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Álgebra para todos: Tomo I: geometría analítica by Silva, Juan Ignacio

Álgebra para todos: Tomo I: geometría analítica

by Juan Ignacio Silva
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Book cover type: Paperback
  • ISBN13: 9788409713196
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Juan I. Silva
  • Publisher Imprint: Juan I. Silva
  • Publication Date:
  • Pages: 470
  • Original Price: GBP 15.71
  • Language: Spanish
  • Edition: N/A
  • Item Weight: 622 grams
  • BISAC Subject(s): NON-CLASSIFIABLE

Esta segunda edici�n de �lgebra para todos llega con una propuesta renovada para la ense�anza de la geometr�a anal�tica. Con un enfoque centrado en la comprensi�n intuitiva de los conceptos, este libro sigue desafiando las metodolog�as tradicionales, apostando por una did�ctica m�s visual e interactiva.

En esta nueva versi�n, el contenido ha sido completamente reformulado en LaTeX, garantizando una presentaci�n clara y profesional.

Manteniendo su esp�ritu innovador, el libro sigue integrando c�digos QR y archivos de GeoGebra, ofreciendo un puente entre la teor�a y la experimentaci�n digital. M�s que un simple texto, es una herramienta dise�ada para que cada estudiante logre una comprensi�n profunda de la geometr�a anal�tica.

Es hora de ver la geometr�a anal�tica desde una nueva perspectiva!

�ndice general

Unidad 1: Vectores
1.1. Sistemas de referencia en el plano 1
1.2. Vectores 11
1.3. Operaciones con vectores 21
1.4. Ejercicios resueltos 54

Unidad 2: Recta y plano 81
2.1. Ecuaciones de la recta en el plano 83
2.2. Ecuaciones de la recta en el espacio 101
2.3. C�mo graficar rectas 102
2.4. Ecuaciones del plano 104
2.5. Configuraci�n espacial 119
2.6. Intersecciones 131
2.7. Proyecciones 139
2.8. Distancias 158
2.9. Simetr�a 168
2.9.1. Simetr�a de punto respecto a recta 168
2.9.2. Simetr�a de punto respecto a plano 169
2.9.3. Simetr�a de recta respecto a plano 169
2.10. Familia de rectas y planos 171
2.11. Haz de planos 179
2.12. Ejercicios resueltos de recta y plano 184

Unidad 3: C�nicas 201
3.1. Lugar geom�trico 201
3.2. Secciones c�nicas 204
3.3. Circunferencia 208
3.4. Elipse 232
3.5. Par�bola 251
3.6. Hip�rbola 262
3.7. Ecuaci�n general de segundo grado 276
3.8. Ejercicios resueltos de c�nicas 308

Unidad 4. Superficies cu�dricas 335
4.1. El origen del nombre "cu�dricas" 335
4.2. Superficies de revoluci�n 337
4.3. Superficies cil�ndricas 357
4.4. Paraboloide hiperb�lico o "silla de montar" 364
4.5. Mapas conceptuales 366
4.6. Ecuaci�n de segundo grado 371
4.7. Ejercicios resueltos de superficies cu�dricas 409

Ap�ndice 435
A. Simetr�a . . . . . . . . . . . . . . . . . . . . . . . . . 436
A.1. Simetr�a de c�nicas . . . . . . . . . . . . . . . 436
A.2. Simetr�a de superficies cu�dricas . . . . . . . . 438
B. Transformaci�n de coordenadas . . . . . . . . . . . . 442
B.1. Traslaci�n . . . . . . . . . . . . . . . . . . . . 442
B.2. Dilataci�n y contracci�n . . . . . . . . . . . . 445
C. Reflexi�n . . . . . . . . . . . . . . . . . . . . . . . . . 452
Notas Finales para el Estudiante 455

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