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Introduction to the Calculus of Variations (Dover Books on Mathematics)

Introduction to the Calculus of Variations

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Introduction to the Calculus of Variations (Dover Books on Mathematics)

Introduction to the Calculus of Variations

4.85 75,213 ratings · 7,129 reviews
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Overview: Excellent text provides basis for thorough understanding of the problems, methods, and techniques of the calculus of variations and prepares readers for the study of modern optimal control theory. Treatment limited to extensive coverage of single integral problems in one and more unknown functions. Carefully chosen variational problems and over 400 exercises. 1969 edition. Bibliography.

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Published December 21, 1992
ISBN 1429475
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Hans Sagan
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Hans Sagan is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Hans Sagan enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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Gary Gomez
Gary Gomez July 26, 2025
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
George Lee
George Lee February 23, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Amanda Sanchez
Amanda Sanchez November 26, 2024
A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perhaps more aligned with a different audience's tastes.
Robert Clark
Robert Clark July 23, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
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Donald Nelson June 30, 2025
Honestly one of the most premium reading experiences lately. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Richard Wright
Richard Wright May 19, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Margaret Thomas
Margaret Thomas August 11, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Linda White
Linda White August 19, 2024
A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Richard Nelson
Richard Nelson September 14, 2024
Not entirely to my refined tastes. The prose was competent, yet the characters lacked the depth I usually seek. Perhaps more aligned with a different audience's tastes.
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John Smith June 24, 2025
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
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Kenneth Turner March 22, 2025
Excellent, though slightly flawed. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
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Dorothy Garcia April 06, 2024
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Richard Hill
Richard Hill October 08, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
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Steven Wilson January 18, 2024
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
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I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
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Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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Joseph Rivera March 11, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
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Joseph Rodriguez February 16, 2025
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Laura Turner December 29, 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.
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Paul Cruz November 13, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Dorothy Allen
Dorothy Allen December 21, 2025
A decent, if standard, experience. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
Charles Lopez
Charles Lopez June 22, 2024
Honestly one of the most premium reading experiences lately. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
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James Harris July 08, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
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Donald Mitchell July 24, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Eric Sanchez
Eric Sanchez November 11, 2024
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
Gary Baker
Gary Baker May 20, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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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.
Gary Wilson
Gary Wilson September 28, 2024
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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Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A wonderful companion for a quiet weekend.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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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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Robert Gomez
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Susan Lopez
Susan Lopez April 24, 2024
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
Ryan Thomas
Ryan Thomas January 21, 2025
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
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Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Honestly one of the most premium reading experiences lately. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
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Christopher Flores June 02, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Joseph Rivera
Joseph Rivera December 27, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I will undoubtedly revisit this masterpiece.
Charles Flores
Charles Flores May 06, 2025
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I will undoubtedly revisit this masterpiece.
Joseph Rodriguez
Joseph Rodriguez June 16, 2025
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
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Michael Wright
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I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Joseph Hill
Joseph Hill September 13, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
Edward Wright
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I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. Worth every moment spent reading.
Nicholas Thomas
Nicholas Thomas December 23, 2025
I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Laura Green
Laura Green October 09, 2025
A highly sophisticated read. A brilliant concept executed with flair. Just a few pacing choices I would change. Quite impressive overall.
Joshua Gomez
Joshua Gomez May 24, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
Joseph Thomas
Joseph Thomas April 04, 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.
Elizabeth Harris
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Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
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Thomas Turner May 05, 2025
