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"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 covers the ground 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 text shows the student how to compute orbits and rocket trajectories, model flows and force fields and how to derive the laws of electricity and magnetism. The exercises and observations of mathematical symmetry are designed to enable the student to better understand the interaction of physics and mathematics. ... Read more

Customer Reviews (5)

A Mediocre, Low-Caliber Textbook
I regard this as a mediocre and second-rate textbook that lacks the necessary depth, breadth, and formality expected of a calculus text. The table of content certainly lists all the essential headlines of introductory vector calculus. But, virtually every single topic seems to exist only in the most minimal form and amount. Things are just "dumb-ed down" and presented in as few words - and as simplistically - as possible.

Having said that, there may be circumstances where some people actually find the book useful specifically because of its watered-down and simple-minded nature.

Almost without exception, in-text examples are trivial cases of plug-n-chug for the immediately preceding equation/discussion. I read more than 75% of the book and I saw very few good examples that are thoughtful and illustrate interesting or special cases, or bring out subtleties.Most (but not all) of the end-of-section exercises that I sampled are equally uninspiring and unimaginative, "busy-work" type of problems.

I got interested in this book because it claimed to develop the subject in close connection with problems from Mechanics. Well, while this material has some value, it is again so thin that it's hardly special.

Clearest intro to Multivariable Calculus and Differential Forms
I do not know another book that presents Differential Forms and their usage in the framework of Calculus better than this one. (I've looked at several.) A lot of the other bookspresent this material at a high level that loses the reader in ten pages or less. Professor Bressoud's book, by contrast, is a model of the clarity that I would love to see more Math Book writers adopt.
The subject is potentially confusing because the notation of first-year calculus -- dx, dy, dz -- is here used in a way, and with a revised meaning, that you may not have seen before. Bressoud takes the time to EXPLAIN Forms to the reader carefully, and in sufficient detail, to be understood. Heeven explicitly warns the reader about situationsin which the new notation may cause confusion, given the new usage. ( in multiple vs iterated integrals, for example ).
It's clear enough to be used for self-study. Strongly recommended. After you finish thebook, you will be in a position to tackle a moreextended treatment, such as H. Edward's Advanced Calculus: A Differential Forms Approach.
But do start with this book.

formulaic formalism
The author appears to be terminally addicted to
reams of calculation without much in the way of
motivation.Take the section on celestial mechanics
(please), which is one of the worst I have ever seen.
He has page after page of relentless calculations
which would leave the uninitiated reader utterly
lost in this dense mess.Much more to the point
would be an appropriate diagram to illustrate this
highly visual subject.Sadly, the author remains
stuck in his LH method of exposition and seems not
to grasp when to bring in geometry to aid and abet
the raft of algebraic manipulations.

The emphasis is on working out problems . . .
I agree with the review of "gsibbery" (Baton Rouge, LA)

Chapters:
1 F=ma
2 Vector Algebra
3 Celestial Mechanics
4 Differential Forms
5 Line Integrals, Multiple Integrals
6 Linear Transformations
7 Differential Calculus
8 Integration by Pullback
9 Techniques of Differential Calculus
10 The Fundamental Theorem of Calculus
11 E=mc^2

Plus a great collection of problems!

Calculus For Physics Students
Ok, for all those of you out there who always wanted to learn the math that you need to know to be able to do some really fun physics, THIS IS IT!Most introductions to "higher mathematics" tend to berather impractical and largely useless and uninteresting topics (to thephysical scientist) such as set theory or abelian group theory, but thisbook really delivers. The emphasis is on working out problems . . . thereis some theory, but this is really meant for engineers and physicistsrather than for mathematicians who are interested in theory alone. You needa very solid grounding in first year calculus before you even think ofbeginning this course. But once you get going, the topics that areintroduced include: multiple integrals, vectors, differential forms(including tensors), and continues in this fashion until the last chapterson electromagnetics, celestial mechanics and special relativity. Now, thisis not an easy book, but unlike many math texts that I have seen, it is byno means impossible to learn all own your own. Thus, if something thatreally interest you in the classroom is not covered, then this book wouldmake a great supplement. It is superb for self-study and contains most ofwhat you need to know to begin studying real physics and more advancedparactical mathematics. I can't thank Dr. Bressoud enough for writing thismuch-needed book! I only wish that I could give in ten stars instead ofonly five! ... Read more

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This volume contains nine essays dealing with historical issues of mathematics. The topics covered span three different approaches to the history of mathematics that may be considered both representative and vital tothe field. The first section, Images of Mathematics, addresses the historiographical and philosophical issues involved in determining the meaning of mathematical history. The second section, Differential Geometry and Analysis, traces the convoluted development of the ideas of differential geometry and analysis. The third section, Research Communities and International Collaboration, discusses the structure and interaction of mathematical communities through studies of the social fabric of the mathematical communities of the U.S. and China.

