Short Calculus

From the reviews "This is a reprint of the original edition of Lang's ‘A First Course in Calculus', which was first published in 1964....The treatment is ‘as rigorous as any mathematician would wish i

Nearly two generations of undergraduate social science and business majors are grateful to Gemignani for this text that works through the basics of calculus asking for no more preparation than high sc

This second edition retains the positive features of being clearly written, well organized, and incorporating calculus in the text, while adding expanded coverage on game theory, experimental economics, and behavioural economics. It remains more focused and manageable than similar textbooks, and provides a concise yet comprehensive treatment of the core topics of microeconomics, including theories of the consumer and of the firm, market structure, partial and general equilibrium, and market failures caused by public goods, externalities and asymmetric information. The book includes helpful solved problems in all the substantive chapters, as well as over seventy new mathematical exercises and enhanced versions of the ones in the first edition. The authors make use of the book's full color with sharp and helpful graphs and illustrations. This mathematically rigorous textbook is meant for students at the intermediate level who have already had an introductory course in microeconomics, and

This second edition retains the positive features of being clearly written, well organized, and incorporating calculus in the text, while adding expanded coverage on game theory, experimental economics, and behavioural economics. It remains more focused and manageable than similar textbooks, and provides a concise yet comprehensive treatment of the core topics of microeconomics, including theories of the consumer and of the firm, market structure, partial and general equilibrium, and market failures caused by public goods, externalities and asymmetric information. The book includes helpful solved problems in all the substantive chapters, as well as over seventy new mathematical exercises and enhanced versions of the ones in the first edition. The authors make use of the book's full color with sharp and helpful graphs and illustrations. This mathematically rigorous textbook is meant for students at the intermediate level who have already had an introductory course in microeconomics, and

This book provides a concise treatment of the core concepts of microeconomic theory at the intermediate level with calculus integrated into the text. The authors, Roberto Serrano and Allan M. Feldman,

This book provides a concise treatment of the core concepts of microeconomic theory at the intermediate level with calculus integrated into the text. The authors, Roberto Serrano and Allan M. Feldman,

Originally published in 1926, this book was written to provide mathematical and scientific students with an introduction to the subject of integral calculus. The text was largely planned around the syllabus for the Higher Certificate Examination. A short historical survey is included. This book will be of value to anyone with an interest in integral calculus, mathematics and the history of education.

For each section of Stewart's Multivariable text, the Study Guide provides students with a brief introduction, a short list of concepts to master, as well as summary and focus questions with explained

For each section of Stewart's Single Variable text, the Study Guide provides students with a brief introduction, a short list of concepts to master, as well as summary and focus questions with explain

For each section of Stewart's Multivariable text, the Study Guide provides students with a brief introduction, a short list of concepts to master, as well as summary and focus questions with explained

For each section of Stewart's Single Variable text, the Study Guide provides a brief introduction, a short list of concepts to master, as well as summary and focus questions with explained answers. It

In this short monograph Newton-likeand other similar numerical methods with applications to solving multivariateequations are developed, which involve Caputotype fractional mixed partial derivatives a

For each section of the text, the Study Guide provides students with a brief introduction, a short list of concepts to master, as well as summary and focus questions with explained answers. The Study

Calculus Success in 20 Minutes a Day gives students tools to master essential skills in short, easy-to-manage lessons. Whether you're preparing for exams, tackling homework problems, or trying to refr

In Infinite Ascent, David Berlinski, the acclaimed author of The Advent of the Algorithm, A Tour of the Calculus, and Newton’s Gift, tells the story of mathematics, bringing to life with wit, elegance

本書序言This text is intended for a calculus-based introductory physics course for science and engineering students. Ideally,students should have completed one semester of calculus. However, calculus may also be taken concurrently. Derivativesare used sparingly in the early chapters in Mechanics, and integrals appear for the first time in Chapter 7 (Work and Energy)but are not crucial for the understanding of basic concepts.This 4th. edition of University Physics incorporates several changes meant to enhance the appeal and effectiveness of thetext and includes several new applications of Physics in Science, Engineering and everyday life. Despite the addition of newmaterial this 4th. edition remains relatively short.Now to This Edition● New Layout: The page layout and artwork have been revamped and updated.● Self-Test: each chapter now includes a short Self-Test with complete solutions provided at the back of the book. This feature is meant to give the student some feedback on how well the

This concise textbook, designed specifically for a one-semester course in astrophysics, introduces astrophysical concepts to undergraduate science and engineering students with a background in college-level, calculus-based physics. The text is organized into five parts covering: stellar properties; stellar structure and evolution; the interstellar medium and star/planet formation; the Milky Way and other galaxies; and cosmology. Structured around short easily digestible chapters, instructors have flexibility to adjust their course's emphasis as it suits them. Exposition drawn from the author's decade of teaching his course guides students toward a basic but quantitative understanding, with 'quick questions' to spur practice in basic computations, together with more challenging multi-part exercises at the end of each chapter. Advanced concepts like the quantum nature of energy and radiation are developed as needed. The text's approach and level bridge the wide gap between introductory a

