for students and all who are interested in physics.

Reviewer: Bogoljub Stanković (Novi Sad)

##### MSC:

26-01 | Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions |

00A06 | Mathematics for nonmathematicians (engineering, social sciences, etc.) |