Vector Calculus
Second Edition

by Barr

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Select a chapter: Section 1.1: Rectangular Coordinates and Distance Section 1.2: Graphs of Functions of Two Variables Section 1.3: Quadric Surfaces Section 1.4: Cylindrical and Spherical Coordinates Section 1.5: Vectors in Three-Dimensional Space Section 1.6: The Dot Product, Projection, and Work Section 1.7: The Cross Product and Determinants Section 1.8: Planes and Lines in R3 Section 1.9: Vector-Valued Functions Section 1.10: Derivatives and Motion Section 2.1: Vectors and Coordinate Geometry in Rn Section 2.2: Matrices Section 2.3: Linear Transformations Section 2.4: Geometry of Linear Transformations Section 2.5: Quadratic Forms Section 3.1: Graphs, Level Sets, and Vector Fields Geometry Section 3.2: Limits and Continuity Section 3.3: Open Sets, Closed Sets, and Continuity Section 3.4: Partial Derivatives Section 3.5: Differentiation and the Total Derivative Section 3.6: The Chain Rule Section 4.1: The Gradient and Directional Derivative Section 4.2: Divergence and Curl Section 4.3: Taylor's Theorem Section 4.4: Local Extrema Section 4.5: Constrained Optimization and Lagrange Multipliers Section 5.1: Paths and Arclength Section 5.2: Line Integrals Section 5.3: Double Integrals Section 5.4: Triple Integrals Section 5.5: Parametrized Surfaces and Surface Area Section 5.6: Surface Integrals Section 5.7: Change of Variables in Double Integrals Section 5.8: Change of Variables in Triple Integrals Section 6.1: The Fundamental Theorem for Path Integrals Section 6.2: Green's Theorem Section 6.3: The Divergence Theorem Section 6.4: Stokes's Theorem