The geometry of space, curves, and surfaces; calculus in several variables; and the fundamental theorems of vector analysis — with interactive demonstrations throughout.
Contents
Geometry of Space
1 Dimensions and Coordinates2 Vectors3 Angles and Projections4 Areas and Orientation5 Planes and Standard Surfaces
Parametric Curves
6 Parameterizing Curves7 Calculus of Vector-Valued Functions8 Arc Length and Scalar Line Integrals9 Curvature, Acceleration, and Motion
Differentiation
10 Scalar Fields, Graphs, and Level Sets11 Partial Derivatives12 Linearization and Approximation13 Gradient and Directional Derivatives14 Unconstrained Optimization15 Constrained Optimization
Integration
16 Double Integrals17 Triple Integrals18 Coordinate Systems19 Change of Variables20 Scalar Surface Integrals
Vector Fields
21 Vector Fields, Divergence, and Curl22 Work and Circulation23 Flux Across Curves and Surfaces
Fundamental Theorems of Calculus
24 Fundamental Theorem for Line Integrals25 Fundamental Theorems in Two Dimensions: Green's Theorem26 Extension: Fundamental Theorems in Three Dimensions27 The Fundamental Theorems of Calculus