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A Matemática do Ensino Médio Volume 3

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A Matemática do Ensino Médio Volume 3

4.85 82,930 ratings · 1,716 reviews
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Overview: O LivroEm continuação aos dois volumes anteriores, esse livro completa a exposição dos principais tópicos matemáticos estudados no Ensino Médio.Os assuntos que ele aborda são a Geometrias Analíticas (plana e espacial), vetores, matrizes, determinantes, sistemas de equações lineares, números complexos, polinômios e equações algébricas. A matéria aqui apresentada, como a dos demais volumes, foi objetivo de vários cursos oferecidos no IMPA a professores do Ensino Médio, dentro do programa Prociências, da CAPES.Os AutoresElon Lages Lima nasceu em Maceió, onde estudou até o curso secundário, começou seu bacharelado em Matemática no Ceará e o concluiu no Rio de Janeiro. Fez mestrado e doutorado na Universidade de Chicago. É um Guggenheim Fellow, membro titular da Academia Brasileira de Ciências, ganhador do Prêmio Anísio Teixeira em Educação (1991), ex-presidente da Sociedade Brasileira de Matemática e ex-Diretor do IMPA, onde começou sua carreira profissional e permanece até hoje. Este é o seu quarto livro no Projeto Euclides, um dos quais (Espeços Métricos) ganhou o Prêmio Jabuti em 1978. Continua interessado em esportes, torcendo pelo Fluminense, escrevendo livros de Matemática e importunando seus colegas para que façam o mesmo, quer dizer, escrevam livros.Paulo Cezar Pinto Carvalho graduou-se pelo IME em 1975, fez mestrado no IMPA e doutorou-se em matemática na Cornell University em 1984. É pesquisador do IMPA, trabalha sobretudo em modelagem geométrica e pesquisa operacional. É membro da Comissão de Olimpíadas de Matemática da SBM e outros.Eduardo Wagner é professor de Matemática no Rio de Janeiro. Vem atuando há 10 anos como professor nos cursos de atualização de professores do Ensino Médio promovidos pelo IMPA. É membro da Comissão de Olimpíadas de Matemática da SBM tendo sido seu coordenador de 1995 a 2000. É membro do Comitê Editorial da Revista do Professor de Matemática da SBM, tendo contribuído com diversos artigos sobre Ensino da Matemática e resolução de problemas. Tem muitos livros publicados no Brasil e no exterior. Além da matemática, a música é sua principal atração.Augusto César de Oliveira Morgado é carioca, botafoguense, foi professor da Escola Naval e da Escola Nacional de Ciências Estatísticas do IBGE. Atualmente trabalha na Fundação Getúlio Vargas, lecionando Estatística e Matemática Financeira. Também tem participado em cursos de atualização para professores de Ensino Médio, no Brasil e no Peru. Autor de vários livros da Coleção do Professor de MatemáticaConteúdoCapítulo 1 - Geometria Analítica Plana1. Introdução2. Coordenadas na reta3. Coordenadas no plano4. A distância entre dois pontos5. Escolhendo o sistema de coordenadas6. As equações da reta7. Ângulo entre duas retas8. Distância de um ponto a uma reta9. Área de um triângulo10. Equação da circunferência11. Vetores no planoExercíciosCapítulo 2 - Geometria Analítica Espacial1. Introdução2. Coordenadas no espaço3. As equações paramétricas de uma reta4. Distância entre dois pontos no espaço5. Vetores no espaço6. Equações do plano7. Distância de um ponto a um planoExercíciosCapítulo 3 - Sistemas de Equações Lineares1. Sistemas com duas incógnitas2. Duas equações com três incógnitas3. Três equações com três incógnitas4. Escalonamento (eliminação gaussiana)ExercícioCapítulo 4 - Matrizes e Determinantes1. Introdução2. Multiplicação de matrizes3. Determinantes4. A regra de Cramer5. O determinante do produto de duas matrizes6. Caracterização das matrizes invertíveis ExercíciosCapítulo 5 - Números Complexos1. Introdução2. A forma algébrica3. A forma trigonométrica4. Raízes da unidade 5. InversãoCapítulo 6 - Equações Algébricas1. Introdução 2. Polinômios complexos 3. Divisão de polinômios4. Divisão de um polinômio por x - a 5. Reduzindo o grau de uma equação algébrica 6. O teorema fundamental da Álgebra7. Relações entre coeficientes e raízes8. Equações algébricas com coeficientes reais9. Demonstrando o Teorema Fundamental da Álgebra10. Resolução numérica de equações

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Pages 247
Language Por
Publisher SBM
Published N/A
ISBN 24703189
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Elon Lages Lima
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Elon Lages Lima is the author of several novels. Originally from the East Coast, they now live in the Midwest with family. In addition to writing, Elon Lages Lima enjoys gardening, cooking, and reading way past bedtime. Their work often explores the complexities of everyday life and human relationships.

