The History of the Priority Di∫pute between Newton and Leibniz

 

This book provides a thrilling history of the famous priority dispute between Gottfried Wilhelm Leibniz and Isaac Newton, presenting the episode for the first time in the context of cultural history. It introduces readers to the background of the dispute, details its escalation, and discusses the aftermath of the big divide, which extended well into rThe Early Challengesnd the story is very intelligibly explained – an approach that offers general readers interested in the history of sciences and mathematics a window into the world of these two giants in their field. 

From the epilogue to the German edition by Eberhard Knobloch:
Thomas Sonar has traced the emergence and the escalation of this conflict, which was heightened by Leibniz’s rejection of Newton’s gravitation theory, in a grandiose, excitingly written monograph. With absolute competence, he also explains the mathematical context so that non-mathematicians will also profit from the book. Quod erat demonstrandum!

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3000 Years of Analysis

 

What exactly is analysis? What are infinitely small or infinitely large quantities? What are indivisibles and infinitesimals? What are real numbers, continuity, the continuum, differentials, and integrals?

You’ll find the answers to these and other questions in this unique book! It explains in detail the origins and evolution of this important branch of mathematics, which Euler dubbed the “analysis of the infinite.” A wealth of diagrams, tables, color images and figures serve to illustrate the fascinating history of analysis from Antiquity to the present. Further, the content is presented in connection with the historical and cultural events of the respective epochs, the lives of the scholars seeking knowledge, and insights into the subfields of analysis they created and shaped, as well as the applications in virtually every aspect of modern life that were made possible by analysis.

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Estallido en los andes

 

 

Estallido en los andes es un libro que aborda, para nuestra generación universitaria uno de los mayores episodios de efervescencia social en el  Perú. El texto tiene una importancia ambivalente, de forme y de fondo, no solo interesa el momento histórico en el que se sitúa, sino también la forma en que lo hace. Atañe a un carácter fundamental de las CC.SS., preguntarse por lo vivido, esforzarse por comprender que ha sucedido. Gestado desde una visión académica, no peca de academicista, el léxico es liviano y utiliza unas herramientas que es importante a mi parecer e incluso podría ser parte de estudios posteriores, hablo de las herramientas testimoniales para encausar su relato y lectura. El contenido del libro presenta 4 capítulos y una reflexión final (pero no conclusión) titulada tiempos de Pachacuti.

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Fundamentals of Mathematical Analysis (Adel N. Boules)

 

Fundamentals of Mathematical Analysis explores real and functional analysis with a substantial component on topology. The three leading chapters furnish background information on the real and complex number fields, a concise introduction to set theory, and a rigorous treatment of vector spaces.

Fundamentals of Mathematical Analysis is an extensive study of metric spaces, including the core topics of completeness, compactness and function spaces, with a good number of applications. The later chapters consist of an introduction to general topology, a classical treatment of Banach and Hilbert spaces, the elements of operator theory, and a deep account of measure and integration theories. Several courses can be based on the book. This book is suitable for a two-semester course on analysis, and material can be chosen to design one-semester courses on topology or real analysis. It is designed as an accessible classical introduction to the subject and aims to achieve excellent breadth and depth and contains an abundance of examples and exercises. The topics are carefully sequenced, the proofs are detailed, and the writing style is clear and concise. The only prerequisites assumed are a thorough understanding of undergraduate real analysis and linear algebra, and a degree of mathematical maturity.

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Fundamental Mathematical Analysis (Robert Magnus)

 

This textbook offers a comprehensive undergraduate course in real analysis in one variable. Taking the view that analysis can only be properly appreciated as a rigorous theory, the book recognises the difficulties that students experience when encountering this theory for the first time, carefully addressing them throughout.

Historically, it was the precise description of real numbers and the correct definition of limit that placed analysis on a solid foundation. The book therefore begins with these crucial ideas and the fundamental notion of sequence. Infinite series are then introduced, followed by the key concept of continuity. These lay the groundwork for differential and integral calculus, which are carefully covered in the following chapters. Pointers for further study are included throughout the book, and for the more adventurous there is a selection of "nuggets", exciting topics not commonly discussed at this level. Examples of nuggets include Newton's method, the irrationality of π, Bernoulli numbers, and the Gamma function.

