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The title of this book gives the clue to our main aim, which is to initiate the reader into the realm of differential and integral calculus and, by applying these methods to the more important divisions of physics, to demonstrate the significance and power of higher mathematics.
In this book, the student is regarded as a friend and ally who puts his faith in the teacher and the textbook and wishes ardently to make use of and apply to nature and technology the mathematical techniques offered to him. Comprehension of the subject expands as the result of analyzing examples and applications. In the strictly logical approach, the question of the significance and usefulness of the theorems studied remains in the background. In the present text, by contrast, we bring to the fore the mathematical ideas and their relationship with the study of nature.
The notorious pitting of poets against physicists (mathematicians too) is a figment of the imagination of the poet B. Slutsky. In mathematics there is more poetry than any poet ever imagined. The history of science is proof that good mathematics is prophetic: mathematical analysis of the known opens up the path into the realm of the unknown and leads to new physical notions.
In “Higher Mathematics for Beginners” I strove towards a constructive approach, to the eliciting of the meaning and aims of mathe¬matical concepts and attempted, at least in part, to convey the spirit of the heroic period when these notions were born.
The last two chapters (Dirac’s Remarkable Delta Function and What Next) are entirely different from the remainder of the book. The style too is quite changed. The aim there is to give the reader a feeling (of necessity, very superficial) of what complicated things lie ahead