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I thoroughly enjoyed the elegance of it. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. A solid 4 stars from me.
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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. Quite impressive overall.
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An acceptable diversion. Certain acts were fascinating, while others felt like a slight endeavor to complete. Perfectly average.
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I was completely blown away. The author orchestrated a breathtaking finale. Truly a work of art. I am now a lifelong fan of this author.
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A profoundly satisfying read. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An absolute must-read for connoisseurs of the genre.
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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.
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A highly sophisticated read. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Excellent, though slightly flawed. A brilliant concept executed with flair. Just a few pacing choices I would change. A very distinguished novel.
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Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An effortless 5 stars.
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Michelle Wilson September 07, 2024
A very strong entry. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Cynthia Rodriguez
Cynthia Rodriguez June 08, 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.
Karen Turner
Karen Turner October 12, 2024
Exceeded all my expectations. I adored how the story unfolded. It kept me captivated without sacrificing elegance. I am now a lifelong fan of this author.
John Torres
John Torres December 31, 2024
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
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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.
Robert Diaz
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I was completely blown away. I became deeply invested in the protagonist's journey. A masterclass in storytelling. A true literary gem.
Sharon Taylor
Sharon Taylor October 14, 2025
It was adequate. The prose was competent, yet the characters lacked the depth I usually seek. Unlikely to reread, but a reasonable expenditure of time.
Amanda Clark
Amanda Clark August 18, 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.
John Gonzalez
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Karen Campbell April 11, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Stephanie Wright
Stephanie Wright February 06, 2025
Took a moment to build, but the payoff was spectacular. The protagonist was compelling, though some subplots felt slightly overshadowed. Quite impressive overall.
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Kevin Parker March 25, 2025
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.
Stephanie Ramirez
Stephanie Ramirez April 30, 2025
Such a rich narrative. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Sharon Scott
Sharon Scott June 11, 2024
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Thomas Walker
Thomas Walker December 31, 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.
Joshua Ramirez
Joshua Ramirez January 20, 2024
Exceeded all my expectations. I became deeply invested in the protagonist's journey. A masterclass in storytelling. Worth every moment spent reading.
Michael Turner
Michael Turner February 27, 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.
Daniel Clark
Daniel Clark August 05, 2025
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. I would highly recommend this to discerning readers.
Gary Sanchez
Gary Sanchez September 26, 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.
David Wright
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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.
David Roberts
David Roberts July 17, 2025
An acceptable diversion. The prose was competent, yet the characters lacked the depth I usually seek. A fair 3 stars.
Melissa Ramirez
Melissa Ramirez September 17, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Kenneth Brown
Kenneth Brown February 13, 2025
Honestly one of the most premium reading experiences lately. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Carol Clark
Carol Clark December 26, 2025
A profoundly satisfying read. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. Worth every moment spent reading.
Kenneth Wright
Kenneth Wright April 12, 2024
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Margaret Thomas
Margaret Thomas April 11, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
David Gomez
David Gomez June 06, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Michael Cruz
Michael Cruz December 25, 2024
A profoundly satisfying read. I adored how the story unfolded. It kept me captivated without sacrificing elegance. An absolute must-read for connoisseurs of the genre.
Kevin Taylor
Kevin Taylor July 16, 2025
Absolutely brilliant. I became deeply invested in the protagonist's journey. A masterclass in storytelling. An effortless 5 stars.
Michelle Wright
Michelle Wright August 07, 2024
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Nicholas Lopez
Nicholas Lopez March 07, 2024
A very strong entry. It held my rapt attention, even when certain twists were telegraphed. I would highly recommend this to discerning readers.
Mark Clark
Mark Clark March 06, 2024
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An effortless 5 stars.
Nicholas Lopez
Nicholas Lopez November 13, 2025
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.
