This book successfully blends intuition and logical reasoning. It deals with more advanced material than most textbooks of its kind but does so in a way that is accessible to advanced undergraduate audiences. It helps students understand the basic “what” and “why” questions and learn material at several levels, thus extending their capabilities. Software packages evolve and are even replaced, but the “what” and “why” questions they address are more constant. The habits needed to discern these questions will serve engineers well as they progress through their careers.For most engineering students a deductive, “theorem/proof/special case” style of exposition is alien to their ways of learning things. But most people appreciate the need to explain things that they are interested in. Sometimes, a plausibility argument is the most
accessible explanation. Most engineering graduate students need more practice with logical arguments that explain why techniques are correct or at least plausible, and this will enhance their problem-solving and communication skills.Often an example leads to its standardization in a definition or a theorem with general applicability. The style of exposition is usually inductive rather than deductive. Also, in order to not overwhelm them, I show students the difficulties gradually and often begin with analogies to familiar topics. It is precisely the students who are less well prepared who need this book the most.As Epsteen (1913) wrote, “The professor of engineering is certainly on firm ground when he takes the stand that the mathematics taught to his students should not be too abstract
on the one hand nor too concrete on the other. If the subject matter is too abstract it is unintelligible or uninteresting to the beginner; if it is too concrete the science degenerates to the mere performing of certain mechanical operations to a common tool instead of a valuable instrument.” This is still a very good guide to follow.