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A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics)

A History of Vector Analysis: The Evolution of the Idea of a Vectorial System

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A History of Vector Analysis: The Evolution of the Idea of a Vectorial System (Dover Books on Mathematics)

A History of Vector Analysis: The Evolution of the Idea of a Vectorial System

4.85 15,265 ratings · 2,732 reviews
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Overview: On October 16, 1843, Sir William Rowan Hamilton discovered quaternions and, on the very same day, presented his breakthrough to the Royal Irish Academy. Meanwhile, in a less dramatic style, a German high school teacher, Hermann Grassmann, was developing another vectorial system involving hypercomplex numbers comparable to quaternions. The creations of these two mathematicians led to other vectorial systems, most notably the system of vector analysis formulated by Josiah Willard Gibbs and Oliver Heaviside and now almost universally employed in mathematics, physics and engineering. Yet the Gibbs-Heaviside system won acceptance only after decades of debate and controversy in the latter half of the nineteenth century concerning which of the competing systems offered the greatest advantages for mathematical pedagogy and practice.This volume, the first large-scale study of the development of vectorial systems, traces the rise of the vector concept from the discovery of complex numbers through the systems of hypercomplex numbers created by Hamilton and Grassmann to the final acceptance around 1910 of the modern system of vector analysis. Professor Michael J. Crowe (University of Notre Dame) discusses each major vectorial system as well as the motivations that led to their creation, development, and acceptance or rejection.The vectorial approach revolutionized mathematical methods and teaching in algebra, geometry, and physical science. As Professor Crowe explains, in these areas traditional Cartesian methods were replaced by vectorial approaches. He also presents the history of ideas of vector addition, subtraction, multiplication, division (in those systems where it occurs) and differentiation. His book also contains refreshing portraits of the personalities involved in the competition among the various systems.

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Topics & Genres

Pages N/A
Publisher Dover Publications
Published 1967
ISBN 2197718
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Michael J. Crowe
About the Author
Michael J. Crowe
18,938 Followers

Michael J. Crowe is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Michael J. Crowe enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Elizabeth Sanchez March 30, 2025
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I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Richard Nelson
Richard Nelson June 09, 2024
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Richard Young April 21, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Anthony Walker
Anthony Walker March 17, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Kevin Evans
Kevin Evans September 23, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
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Susan Lee August 30, 2025
Masterpiece from start to finish. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Edward Taylor
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I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
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I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Susan Davis March 04, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Edward Wright
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A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
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Robert Lee July 10, 2025
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Susan Nguyen February 07, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
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Kenneth Nguyen March 03, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
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Nancy Martin November 09, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
James Phillips
James Phillips March 16, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I will undoubtedly revisit this masterpiece.
Betty  Davis
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A decent, if standard, experience. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. A fair 3 stars.
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Barbara Parker February 06, 2025
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A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Emily Hernandez
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A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Jessica Mitchell
Jessica Mitchell December 25, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
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Amanda Johnson August 23, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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James King June 09, 2024
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Stephanie Collins August 31, 2024
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
James Phillips
James Phillips August 07, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
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Christopher Sanchez May 12, 2025
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Gary Collins
Gary Collins July 20, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Eric Walker
Eric Walker February 13, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Kenneth Moore
Kenneth Moore August 31, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Brian Scott
Brian Scott March 16, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Donald King
Donald King December 22, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Steven Hall
Steven Hall May 22, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Jacob Anderson
Jacob Anderson January 16, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Edward Nelson
Edward Nelson February 06, 2024
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Karen Anderson January 11, 2024
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Thomas Jones May 21, 2024
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Melissa Baker May 20, 2025
An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
Nancy Martin
Nancy Martin April 24, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Nancy  Parker
Nancy Parker September 29, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
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Karen Rodriguez September 04, 2024
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Jacob Clark June 25, 2024
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Robert Scott
Robert Scott June 04, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Richard Young
Richard Young March 22, 2024
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Robert Torres
Robert Torres June 21, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
Barbara  Parker
Barbara Parker October 16, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Lisa Ramirez
Lisa Ramirez November 16, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Andrew Lopez
Andrew Lopez May 25, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
Robert Wright
Robert Wright July 13, 2025
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Mark Turner
Mark Turner April 03, 2025
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Suitable if your reading queue is empty.
Joshua Hill
Joshua Hill November 24, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Rebecca Williams
Rebecca Williams August 06, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
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Thomas Campbell
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Deborah Scott August 25, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Donna Phillips
Donna Phillips April 06, 2025
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Melissa Roberts
Melissa Roberts March 10, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Linda Turner
Linda Turner November 18, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Sharon Anderson
Sharon Anderson January 06, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Jacob Phillips
Jacob Phillips December 14, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Joseph Green
Joseph Green April 28, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Michelle Rodriguez
Michelle Rodriguez September 21, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Donna Allen
Donna Allen July 17, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Ashley Miller
Ashley Miller November 21, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
George King
George King July 28, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Anthony Anderson
Anthony Anderson November 29, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Richard Campbell
Richard Campbell December 31, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Gary Collins
Gary Collins December 08, 2024
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
Thomas Green
Thomas Green November 20, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Donald King
Donald King July 28, 2024
Absolutely brilliant. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
George Hill
George Hill May 27, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Lisa Garcia
Lisa Garcia April 10, 2024
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Margaret White
Margaret White December 16, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Kimberly Nguyen
Kimberly Nguyen February 23, 2025
Took a moment to build, but the payoff was spectacular. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Daniel Allen
Daniel Allen March 24, 2024
Honestly one of the most premium reading experiences lately. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Karen Perez
Karen Perez September 17, 2025
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Thomas Campbell
Thomas Campbell May 31, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Joshua Turner
Joshua Turner May 31, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Rebecca Williams
Rebecca Williams October 25, 2025
Masterpiece from start to finish. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Andrew Martin
Andrew Martin April 03, 2025
Exceeded all my expectations. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Amanda Hernandez
Amanda Hernandez January 23, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Jessica Mitchell
Jessica Mitchell May 08, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Deborah Lopez
Deborah Lopez March 28, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Kenneth Collins
Kenneth Collins November 20, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Stephanie Torres
Stephanie Torres September 08, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Brian Diaz
Brian Diaz February 01, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. A very distinguished novel.
Eric Walker
Eric Walker September 13, 2024
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Susan Allen
Susan Allen October 13, 2024
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Donna Williams
Donna Williams May 25, 2025
It was adequate. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Unlikely to reread, but a reasonable expenditure of time.
Richard Young
Richard Young December 10, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
Rebecca Mitchell
Rebecca Mitchell May 21, 2024
An acceptable diversion. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Matthew Lee
Matthew Lee June 26, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Deborah Lopez
Deborah Lopez March 28, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Stephanie Torres
Stephanie Torres May 14, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Barbara King
Barbara King May 11, 2025
I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Mark Hall
Mark Hall May 14, 2025
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A solid 4 stars from me.
William Turner
William Turner November 29, 2024
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Donna Williams
Donna Williams February 21, 2025
Not entirely to my refined tastes. The tempo was somewhat languid, and I found my mind wandering. Not poor, simply average. Perfectly average.
Melissa Phillips
Melissa Phillips April 18, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Brian Gonzalez
Brian Gonzalez October 13, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
Jessica Robinson
Jessica Robinson December 29, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
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