Second Year Calculus

From Celestial Mechanics to Special Relativity

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Author: David M. Bressoud

Publisher: Springer Science & Business Media

ISBN: 1461209595

Category: Mathematics

Page: 404

View: 5738

Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book guides us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

Second Year Calculus

From Celestial Mechanics to Special Relativity

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Author: David Bressoud

Publisher: Springer Science & Business Media

ISBN: 9780387976068

Category: Mathematics

Page: 386

View: 8406

Second Year Calculus: From Celestial Mechanics to Special Relativity covers multi-variable and vector calculus, emphasizing the historical physical problems which gave rise to the concepts of calculus. The book carries us from the birth of the mechanized view of the world in Isaac Newton's Mathematical Principles of Natural Philosophy in which mathematics becomes the ultimate tool for modelling physical reality, to the dawn of a radically new and often counter-intuitive age in Albert Einstein's Special Theory of Relativity in which it is the mathematical model which suggests new aspects of that reality. The development of this process is discussed from the modern viewpoint of differential forms. Using this concept, the student learns to compute orbits and rocket trajectories, model flows and force fields, and derive the laws of electricity and magnetism. These exercises and observations of mathematical symmetry enable the student to better understand the interaction of physics and mathematics.

A Radical Approach to Lebesgue's Theory of Integration

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Author: David M. Bressoud

Publisher: Cambridge University Press

ISBN: 0521884748

Category: Mathematics

Page: 329

View: 5113

Meant for advanced undergraduate and graduate students in mathematics, this introduction to measure theory and Lebesgue integration is motivated by the historical questions that led to its development. The author tells the story of the mathematicians who wrestled with the difficulties inherent in the Riemann integral, leading to the work of Jordan, Borel, and Lebesgue.

Understanding Relativity

A Simplified Approach to Einstein's Theories

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Author: Leo Sartori

Publisher: Univ of California Press

ISBN: 9780520916241

Category: Science

Page: 376

View: 8764

Nonspecialists with no prior knowledge of physics and only reasonable proficiency with algebra can now understand Einstein's special theory of relativity. Effectively diagrammed and with an emphasis on logical structure, Leo Sartori's rigorous but simple presentation will guide interested readers through concepts of relative time and relative space. Sartori covers general relativity and cosmology, but focuses on Einstein's theory. He tracks its history and implications. He explores illuminating paradoxes, including the famous twin paradox, the "pole-in-the-barn" paradox, and the Loedel diagram, which is an accessible, graphic approach to relativity. Students of the history and philosophy of science will welcome this concise introduction to the central concept of modern physics.

A Radical Approach to Real Analysis

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Author: David M. Bressoud

Publisher: MAA

ISBN: 9780883857472

Category: Mathematics

Page: 323

View: 9697

Second edition of this introduction to real analysis, rooted in the historical issues that shaped its development.

An Introduction to Mechanics

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Author: Daniel Kleppner,Robert Kolenkow

Publisher: Cambridge University Press

ISBN: 0521198119

Category: Science

Page: 566

View: 493

This second edition is ideal for classical mechanics courses for first- and second-year undergraduates with foundation skills in mathematics.

A First Course in General Relativity

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Author: Bernard Schutz

Publisher: Cambridge University Press

ISBN: 0521887054

Category: Science

Page: 393

View: 8419

Second edition of a widely-used textbook providing the first step into general relativity for undergraduate students with minimal mathematical background.

Introduction to Classical Mechanics

With Problems and Solutions

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Author: David Morin

Publisher: Cambridge University Press

ISBN: 1139468375

Category: Science

Page: N.A

View: 456

This textbook covers all the standard introductory topics in classical mechanics, including Newton's laws, oscillations, energy, momentum, angular momentum, planetary motion, and special relativity. It also explores more advanced topics, such as normal modes, the Lagrangian method, gyroscopic motion, fictitious forces, 4-vectors, and general relativity. It contains more than 250 problems with detailed solutions so students can easily check their understanding of the topic. There are also over 350 unworked exercises which are ideal for homework assignments. Password protected solutions are available to instructors at www.cambridge.org/9780521876223. The vast number of problems alone makes it an ideal supplementary text for all levels of undergraduate physics courses in classical mechanics. Remarks are scattered throughout the text, discussing issues that are often glossed over in other textbooks, and it is thoroughly illustrated with more than 600 figures to help demonstrate key concepts.

