Educators and publishers are increasingly concerned with the rising demand for engineers. Their answer to the problem is greater proficiency in the training of science students by speeding up the introduction of specialty courses (particularly mathematics, the basic prerequisite) during the freshman year. "Unified" and "Integrated" courses give the departments of science and engineering an early hold on the student during his most formative years.
The present, unified text not only reviews just about every important phase of algebra, while actually developing analytical geometry, but it introduces and develops trigonometry simultaneously. And while the student becomes acquainted with the necessary mathematical tools, his imagination is stimulated by numerous references to such fields as chemistry, physics, astronomy, statics, dynamics, ballistics, and statistics. Add to these some calculus in later chapters and you have a "practical" volume that must inevitably lead to familiarity with the basic concepts and notions in those fields. Many topics from geometry help refresh the students' memory and advanced notation is employed whenever feasible. The first chapter alone introduces the summation symbol, first and second derivative notation, substitution for upper and lower limits, functions of one or more variables, the scientific notation of numbers, approximate numbers and errors, and the use of formulas through substitution of decimal values. Later chapters include vectors, infinite series, limits, determinants, even spherical and cylindrical coordinates and the book closes with an entire chapter on probability and statistics.
A good teacher, well versed in the many fields from which the author draws, can make such a course a great experience for the college freshman. He can select from two thousand individual exercises and stimulate class-room discussion by extensive use of three hundred "Questions for Discussion" which are distributed throughout the book; they provide a novel answer to the request of Modern Education to supplant formal lectures by informal discussion, even ill mathematics courses. The great diversity of all this material appears sometimes forcibly constrained into catch-all chapters and may make this a difficult volume to teach. Given a mature and experienced teacher, however, a course based upon this text will enable even the many inadequately prepared college freshmeu of today to enter as early as in their second semester into their respective fields of specialization--indeed a major accomplishment.
Some chapters may appear over-saturated with concepts and definitions from applied fields and thus confuse the beginner. Alert students, however, will be quick to discover the only real weakness which is wlde-spread in similar texts: many diagrams are presented without proper scales or even drawn out of proportion (Fig. 12.17 at the origin, 12.19 at the asymptotes, etc.). In addition, there is the usual crop of mistakes, unavoidably encountered in a first printing. Taking everything into consideration, the volume shows that author and publisher have jointly succeeded in taking some steps in the right direction toward a successful text.
CARL HAMMER