This concise textbook, designed specifically for a one-semester course in astrophysics, introduces astrophysical concepts to undergraduate science and engineering students with a background in college-level, calculus-based physics. The text is organized into five parts covering: stellar properties; stellar structure and evolution; the interstellar medium and star/planet formation; the Milky Way and other galaxies; and cosmology. Structured around short easily digestible chapters, instructors have flexibility to adjust their course's emphasis as it suits them. Exposition drawn from the author's decade of teaching his course guides students toward a basic but quantitative understanding, with 'quick questions' to spur practice in basic computations, together with more challenging multi-part exercises at the end of each chapter. Advanced concepts like the quantum nature of energy and radiation are developed as needed. The text's approach and level bridge the wide gap between introductory a

After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems current

Maple is a powerful symbolic computation system that is widely used in universities around the world. This short introduction gives readers an insight into the rules that control how the system works, and how to understand, fix, and avoid common problems. Topics covered include algebra, calculus, linear algebra, graphics, programming, and procedures. Each chapter contains numerous illustrative examples, using mathematics that does not extend beyond first-year undergraduate material. Maple worksheets containing these examples are available for download from the author's personal website. The book is suitable for new users, but where advanced topics are central to understanding Maple they are tackled head-on. Many concepts which are absent from introductory books and manuals are described in detail. With this book, students, teachers and researchers will gain a solid understanding of Maple and how to use it to solve complex mathematical problems in a simple and efficient way.

This is a short tract on the essentials of differential and symplectic geometry together with a basic introduction to several applications of this rich framework: analytical mechanics, the calculus of

By the end of the eighteenth century, British mathematics had been stuck in a rut for a hundred years. Calculus was still taught in the style of Newton, with no recognition of the great advances made in continental Europe. The examination system at Cambridge even mandated the use of Newtonian notation. As discontented undergraduates, Charles Babbage (1791–1871) and John Herschel (1792–1871) formed the Analytical Society in 1811. The group, including William Whewell and George Peacock, sought to promote the new continental mathematics. Babbage's preface to the present work, first published in 1813, may be considered the movement's manifesto. He provided the first paper here, and Herschel the two others. Although the group was relatively short-lived, its ideas took root as its erstwhile members rose to prominence. As the society's sole publication, this remains a significant text in the history of British mathematics.

This comprehensive guide to stochastic processes gives a complete overview of the theory and addresses the most important applications. Pitched at a level accessible to beginning graduate students and researchers from applied disciplines, it is both a course book and a rich resource for individual readers. Subjects covered include Brownian motion, stochastic calculus, stochastic differential equations, Markov processes, weak convergence of processes and semigroup theory. Applications include the Black–Scholes formula for the pricing of derivatives in financial mathematics, the Kalman–Bucy filter used in the US space program and also theoretical applications to partial differential equations and analysis. Short, readable chapters aim for clarity rather than full generality. More than 350 exercises are included to help readers put their new-found knowledge to the test and to prepare them for tackling the research literature.

Since the 1970s social scientists and scientists in a variety of fields - psychology, sociology, education, psychiatry, economics and engineering - have been interested in problems that require the statistical analysis of data over time and there has been in effect a conceptual revolution in ways of thinking about pattern and regularity. This book is a comprehensive introduction to all the major time-series techniques, both time-domain and frequency-domain. It includes work on linear models that simplify the solution of univariate and multivariate problems. The author begins with a non-mathematical overview: throughout, he provides easy-to-understand, fully worked examples drawn from real studies in psychology and sociology. Other, less comprehensive, books on time-series analysis require calculus: this presupposes only a standard introductory statistics course covering analysis of variance and regression. The chapters are short, designed to build concepts (and the reader's confidence)

When Gottfried Wilhelm Leibniz first arrived in Paris in 1672 he was a well-educated, sophisticated young diplomat who had yet to show any real sign of his latent mathematical abilities. Over his next four crowded, formative years, which Professor Hofmann analyses in detail, he grew to be one of the outstanding mathematicians of the age and to found the modern differential calculus. In Paris, Leibniz rapidly absorbed the advanced exact science of the day. During a short visit to London in 1673 he made a fruitful contact with Henry Oldenburg, the secretary of the Royal Society, who provided him with a wide miscellany of information regarding current British scientific activities. Returning to Paris, Leibniz achieved his own first creative discoveries, developing a method of integral `transmutation' through which lie derived the 'arithmetical' quadrature of the circle by an infinite series. He also explored the theory of algebraic equations. Later, by codifying existing tangent and quadr

This text for undergraduates was designed as a short introductory course to give students the tools of vector algebra and calculus, as well as a brief glimpse into the subjects' manifold applications.