I thoroughly enjoyed the elegance of it. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Margaret Lee
Margaret Lee November 21, 2024
I find myself somewhat conflicted. The prose was competent, yet the characters lacked the depth I usually seek. Suitable if your reading queue is empty.
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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.
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Took a moment to build, but the payoff was spectacular. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
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Sandra Lopez August 20, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Joshua Allen
Joshua Allen May 17, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
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Elizabeth Jackson June 14, 2024
Exceeded all my expectations. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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Andrew Carter November 03, 2024
A highly sophisticated read. The middle had a deliberate pace, but the climax was phenomenal. A wonderful companion for a quiet weekend.
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Joshua Wright December 22, 2024
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Charles Hill
Charles Hill May 18, 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.
Matthew Baker
Matthew Baker August 30, 2025
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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Betty Edwards October 30, 2024
Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. I would highly recommend this to discerning readers.
Melissa Lopez
Melissa Lopez October 27, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Laura Roberts
Laura Roberts March 03, 2025
Such a rich narrative. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Eric Mitchell
Eric Mitchell March 22, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Michael Thomas
Michael Thomas April 30, 2025
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Emily Clark
Emily Clark October 31, 2025
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Michael Brown
Michael Brown November 10, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Robert Gomez
Robert Gomez May 21, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Thomas Roberts
Thomas Roberts May 15, 2025
A highly sophisticated read. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Lisa Jones
Lisa Jones April 21, 2025
Masterpiece from start to finish. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Karen Hall
Karen Hall September 18, 2025
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perfectly average.
John Mitchell
John Mitchell April 28, 2025
I find myself somewhat conflicted. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Unlikely to reread, but a reasonable expenditure of time.
Patricia Carter
Patricia Carter September 25, 2024
I find myself somewhat conflicted. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
Daniel Wilson
Daniel Wilson April 03, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Joseph Flores
Joseph Flores June 24, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Susan  Parker
Susan Parker May 02, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I am now a lifelong fan of this author.
Amanda Sanchez
Amanda Sanchez July 29, 2025
Took a moment to build, but the payoff was spectacular. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Michelle Sanchez
Michelle Sanchez June 24, 2024
A very strong entry. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. I would highly recommend this to discerning readers.
Ashley Hall
Ashley Hall May 01, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. I will undoubtedly revisit this masterpiece.
Michelle Sanchez
Michelle Sanchez April 20, 2024
Such a rich narrative. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
James Perez
James Perez May 26, 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.
Susan Allen
Susan Allen May 17, 2024
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
Ashley Rivera
Ashley Rivera October 23, 2024
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
Michelle Sanchez
Michelle Sanchez September 09, 2024
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Jacob Hill
Jacob Hill January 11, 2025
I thoroughly enjoyed the elegance of it. The middle had a deliberate pace, but the climax was phenomenal. I would highly recommend this to discerning readers.
Gary Miller
Gary Miller October 02, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Thomas Scott
Thomas Scott September 20, 2025
Masterpiece from start to finish. The prose is exquisite. It’s accessible yet undeniably sophisticated. An absolute must-read for connoisseurs of the genre.
Michael Smith
Michael Smith November 20, 2024
Such a rich narrative. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Laura Turner
Laura Turner March 01, 2024
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. A solid 4 stars from me.
Susan Lopez
Susan Lopez January 23, 2025
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Stephanie Edwards
Stephanie Edwards February 22, 2025
Exceeded all my expectations. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. I am now a lifelong fan of this author.
Kenneth Turner
Kenneth Turner July 27, 2025
Not entirely to my refined tastes. It possessed moments of brilliance, but the narrative felt slightly disjointed ultimately. Perhaps more aligned with a different audience's tastes.
Charles Edwards
Charles Edwards August 30, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. Worth every moment spent reading.
Charles Edwards
Charles Edwards October 07, 2024
Honestly one of the most premium reading experiences lately. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
James Perez
James Perez April 06, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
Dorothy Garcia
Dorothy Garcia May 23, 2024
A highly sophisticated read. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A solid 4 stars from me.
Barbara Harris
Barbara Harris February 06, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Daniel Wilson
Daniel Wilson October 27, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Richard Torres
Richard Torres August 26, 2025
Excellent, though slightly flawed. The protagonist was compelling, though some subplots felt slightly overshadowed. A very distinguished novel.
Joseph Rodriguez
Joseph Rodriguez October 07, 2025
Such a rich narrative. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Rebecca Lewis
Rebecca Lewis January 04, 2024
I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. I am now a lifelong fan of this author.
Mary Rivera
Mary Rivera August 13, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
Amanda Hall
Amanda Hall December 29, 2024
A decent, if standard, experience. Certain acts were fascinating, while others felt like a slight endeavor to complete. Unlikely to reread, but a reasonable expenditure of time.
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