Author(s): Nitecki Z.
Edition: draft
Year: 2009
Language: English
Pages: 799
Preface......Page 3
Contents......Page 9
Locating Points in Space......Page 13
Vectors and Their Arithmetic......Page 32
Lines in Space......Page 44
Projection of Vectors; Dot Products......Page 59
Planes......Page 69
Cross Products......Page 83
Applications of Cross Products......Page 110
Conic Sections......Page 127
Parametrized Curves......Page 147
Calculus of Vector-Valued Functions......Page 166
Regular Curves......Page 180
Integration along Curves......Page 196
Real-Valued Functions: Differentiation......Page 215
Continuity and Limits......Page 216
Linear and Affine Functions......Page 224
Derivatives......Page 231
Level Sets......Page 253
Surfaces and their Tangent Planes......Page 281
Extrema......Page 308
Higher Derivatives......Page 330
Local Extrema......Page 345
The Principal Axis Theorem......Page 355
Quadratic Curves and Surfaces......Page 379
Mappings and Transformations......Page 395
Linear Mappings......Page 397
Differentiable Mappings......Page 406
Linear Systems of Equations......Page 420
Nonlinear Systems......Page 432
Integration over Rectangles......Page 465
Integration over Planar Regions......Page 486
Changing Coordinates......Page 507
Surface Integrals......Page 534
Integration in 3D......Page 554
Line Integrals......Page 567
The Fundamental Theorem for Line Integrals......Page 584
Green's Theorem......Page 606
2-forms in R2......Page 622
Stokes' Theorem......Page 627
2-forms in R3......Page 649
The Divergence Theorem......Page 666
3-forms and the Generalized Stokes Theorem......Page 687
Apollonius......Page 697
Focus-Directrix......Page 705
Kepler and Newton......Page 709
Intrinsic Geometry of Curves......Page 721
Matrix Basics......Page 739
Matrix Algebra......Page 740
Row Reduction......Page 744
Matrices as Transformations......Page 751
Rank......Page 756
22 Determinants......Page 763
33 Determinants......Page 765
Determinants and Invertibility......Page 770
Surface Area......Page 773
Bibliography......Page 781
Index......Page 786
