George F. Simmons - Böcker

Fads are as common in mathematics as in any other human activity, and it is always difficult to separate the enduring from the ephemeral in the achievements of one’s own time. An unfortunate effect of the predominance of fads is that if a student doesn’t learn about such worthwhile topics as the wave equation, Gauss’s hypergeometric function, the gamma function, and the basic problems of the calculus of variations—among others—as an undergraduate, then he/she is unlikely to do so later. The natural place for an informal acquaintance with such ideas is a leisurely introductory course on differential equations. Specially designed for just such a course, Differential Equations with Applications and Historical Notes takes great pleasure in the journey into the world of differential equations and their wide range of applications. The author—a highly respected educator—advocates a careful approach, using explicit explanation to ensure students fully comprehend the subject matter.With an emphasis on modeling and applications, the long-awaited Third Edition of this classic textbook presents a substantial new section on Gauss’s bell curve and improves coverage of Fourier analysis, numerical methods, and linear algebra. Relating the development of mathematics to human activity—i.e., identifying why and how mathematics is used—the text includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout. Provides an ideal text for a one- or two-semester introductory course on differential equations Emphasizes modeling and applications Presents a substantial new section on Gauss’s bell curve Improves coverage of Fourier analysis, numerical methods, and linear algebra Relates the development of mathematics to human activity—i.e., identifying why and how mathematics is used Includes a wealth of unique examples and exercises, as well as the author’s distinctive historical notes, throughout Uses explicit explanation to ensure students fully comprehend the subject matter Outstanding Academic Title of the Year, Choice magazine, American Library Association.

Calculus Gems, a collection of essays written about mathematicians and mathematics, is a spin-off of two appendices (""Biographical Notes"" and ""Variety of Additional Topics"") found in Simmons' 1985 calculus book. With many additions and some minor adjustments, the material will now be available in a separate softcover volume. The text is suitable as a supplement for a calculus course and/or a history of mathematics course, The overall aim is bound up in the question, ""What is mathematics for?"" and in Simmons' answer, ""To delight the mind and help us understand the world"". The essays are independent of one another, allowing the instructor to pick and choose among them. Part A, ""Brief Lives"", is a biographical history of mathematics from earliest times (Thales, 625-547 BC) through the late 19th century (Weierstrass, 1815-1897) that serves to connect mathematics to the broader intellectual and social history of Western civilization. Part B, ""Memorable Mathematics"", is a collection of interesting topics from number theory, geometry, and science arranged in an order roughly corresponding to the order of most calculus courses. Some of these sections have a few problems for the student to solve. Students can gain perspective on the mathematical experience and learn some mathematics not contained in the usual courses, and instructors can assign student papers and projects based on the essays. The book teaches by example that mathematics is more than computation. Original illustrations of influential mathematicians in history and their inventions accompany the brief biographies and mathematical discussions.