Basic Insights in Vector Calculus provides an introduction to three famous theorems of vector calculus, Green's theorem, Stokes' theorem and the divergence theorem (also known as Gauss's theorem). Material is presented so that results emerge in a natural way. As in classical physics, we begin with descriptions of flows.The book will be helpful for undergraduates in Science, Technology, Engineering and Mathematics, in programs that require vector calculus. At the same time, it also provides some of the mathematical background essential for more advanced contexts which include, for instance, the physics and engineering of continuous media and fields, axiomatically rigorous vector analysis, and the mathematical theory of differential forms.There is a Supplement on mathematical understanding. The approach invites one to advert to one's own experience in mathematics and, that way, identify elements of understanding that emerge in all levels of learning and teaching.Prerequisites are competence in single-variable calculus. Some familiarity with partial derivatives and the multi-variable chain rule would be helpful. But for the convenience of the reader we review essentials of single- and multi-variable calculus needed for the three main theorems of vector calculus.Carefully developed Problems and Exercises are included, for many of which guidance or hints are provided.

In modern physics, various fundamental problems have become topics of ongoing debate. There was the 20th century climb to a Standard Model, still accurate at the highest energy levels obtainable so far. But, since the 1970's, a different approach to physics advocates for theories such as string theory, known for their mathematical elegance, even though they either cannot be verified in data or contradict presently known experimental results. In philosophy of physics, there is a gradually emerging consensus that philosophy of physics and physics somehow contribute to a common enterprise. But, there is little sign of progress toward consensus about the nature of that unity. All the while, it is generally recognized that physics is interdisciplinary. There are, of course, differences in focus. But, implicitly at least, there are no 'sharp dividing lines' between physics and philosophy of physics; pure and applied physics; physical chemistry; biophysics; medical physics; history and philosophy of physics; physics and society; physics education; and so on. What, then, is progress in physics? The question here is not about ideal structures, but asks about what is going on in physics. Beginnings in discerning the presence of eight main tasks help reveal the (pre-) emergence of a normative omni-disciplinary basis for collaboration that, once adverted to, promises to be constitutive of a new and increasingly effective control of meaning. Originally discovered by Bernard Lonergan in 1965, progress in the new collaboration will not seek to eliminate specialized expertise. It will, though, divide tasks within an eightfold functional division of labor. This book invites attention to data for each of the eight main tasks evident and self-evident in existing scholarship in the community. The book also makes preliminary efforts toward envisioning something of what functional collaboration will look like - in physics, the Academy and Society.

Bernard Lonergan identified the need and possibility of what he called 'generalized empirical method' in science and philosophy. Implementation will be a future community achievement. The book enters into details of a selection of examples in the sciences and philosophy of science. These are provided not to engage in, or blend the present aim with traditional philosophical debate, but as points of entry to help reveal the possibility and need of balanced empirical method. Taking words of Lonergan: '(Q)uestions of method are practical. So my purpose in these (chapters) is not to demonstrate what is necessary. It is not to forecast what is probable. It is ... to invite you to share in the exploration of a proposal' (Bernard Lonergan, A Third Collection (1985), 114). The main examples are drawn from biochemistry and biology, although heuristics envisioned will include all sciences.

This book serves as an advanced text on fisheries and fishery population dynamics and as a reference for fisheries scientists. It provides a thorough treatment of contemporary topics in quantitative fisheries science and emphasizes the link between biology and theory by explaining the assumptions inherent in the quantitative methods. The analytical methods are accessible to a wide range of biologists, and the book includes numerous examples. The book is unique in covering such advanced topics as optimal harvesting, migratory stocks, age-structured models, and size models.