Based on decades of teaching experience, this book is written with the undergraduate student in mind. A large number of exercises, many with hints, provide the practice necessary for learning, while the included "nuggets" provide opportunities to deepen understanding and broaden horizons.

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Calculus: A Complete Course, 9th edition (Robert A. Adams Christopher Essex)

 

Proven in North America and abroad, this classic text has earned a reputation for excellent accuracy and mathematical rigour.  Previous editions have been praised for providing complete and precise statements of theorems, using geometric reasoning in applied problems, and for offering a range of applications across the sciences.  Written in a clear, coherent, and readable form, Calculus: A Complete Course makes student comprehension a clear priority.

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How to Solve Word Problems in Calculus

 

Considered to be the hardest mathematical problems to solve, word problems continue to terrify students across all math disciplines. This new title in the World Problems series demystifies these difficult problems once and for all by showing even the most math-phobic readers simple, step-by-step tips and techniques. How to Solve World Problems in Calculus reviews important concepts in calculus and provides solved problems and step-by-step solutions. Once students have mastered the basic approaches to solving calculus word problems, they will confidently apply these new mathematical principles to even the most challenging advanced problems. Each chapter features an introduction to a problem type, definitions, related theorems, and formulas. Topics range from vital pre-calculus review to traditional calculus first-course content. Sample problems with solutions and a 50-problem chapter are ideal for self-testing. Fully explained examples with step-by-step solutions.

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Infinite Powers: How Calculus Reveals the Secrets of the Universe

 

A brilliant and endlessly appealing explanation of calculus—how it works and why it makes our lives immeasurably better.

Without calculus, we wouldn’t have cell phones, TV, GPS, or ultrasound. We wouldn’t have unraveled DNA or discovered Neptune or figured out how to put 5,000 songs in your pocket.

Though many of us were scared away from this essential, engrossing subject in high school and college, Steven Strogatz’s brilliantly creative, down to earth history shows that calculus is not about complexity; it’s about simplicity. It harnesses an unreal number—infinity—to tackle real world problems, breaking them down into easier ones and then reassembling the answers into solutions that feel miraculous.

Infinite Powers recounts how calculus tantalized and thrilled its inventors, starting with its first glimmers in ancient Greece and bringing us right up to the discovery of gravitational waves (a phenomenon predicted by calculus). Strogatz reveals how this form of math rose to the challenges of each age: how to determine the area of a circle with only sand and a stick; how to explain why Mars goes “backwards” sometimes; how to make electricity with magnets; how to ensure your rocket doesn’t miss the moon; how to turn the tide in the fight against AIDS.

As Strogatz proves, calculus is truly the language of the universe. By unveiling the principles of that language, Infinite Powers makes us marvel at the world anew.

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Mathematical Analysis, Probability and Applications – Plenary Lectures

Introduction

This book collects lectures given by the plenary speakers at the 10th International ISAAC Congress, held in Macau, China in 2015. The contributions, authored by eminent specialists, present some of the most exciting recent developments in mathematical analysis, probability theory, and related applications. Topics include: partial differential equations in mathematical physics, Fourier analysis, probability and Brownian motion, numerical analysis, and reproducing kernels. The volume also presents a lecture on the visual exploration of complex functions using the domain coloring technique. Thanks to the accessible style used, readers only need a basic command of calculus.

 

 

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Precálculo: Matemáticas para el cálculo. 7ma. edición - James Stewart

 

Precálculo. Matemáticas para el cálculo séptima edición proporciona a los estudiantes las herramientas necesarias para prepararlos en esta materia. La obra contiene además de los conocimientos técnicos una clara comprensión de los conceptos, por lo que promueve que la comprensión conceptual y los conocimientos técnicos vayan de la mano y se refuercen entre sí. En particular, cada tema se presenta algebraicamente, gráficamente, numéricamente y verbalmente, enfatizando las relaciones entre cada tipo de representación.

 

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