Mathematics and Its History

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Author: John Stillwell

Publisher: Springer Science & Business Media

ISBN: 144196052X

Category: Mathematics

Page: 662

View: 5427

From a review of the second edition: "This book covers many interesting topics not usually covered in a present day undergraduate course, as well as certain basic topics such as the development of the calculus and the solution of polynomial equations. The fact that the topics are introduced in their historical contexts will enable students to better appreciate and understand the mathematical ideas involved...If one constructs a list of topics central to a history course, then they would closely resemble those chosen here." (David Parrott, Australian Mathematical Society) This book offers a collection of historical essays detailing a large variety of mathematical disciplines and issues; it’s accessible to a broad audience. This third edition includes new chapters on simple groups and new sections on alternating groups and the Poincare conjecture. Many more exercises have been added as well as commentary that helps place the exercises in context.

Gravity from the Ground Up

An Introductory Guide to Gravity and General Relativity

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Author: Bernard Schutz

Publisher: Cambridge University Press

ISBN: 1139457349

Category: Science

Page: N.A

View: 7694

This book invites the reader to understand our Universe, not just marvel at it. From the clock-like motions of the planets to the catastrophic collapse of a star into a black hole, gravity controls the Universe. Gravity is central to modern physics, helping to answer the deepest questions about the nature of time, the origin of the Universe and the unification of the forces of nature. Linking key experiments and observations through careful physical reasoning, the author builds the reader's insight step-by-step from simple but profound facts about gravity on Earth to the frontiers of research. Topics covered include the nature of stars and galaxies, the mysteries of dark matter and dark energy, black holes, gravitational waves, inflation and the Big Bang. Suitable for general readers and for undergraduate courses, the treatment uses only high-school level mathematics, supplemented by optional computer programs, to explain the laws of physics governing gravity.

Classical Mechanics

Theory and Mathematical Modeling

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Author: Emmanuele DiBenedetto

Publisher: Springer Science & Business Media

ISBN: 9780817646486

Category: Mathematics

Page: 351

View: 7402

* Offers a rigorous mathematical treatment of mechanics as a text or reference * Revisits beautiful classical material, including gyroscopes, precessions, spinning tops, effects of rotation of the Earth on gravity motions, and variational principles * Employs mathematics not only as a "unifying" language, but also to exemplify its role as a catalyst behind new concepts and discoveries

Introduction to General Relativity

Solutions to Problems

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Author: John Dirk Walecka

Publisher: World Scientific Publishing Company

ISBN: 9813227710

Category:

Page: 216

View: 7587

It is important for every physicist today to have a working knowledge of Einstein's theory of general relativity. Introduction to General Relativity published in 2007 was aimed at first-year graduate students, or advanced undergraduates, in physics. Only a basic understanding of classical lagrangian mechanics is assumed; beyond that, the reader should find the material to be self-contained. The mechanics problem of a point mass constrained to move without friction on a two-dimensional surface of arbitrary shape serves as a paradigm for the development of the mathematics and physics of general relativity. Special relativity is reviewed. The basic principles of general relativity are then presented, and the most important applications are discussed. The final special topics section takes the reader up to a few areas of current research. An extensive set of accessible problems enhances and extends the coverage. As a learning and teaching tool, this current book provides solutions to those problems. This text and solutions manual are meant to provide an introduction to the subject. It is hoped that these books will allow the reader to approach the more advanced texts and monographs, as well as the continual influx of fascinating new experimental results, with a deeper understanding and sense of appreciation.

Calculus and Analysis in Euclidean Space

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Author: Jerry Shurman

Publisher: Springer

ISBN: 3319493140

Category: Mathematics

Page: 507

View: 6734

The graceful role of analysis in underpinning calculus is often lost to their separation in the curriculum. This book entwines the two subjects, providing a conceptual approach to multivariable calculus closely supported by the structure and reasoning of analysis. The setting is Euclidean space, with the material on differentiation culminating in the inverse and implicit function theorems, and the material on integration culminating in the general fundamental theorem of integral calculus. More in-depth than most calculus books but less technical than a typical analysis introduction, Calculus and Analysis in Euclidean Space offers a rich blend of content to students outside the traditional mathematics major, while also providing transitional preparation for those who will continue on in the subject. The writing in this book aims to convey the intent of ideas early in discussion. The narrative proceeds through figures, formulas, and text, guiding the reader to do mathematics resourcefully by marshaling the skills of geometric intuition (the visual cortex being quickly instinctive) algebraic manipulation (symbol-patterns being precise and robust) incisive use of natural language (slogans that encapsulate central ideas enabling a large-scale grasp of the subject). Thinking in these ways renders mathematics coherent, inevitable, and fluid. The prerequisite is single-variable calculus, including familiarity with the foundational theorems and some experience with proofs.