Melissa King
Melissa King October 04, 2025
A profoundly satisfying read. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An effortless 5 stars.
Christopher Gonzalez
Christopher Gonzalez September 15, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. An effortless 5 stars.
George Miller
George Miller December 18, 2025
Excellent, though slightly flawed. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. A very distinguished novel.
Eric Evans
Eric Evans September 15, 2025
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I will undoubtedly revisit this masterpiece.
David Green
David Green March 13, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Mary Garcia
Mary Garcia September 27, 2024
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Richard Johnson
Richard Johnson November 17, 2025
A very strong entry. The middle had a deliberate pace, but the climax was phenomenal. Quite impressive overall.
Amanda Clark
Amanda Clark November 08, 2025
A profoundly satisfying read. The prose is exquisite. It’s accessible yet undeniably sophisticated. A true literary gem.
Donald Nelson
Donald Nelson April 07, 2025
I thoroughly enjoyed the elegance of it. It held my rapt attention, even when certain twists were telegraphed. Quite impressive overall.
Brian Anderson
Brian Anderson December 30, 2024
A very strong entry. The protagonist was compelling, though some subplots felt slightly overshadowed. A wonderful companion for a quiet weekend.
Eric Johnson
Eric Johnson May 11, 2024
I was completely blown away. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Daniel Jones
Daniel Jones August 27, 2025
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. Worth every moment spent reading.
Christopher Nguyen
Christopher Nguyen February 23, 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.
Gary Brown
Gary Brown February 22, 2024
I thoroughly enjoyed the elegance of it. A brilliant concept executed with flair. Just a few pacing choices I would change. A wonderful companion for a quiet weekend.
Carol Nelson
Carol Nelson December 27, 2025
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Melissa Edwards
Melissa Edwards September 26, 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.
Robert Jones
Robert Jones May 07, 2025
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 Edwards
Karen Edwards July 30, 2025
Took a moment to build, but the payoff was spectacular. Beautiful writing, though I craved slightly more depth in the lore. Still, undeniably engaging. Quite impressive overall.
Emily Brown
Emily Brown April 12, 2024
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.
Mary Torres
Mary Torres September 09, 2025
I was completely blown away. I adored how the story unfolded. It kept me captivated without sacrificing elegance. Worth every moment spent reading.
Kevin Taylor
Kevin Taylor July 04, 2024
Excellent, though slightly flawed. The middle had a deliberate pace, but the climax was phenomenal. A very distinguished novel.
Richard Collins
Richard Collins November 25, 2025
I was completely blown away. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. A true literary gem.
Anthony Rodriguez
Anthony Rodriguez May 28, 2024
Masterpiece from start to finish. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
Kevin Campbell
Kevin Campbell December 05, 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.
George Moore
George Moore February 03, 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.
Michael Cruz
Michael Cruz February 17, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. I am now a lifelong fan of this author.
Michelle Wilson
Michelle Wilson September 24, 2024
I was completely blown away. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An absolute must-read for connoisseurs of the genre.
Stephanie King
Stephanie King July 16, 2025
Masterpiece from start to finish. I adored how the story unfolded. It kept me captivated without sacrificing elegance. A true literary gem.
Kenneth Walker
Kenneth Walker December 29, 2025
Absolutely brilliant. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. A true literary gem.
Sarah  Davis
Sarah Davis October 30, 2025
Absolutely brilliant. The author orchestrated a breathtaking finale. Truly a work of art. An absolute must-read for connoisseurs of the genre.
Susan Green
Susan Green May 28, 2024
Absolutely brilliant. The prose is exquisite. It’s accessible yet undeniably sophisticated. I will undoubtedly revisit this masterpiece.
Sandra Lewis
Sandra Lewis May 02, 2024
Such a rich narrative. It strikes a perfect harmony of dialogue and world-building. Every chapter felt necessary. An effortless 5 stars.
Betty Perez
Betty Perez October 06, 2024
A profoundly satisfying read. The author orchestrated a breathtaking finale. Truly a work of art. A true literary gem.
Donald Hernandez
Donald Hernandez January 21, 2024
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.
Nancy Nelson
Nancy Nelson December 29, 2024
Exceeded all my expectations. The pacing was impeccable and the characters felt incredibly authentic. I was completely immersed. An absolute must-read for connoisseurs of the genre.
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