Please provide. ... Read more

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This scarce antiquarian book is a selection from Kessinger Publishings Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the worlds literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

Product Description
This scarce antiquarian book is a selection from Kessinger Publishing's Legacy Reprint Series. Due to its age, it may contain imperfections such as marks, notations, marginalia and flawed pages. Because we believe this work is culturally important, we have made it available as part of our commitment to protecting, preserving, and promoting the world's literature. Kessinger Publishing is the place to find hundreds of thousands of rare and hard-to-find books with something of interest for everyone! ... Read more

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This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

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DIFFERENTIAL AND INTEGRAL CALCULUS BY AUGUSTUS DE MORGAN CONTENTS: On the Ratio or Proportion of Two Magnitudes On the Ratio of Magnitudes that Vanish Together On the Ratios of Continuously Increasing or Decreasing Quantities The Notion of Infinitely Small Quantities On Functions Infinite Series Convergent and Divergent Series. Taylors Theorem, Derived Functions. Differential Coefficients The Notation of the Differential Calculus Algebraical Geometry On the Connexion of the Signs of Algebraical and the. Directions of Geometrical .Magnitudes The Drawing of a Tangent to a Curve. Rational Explanation of the Language of Leibnitz Orders of Infinity A Geometrical Illustration : Limit of the Intersections of Two Coinciding Straight Lines, The Same Problem Solved by the Principles of Leibnitz An Illustration from Dynamics Velocity, Acceleration, etc, Simple Harmonic Motion The Method of Fluxions Accelerated Motion Limiting Ratios of Magnitudes that Increase Without Limit. Recapitulation of Results Retched in the Theory of Functions, Approximations by the Differential Calculus Solution, of Equations by the Differential Calculus Partial and Total Differentials Application of the Theorem for Total Differentials to the Determination of Total Resultant Errors Rules for Differentiation.. Illustration of the Rules for Differentiation Differential Coefficients of Differential Coefficients Calculus of Finite Differences. Successive Differentiation Total and Partial Differential Coefficients. Implicit Differentiation Applications of the Theorem for Implicit Differentiation Inverse Functions. Implicit Functions. Fluxions, and the Idea of Time The Differential Coefficient Considered with Respect to Its Magnitude. The Integral Calculus Connexion of the Integral with the Differential Calculus Nature of Integration. Determination of Curvilinear Areas. The Parabola Method of Indivisibles. Concluding Remarks on the Study of the Calculus Bibliography of Standard Textbooks and Works of Reference on the Calculus. ... Read more

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Since Plato, there have been many interpretations of the ideasof analysis and synthesis, which are related to mathematical thought.Mathematicians have appealed to them to distinguish different formsand styles in their argumentations and expositions. Philosophers havereferred to them for clarification of the specific character ofmathematical knowledge. In the present volume various instances of theanalytic--synthetic distinction are discussed in relation to thehistory and philosophy of mathematics, and some new perspectives aboutpossible interpretations and consequences are suggested. Such aninquiry is motivated by two convictions. First, behind such a varietyof interpretations, an invariant kernel seems to subsist. Second, thediscussion of these interpretations seems to be a Konigswegfor tackling one of the essential problems mathematics presents forhistorians and philosophers, the problem of objectivity as a form ofknowledge. Audience: The book is aimed at scholars in philosophy,especially philosophy of mathematics and logic, historians of science,historians of mathematics, and philosophers of science. ... Read more

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Written by a great English mathematician, this classic text begins with the differences of elementary functions and explores interpolation, mechanical quadrature, finite integration, and the summation of series. Several useful tests for the convergence and divergence of series are developed, as is a method for finding the limits of error in series expansions. The latter half of the book discusses difference-equations, including linear, mixed, and partial difference-equations, and concludes with applications to problems in geometry and optics. The text pays particular attention to the connection of the calculus of finite differences with the differential calculus, and more than 200 problems appear in the text (some with solutions). Unabridged republication of the classic 1872 edition.
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This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

Product Description
This volume is produced from digital images created through the University of Michigan University Library's preservation reformatting program. ... Read more

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Judith Grabiner, the author of A Historian Looks Back, has long been interested in investigating what mathematicians actually do, and how mathematics actually has developed. She addresses the results of her investigations not principally to other historians, but to mathematicians and teachers of mathematics. This book brings together much of what she has had to say to this audience.

The centerpiece of the book is The Calculus as Algebra: J.-L. Lagrange, 1736-1813. The book describes the achievements, setbacks, and influence of Lagrange s pioneering attempt to reduce the calculus to algebra. Nine additional articles round out the book describing the history of the derivative; the origin of delta-epsilon proofs; Descartes and problem solving; the contrast between the calculus of Newton and Maclaurin, and that of Lagrange; Maclaurin s way of doing mathematics and science and his surprisingly important influence; some widely held myths about the history of mathematics; Lagrange s attempt to prove Euclid s parallel postulate; and the central role that mathematics has played throughout the history of western civilization.

The development of mathematics cannot be programmed or predicted. Still, seeing how ideas have been formed over time and what the difficulties were can help teachers find new ways to explain mathematics. Appreciating its cultural background can humanize mathematics for students. And famous mathematicians struggles and successes should interest -- and perhaps inspire -- researchers. Readers will see not only what the mathematical past was like, but also how important parts of the mathematical present came to be.