Intermediate Calculus

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Author: Murray H. Protter,Charles B. Jr. Morrey

Publisher: Springer

ISBN: 0387960589

Category: Mathematics

Page: 655

View: 8573

General Relativity Without Calculus

A Concise Introduction to the Geometry of Relativity

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Author: Jose Natario

Publisher: Springer Science & Business Media

ISBN: 9783642214523

Category: Science

Page: 128

View: 9503

“General Relativity Without Calculus” offers a compact but mathematically correct introduction to the general theory of relativity, assuming only a basic knowledge of high school mathematics and physics. Targeted at first year undergraduates (and advanced high school students) who wish to learn Einstein’s theory beyond popular science accounts, it covers the basics of special relativity, Minkowski space-time, non-Euclidean geometry, Newtonian gravity, the Schwarzschild solution, black holes and cosmology. The quick-paced style is balanced by over 75 exercises (including full solutions), allowing readers to test and consolidate their understanding.

Understanding the Universe

An Introduction to Physics and Astrophysics

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Author: James B. Seaborn

Publisher: Springer Science & Business Media

ISBN: 1461206898

Category: Science

Page: 304

View: 7433

Intended for undergraduate non-science majors, satisfying a general education requirement or seeking an elective in natural science, this is a physics text, but with the emphasis on topics and applications in astronomy. The perspective is thus different from most undergraduate astronomy courses: rather than discussing what is known about the heavens, this text develops the principles of physics so as to illuminate what we see in the heavens. The fundamental principles governing the behaviour of matter and energy are thus used to study the solar system, the structure and evolution of stars, and the early universe. The first part of the book develops Newtonian mechanics towards an understanding of celestial mechanics, while chapters on electromagnetism and elementary quantum theory lay the foundation of the modern theory of the structure of matter and the role of radiation in the constitution of stars. Kinetic theory and nuclear physics provide the basis for a discussion of stellar structure and evolution, and an examination of red shifts and other observational data provide a basis for discussions of cosmology and cosmogony.

Orbital Mechanics

For Engineering Students

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Author: Howard D Curtis

Publisher: Elsevier

ISBN: 0080470548

Category: Technology & Engineering

Page: 704

View: 8322

Orbital mechanics is a cornerstone subject for aerospace engineering students. However, with its basis in classical physics and mechanics, it can be a difficult and weighty subject. Howard Curtis - Professor of Aerospace Engineering at Embry-Riddle University, the US's #1 rated undergraduate aerospace school - focuses on what students at undergraduate and taught masters level really need to know in this hugely valuable text. Fully supported by the analytical features and computer based tools required by today's students, it brings a fresh, modern, accessible approach to teaching and learning orbital mechanics. A truly essential new resource. A complete, stand-alone text for this core aerospace engineering subject Richly-detailed, up-to-date curriculum coverage; clearly and logically developed to meet the needs of students Highly illustrated and fully supported with downloadable MATLAB algorithms for project and practical work; with fully worked examples throughout, Q&A material, and extensive homework exercises.

Essential Relativity

Special, General, and Cosmological

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Author: W. Rindler

Publisher: Springer

ISBN: 1475711352

Category: Science

Page: 319

View: 3265

This book is an attempt to bring the full range of relativity theory within reach of advanced undergraduates, while containing enough new material and simplifications of old arguments so as not to bore the expert teacher. Roughly equal coverage is given tospecial relativity, general relativity, and cosmology. With many judicious omissions it can be taught in one semester, but it would better serve as the basis of a year's work. It is my hope, anyway, that its level and style of presentation may appeal also to wider c1asses of readers unrestricted by credit considerations. General relativity, the modern theory of gravitation in which free particles move along "straightest possible" lines in curved spacetime, and cosmology, with its dynamics for the whole possibly curved uni verse, not only seem necessary for a scientist's balanced view of the world, but offer some of the greatest intellectual thrills of modern physics. Nevertheless, considered luxuries, they are usu ally squeezed out of the graduate curriculum by the pressure of specialization. Special relativity escapes this tag with a ven geance, and tends to be taught as a pure service discipline, with too little emphasis on its startling ideas. What better time, there fore, to enjoy these subjects for their own sake than as an und- v vi PREFACE graduate? In spite of its forbidding mathematical reputation, even general relativity is accessible at that stage.

Nonlinear Dynamics

A Two-Way Trip from Physics to Math

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Author: H.G Solari,M.A Natiello,G.B Mindlin

Publisher: CRC Press

ISBN: 9780750303804

Category: Science

Page: 366

View: 2351

Nonlinear Dynamics: A Two-Way Trip from Physics to Math provides readers with the mathematical tools of nonlinear dynamics to tackle problems in all areas of physics. The selection of topics emphasizes bifurcation theory and topological analysis of dynamical systems. The book includes real-life problems and experiments as well as exercises and worked examples to test understanding.