Vector Calculus (3rd Edition)

this article makes use of the language and notation of vectors and matrices to elucidate matters in multivariable calculus. obtainable to somebody with an exceptional heritage in single-variable calculus, it offers extra linear algebra than often present in a multivariable calculus ebook. Colley balances this with very transparent and expansive exposition, many figures, and diverse, wide-ranging routines. teachers will delight in Colley’s writing variety, mathematical precision, point of rigor, and entire choice of subject matters treated.

Vectors: Vectors in and 3 Dimensions. extra approximately Vectors. The Dot Product. The move Product. Equations for Planes; Distance difficulties. a few n-Dimensional Geometry. New Coordinate structures. Differentiation in numerous Variables: Functions of a number of Variables; Graphing Surfaces. Limits. The by-product. houses; Higher-Order Partial Derivatives; Newton’s technique. The Chain Rule. Directional Derivatives and the Gradient. Vector-Valued features: Parametrized Curves and Kepler's legislation. Arclength and Differential Geometry. Vector Fields: An creation. Gradient, Divergence, Curl, and the Del Operator. Maxima and Minima in numerous Variables: Differentials and Taylor's Theorem. Extrema of capabilities. Lagrange Multipliers. a few purposes of Extrema. a number of Integration: Introduction: components and Volumes. Double Integrals. altering the Order of Integration. Triple Integrals. switch of Variables. functions of Integration. Line Integrals: Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields. floor Integrals and Vector research: Parametrized Surfaces. floor Integrals. Stokes's and Gauss's Theorems. additional Vector research; Maxwell's Equations. Vector research in larger Dimensions: An advent to Differential varieties. Manifolds and Integrals of k-forms. The Generalized Stokes's Theorem.

For all readers drawn to multivariable calculus.