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! colspan="3" | 13. APPLICATIONS OF VECTOR ALGEBRA TO ANALYTIC GEOMETRY
! colspan="3" | 13. APPLICATIONS OF VECTOR ALGEBRA TO ANALYTIC GEOMETRY
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| 1 || Introduction || 471
| 13.1 || Introduction || 471
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| 2 || Lines in n-space || 472
| 13.2 || Lines in n-space || 472
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! colspan="3" | Chapter 16: Induction and Summations
| 13.3 || Some simple properties of straight lines || 473
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| 1 || Induction || 383
| 13.4 || Lines and vector-valued functions || 474
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| 2 || Summations || 388
| 13.5 || Exercises || 477
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| 3 || Geometric series || 396
| 13.6 || Planes in Euclidean n-space || 478
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! colspan="3" | Chapter 17: Determinants
| 13.7 || Planes and vector-valued functions || 481
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| 1 || Matrices || 401
| 13.8 || Exercises || 482
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| 2 || Determinants of order 2 || 406
| 13.9 || The cross product || 483
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| 3 || Properties of 2 x 2 determinants || 409
| 13.10 || The cross product expressed as a determinant || 486
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| 4 || Determinants of order 3 || 414
| 13.11 || Exercises || 487
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| 5 || Properties of 3 x 3 determinants || 418
| 13.12 || The scalar triple product || 488
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| 6 || Cramer's Rule || 424
| 13.13 || Cramer's rule for solving a system of three linear equations || 490
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! colspan="2" | Index || 429
| 13.14 || Exercises || 491
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| 13.15 || Normal vectors to planes || 493
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| 13.16 || Linear Cartesian equations for planes || 494
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| 13.17 || Exercises || 496
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| 13.18 || The conic sections || 497
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| 13.19 || Eccentricity of conic sections || 500
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| 13.20 || Polar equations for conic sections || 501
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| 13.21 || Exercises || 503
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| 13.22 || Conic sections symmetric about the origin || 504
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| 13.23 || Cartesian equations for the conic sections || 505
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| 13.24 || Exercises || 508
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| 13.25 || Miscellaneous exercises on conic sections || 509
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! colspan="3" | 14. CALCULUS OF VECTOR-VALUED FUNCTIONS
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| 14.1 || Vector-valued functions of a real variable || 512
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| 14.2 || Algebraic operations. Components || 512
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| 14.3 || Limits, derivatives, and integrals || 513
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| 14.4 || Exercises || 516
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| 14.5 || Applications to curves. Tangency || 517
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| 14.6 || Applications to curvilinear motion. Velocity, speed, and acceleration || 520
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| 14.7 || Exercises || 524
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| 14.8 || The unit tangent, the principal normal, and the osculating plane of a curve || 525
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| 14.9 || Exercises || 528
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| 14.10 || The definition of arc length || 529
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| 14.11 || Additivity of arc length || 532
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| 14.12 || The arc-length function || 533
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| 14.13 || Exercises || 535
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| 14.14 || Curvature of a curve || 536
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| 14.15 || Exercises || 538
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| 14.16 || Velocity and acceleration in polar coordinates || 540
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| 14.17 || Plane motion with radial acceleration || 542
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| 14.18 || Cylindrical coordinates || 543
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| 14.19 || Exercises || 543
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| 14.20 || Applications to planetary motion || 545
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| 14.21 || Miscellaneous review exercises || 549
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! colspan="3" | 15. LINEAR SPACES
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| 15.1 || Introduction || 551
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| 15.2 || The definition of a linear space || 551
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| 15.3 || Examples of linear spaces || 552
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| 15.4 || Elementary consequences of the axioms || 554
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| 15.5 || Exercises || 555
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| 15.6 || Subspaces of a linear space || 556
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| 15.7 || Dependent and independent sets in a linear space || 557
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| 15.8 || Bases and dimension || 559
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| 15.9 || Exercises || 560
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| 15.10 || Inner products, Euclidean spaces, norms || 561
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| 15.11 || Orthogonality in a Euclidean space || 564
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| 15.12 || Exercises || 566
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| 15.13 || Construction of orthogonal sets. The Gram-Schmidt process || 568
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| 15.14 || Orthogonal complements. Projections || 572
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| 15.15 || Best approximation of elements in a Euclidean space by elements in a finite-dimensional subspace || 574
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| 15.16 || Exercises || 576
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! colspan="3" | 16. LINEAR TRANSFORMATIONS AND MATRICES
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| 16.1 || Linear transformations || 578
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| 16.2 || Null space and range || 579
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| 16.3 || Nullity and rank || 581
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| 16.4 || Exercises || 582
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| 16.5 || Algebraic operations on linear transformations || 583
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| 16.6 || Inverses || 585
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| 16.7 || One-to-one linear transformations || 587
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| 16.8 || Exercises || 589
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| 16.9 || Linear transformations with prescribed values || 590
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| 16.10 || Matrix representations of linear transformations || 591
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| 16.11 || Construction of a matrix representation in diagonal form || 594
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| 16.12 || Exercises || 596
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| 16.13 || Linear spaces of matrices || 597
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| 16.14 || Isomorphism between linear transformations and matrices || 599
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| 16.15 || Multiplication of matrices || 600
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| 16.16 || Exercises || 603
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| 16.17 || Systems of linear equations || 605
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| 16.18 || Computation techniques || 607
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| 16.19 || Inverses of square matrices || 611
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| 16.20 || Exercises || 613
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| 16.21 || Miscellaneous exercises on matrices || 614
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! colspan="2" | Answers to exercises || 617
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! colspan="2" | Index || 657
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[[Category:Mathematics]]
[[Category:Mathematics]]
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