Calculus: Concepts and Methods

Author: Ken Binmore
Publisher: Cambridge University Press
ISBN: 1139643622
Category : Mathematics
Languages : en
Pages : 574

Book Description
The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science.

Methods of Mathematics Applied to Calculus, Probability, and Statistics

Author: Richard W. Hamming
Publisher: Courier Corporation
ISBN: 0486138879
Category : Mathematics
Languages : en
Pages : 882

Book Description
This 4-part treatment begins with algebra and analytic geometry and proceeds to an exploration of the calculus of algebraic functions and transcendental functions and applications. 1985 edition. Includes 310 figures and 18 tables.

Calculus

Author: K. G. Binmore
Publisher:
ISBN: 9780521247719
Category : Mathematics
Languages : en
Pages : 488

Book Description
This book is concerned with the calculus of several variables and provides an introduction to elementary differential and difference equations. The emphasis is on practical problem-solving rather than the proof of formal theorems. Many worked examples are supplied as well as problems for the student to solve, together with their solutions. The techniques are illustrated with applications drawn chiefly from economics, statistics and operational research. Some elementary knowledge of the calculus of one variable is assumed but revision material is supplied throughout the text. A confident approach to problem-solving is not possible without some understanding of the background theory. In this book the theory is presented systematically but informally. Wherever possible, geometric arguments are used and the text is illustrated with numerous diagrams. Particular care has been taken to make the main body of the text suitable for students who are studying independently of a taught course. The book will interest students at universities and other higher education institutions. At the London School of Economics, the course on which this book is based is attended by students reading for a variety of different degrees and with a wide disparity in their previous levels of mathematical training. Some are graduates and some are first-year undergraduates. It is hoped that this book will attract a similar audience: not only of economists, statisticians and other social scientists but also physical scientists, engineers and mathematicians.

Mathematics for Economics and Finance

Author: Martin Anthony
Publisher: Cambridge University Press
ISBN: 1139643266
Category : Mathematics
Languages : en
Pages : 414

Book Description
Mathematics has become indispensable in the modelling of economics, finance, business and management. Without expecting any particular background of the reader, this book covers the following mathematical topics, with frequent reference to applications in economics and finance: functions, graphs and equations, recurrences (difference equations), differentiation, exponentials and logarithms, optimisation, partial differentiation, optimisation in several variables, vectors and matrices, linear equations, Lagrange multipliers, integration, first-order and second-order differential equations. The stress is on the relation of maths to economics, and this is illustrated with copious examples and exercises to foster depth of understanding. Each chapter has three parts: the main text, a section of further worked examples and a summary of the chapter together with a selection of problems for the reader to attempt. For students of economics, mathematics, or both, this book provides an introduction to mathematical methods in economics and finance that will be welcomed for its clarity and breadth.

Advanced Calculus (Revised Edition)

Author: Lynn Harold Loomis
Publisher: World Scientific Publishing Company
ISBN: 9814583952
Category : Mathematics
Languages : en
Pages : 595

Book Description
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.

Calculus Made Easy

Author: Silvanus Phillips Thompson
Publisher:
ISBN:
Category : Calculus
Languages : en
Pages : 200

Book Description

Calculus for Everyone

Author: Mitch Stokes
Publisher:
ISBN: 9781944482541
Category : Mathematics
Languages : en
Pages : 0

Book Description
This book is for only two kinds of people: those who are interested in science and math, and those who aren't. And so, motivated by this powerful idea, Calculus for Everyone presents the mathematics of change in an extremely effective way for anyone with a first-year course in algebra. Yet it does so without dumbing calculus down. In fact, Calculus for Everyone is not only for students who would have never dreamt of taking calculus, it is also for those who have already taken a standard calculus course, as well as for those who will go on to take such a course Based on more than a decade of classroom experience, this book provides mastery of calculus's core by focusing on the foundational concepts of limits, derivatives, and integrals, explaining how all three are united in the fundamental theorem of calculus. Moreover, Calculus for Everyone explains how the story of calculus is central to Western culture, from Plato in ancient Greece, to today's modern physics. Indeed, this book explains why calculus is needed at all-and why it is needed so badly. By mastering the core of calculus-as well as seeing its meaning and significance-students will not only better understand math and science in general, but contemporary culture and their place in it.

Teaching and Learning of Calculus

Author: David Bressoud
Publisher: Springer
ISBN: 3319329758
Category : Education
Languages : en
Pages : 44

Book Description
This survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.

Mathematics for Physicists

Author: Alexander Altland
Publisher: Cambridge University Press
ISBN: 1108651151
Category : Science
Languages : en
Pages : 723

Book Description
This textbook is a comprehensive introduction to the key disciplines of mathematics - linear algebra, calculus, and geometry - needed in the undergraduate physics curriculum. Its leitmotiv is that success in learning these subjects depends on a good balance between theory and practice. Reflecting this belief, mathematical foundations are explained in pedagogical depth, and computational methods are introduced from a physicist's perspective and in a timely manner. This original approach presents concepts and methods as inseparable entities, facilitating in-depth understanding and making even advanced mathematics tangible. The book guides the reader from high-school level to advanced subjects such as tensor algebra, complex functions, and differential geometry. It contains numerous worked examples, info sections providing context, biographical boxes, several detailed case studies, over 300 problems, and fully worked solutions for all odd-numbered problems. An online solutions manual for all even-numbered problems will be made available to instructors.

Calculus of Variations

Author: I. M. Gelfand
Publisher: Courier Corporation
ISBN: 0486135012
Category : Mathematics
Languages : en
Pages : 260

Book Description
Fresh, lively text serves as a modern introduction to the subject, with applications to the mechanics of systems with a finite number of degrees of freedom. Ideal for math and physics students.