Now in its third edition, Mathematical Concepts in the Physical Sciences, 3rd Edition provides a comprehensive introduction to the areas of mathematical physics. It combines all the essential math concepts into one compact, clearly written reference.This book is intended for students who have had a two-semester or three-semester introductory calculus course. Its purpose is to help students develop, in a short time, a basic competence in each of the many areas of mathematics needed in advanced courses in physics, chemistry, and engineering. Students are given sufficient depth to gain a solid foundation (this is not a recipe book). At the same time, they are not overwhelmed with detailed proofs that are more appropriate for students of mathematics. The emphasis is on mathematical methods rather than applications, but students are given some idea of how the methods will be used along with some simple applications.

This book explains the theory and methods by which gas molecules can be polarized by light, a subject of considerable importance for what it tells us about the electronic structure of molecules and properties of chemical reactions. Starting with a brief review of molecular angular momentum, the text goes on to consider resonant absorption, fluorescence, photodissociation and photoionization, as well as collisions and static fields. A variety of macroscopic effects are considered, among them angular distribution and the polarization of emitted light, ground state depopulation, laser-induced dichroism, the effect of collisions and external magnetic and electric field effects. Most examples in the book are for diatomic molecules, but symmetric-top polyatomic molecules are also included. The book concludes with a short appendix of essential formulae, tables for vector calculus, spherical functions, Wigner rotation matrices, Clebsch-Gordan coefficients, and methods for expansion over irredu

This book is meant as a short text in linear algebra for a one-term course. Except for an occasional example or exercise the text is logically independent of calculus, and could be taught early. In pr

This is a lively textbook providing a solid introduction to financial option valuation for undergraduate students armed with a working knowledge of a first year calculus. Written in a series of short chapters, its self-contained treatment gives equal weight to applied mathematics, stochastics and computational algorithms. No prior background in probability, statistics or numerical analysis is required. Detailed derivations of both the basic asset price model and the Black–Scholes equation are provided along with a presentation of appropriate computational techniques including binomial, finite differences and in particular, variance reduction techniques for the Monte Carlo method. Each chapter comes complete with accompanying stand-alone MATLAB code listing to illustrate a key idea. Furthermore, the author has made heavy use of figures and examples, and has included computations based on real stock market data.

In this short and very practical 2002 introduction to econometrics Philip Hans Franses guides the reader through the essential concepts of econometrics. Central to the book are practical questions in various economic disciplines, which can be answered using econometric methods and models. The book focuses on a limited number of the essential, most widely used methods, before going on to review the basics of econometrics. The book ends with a number of case studies drawn from recent empirical work to provide an intuitive illustration of what econometricians do when faced with practical questions. Throughout the book Franses emphasises the importance of specification, evaluation and implementation of models appropriate to the data. Assuming basic familiarity only with matrix algebra and calculus the book is designed to appeal as either a short stand-alone introduction for students embarking on an empirical research project or as a supplement to any standard introductory textbook.

Written for a broad audience of students in mathematics, computer science, operations research, statistics, and engineering, this textbook presents a short, lively survey of several fascinating non-calculus topics in modern applied mathematics. Coverage includes probability, mathematical finance, graphs, linear programming, statistics, computer science algorithms, and groups. A key feature is the abundance of interesting examples not normally found in standard finite mathematics courses, such as options pricing and arbitrage, tournaments, and counting formulas. The author assumes a level of mathematical sophistication at the beginning calculus level, that is, students should have had at least a course in pre-calculus, and the added sophistication attained from studying calculus would be useful.

本書是經典力學領域的經典著作，預備知識要求極低，僅需基礎微積分和本科基礎物理學知識，因此適合本科到研究生入門階段的課程使用，也適合數學、物理和工程專業的學生群體。This is an intuitively motivated presentation ofmany topics in classical mechanics and related areas of control theory and calculus of variations. All topics throughout the book are treated with zero tolerance for unrevealing definitions and for proofs which leave the reader in the dark. Some areas of particular interest are： an extremely short derivation of the ellipticity of planetary orbits; a statement and an explanation of the “tennis racket paradox”; a heuristic explanation (and a rigorous treatment) of the gyroscopic effect; a revealing equivalence between thedynamics of a particle and statics of a spring; a short geometrical explanation of Pontryagin’s Maximum Principle, and more. In the last chapter, aimed at more advanced readers, the Hamiltonian and the momentum are compared to forces in a certain static problem. This gives a palpable physical meaning to some seemingly abstract concepts and theo