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This is chapters 14 and 15 of Contemporary Calculus. Chapter 14 covers double and triple integrals in rectangular, polar, cylindrical and spherical coordinates and changes of variables in those systems. Chapter 15 covers vector calculus including vector fields, divergence curl, the del operator, line integrals and the theorems of Green, Stokes and Gauss. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas. This material has been reviewed and successfully class tested.
This is a textbook for the third semester of calculus. The major topics are multiple integrals in rectangular, polar, cylindrical and spherical coordinates and vector calculus including vector fields, line integrals and the theorems of Green, Stokes and Gauss (divergence). The text has explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. Topics are typically introduced by way of applications, and the text contains the usual theorems and techniques of a third semester of calculus. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas of calculus. The exposition and problem sets have been highly rated by reviewers
This is a textbook for 4th quarter calculus covering the Vectors, Vector-Valued Functions, Functions of Several Variables, and Double Integrals. It has explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas. The exposition and problem sets have been highly rated by reviewers.
This is a textbook for differential calculus with explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. Topics are typically introduced by way of applications, and the text contains the usual theorems and techniques of a first course in calculus. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas of differential calculus. The exposition and problem sets have been highly rated by reviewers.
This is a textbook for integral calculus with explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. The definite integral is introduced by Riemann sums as a way to evaluate "signed" areas, and the text contains the usual theorems and techniques of a first course in calculus. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas of integral calculus. The exposition and problem sets have been highly rated by reviewers.
This is a textbook for 3rd quarter calculus covering the three main topics of (1) calculus with polar coordinates and parametric equations, (2) infinite series, and (3) vectors in 3D. It has explanations, examples, worked solutions, problem sets and answers. It has been reviewed by calculus instructors and class-tested by them and the author. Besides technique practice and applications of the techniques, the examples and problem sets are also designed to help students develop a visual and conceptual understanding of the main ideas. The exposition and problem sets have been highly rated by reviewers.
A print version of Chapters 0-3 from Dale Hoffman's Contemporary Calculus, an open-source calculus text. These chapters cover the concepts of differential calculus (limits, definition of derivative, differentiation rules, and applications). Newly edited and typeset in LaTeX for improved readability. March 23, 2015, printing corrects 14 minor typos and adds 40 problems. Free PDF version available at: www.contemporarycalculus.com
An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades.This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis.The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives.In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds.
With a shift toward problem-based learning and critical thinking in many health science fields, professional pharmacy training faces a shift in focus as well. Although the Accreditation Council for Pharmacy Education (ACPE) has recently suggested guidelines for problem solving to be better integrated into pharmacy curriculum, pharmacy books currently available either address this material inadequately or lack it completely. Theory and Practice of Contemporary Pharmaceutics addresses this problem by challenging pharmacy students to think critically in preparation for situations that arise in clinical practice. This book offers a wealth of up-to-date information, organized in a logical sequence, corresponding to the art and science required for formulators in industry and dispensing pharmacists in the community. It breaks down the subject to its simplest form and includes numerous examples, case studies, and problems. In addition to presenting basic scientific principles, each chapter includes a self-evaluation tutorial designed to help you evaluate your understanding of the subject matter, numerical problems that provide practice in finding mathematical solutions, and case studies that measure your overall grasp of the subject matter by challenging you to craft a plausible solution to a real-life scenario using the concepts presented in that chapter. Written by authors selected from academia, industry, and regulatory agencies, the book presents an objective and balanced view of pharmaceutical science and its application. The authors' insights are extremely helpful to pharmacy students as well as practicing pharmacists involved in the development and/or dispensation of existing and new generation biotechnology-based drug products. This simplified and user-friendly book will present pharmaceutics in a way that it has never been presented before and will help prepare students and pharmacists for the competitive and challenging nature of the professional market.
This textbook, pitched at the advanced-undergraduate to beginning-graduate level, focuses on mathematical topics of relevance in contemporary physics that are not usually covered in texts at the same level. Its main purpose is to help students appreciate and take advantage of the modern trend of very productive symbiosis between physics and mathematics. Three major areas are covered: (1) linear operators; (2) group representations and Lie algebra representations; (3) topology and differential geometry.The following are noteworthy features of this book: the style of exposition is a fusion of those common in the standard physics and mathematics literatures; the level of exposition varies from quite elementary to moderately advanced, so that the book is of interest to a wide audience; despite the diversity of the topics covered, there is a strong degree of thematic unity; much care is devoted to detailed cross-referencing so that, from any part of the book, the reader can trace easily where specific concepts or techniques are introduced.