Vector Calculus (3rd Edition)

This text uses the language and notation of vectors and matrices to clarify issues in multivariable calculus. Accessible to anyone with a good background in single-variable calculus it presents more linear algebra than usually found in a multivariable calculus book. Colley balances this with very clear and expansive exposition many figures and numerous wide-ranging exercises. Instructors will appreciate Colleys writing style mathematical precision level of rigor and full selection of topics treated. Vectors: Vectors in Two and Three Dimensions. More About Vectors. The Dot Product. The Cross Product. Equations for Planes; Distance Problems. Some n-Dimensional Geometry. New Coordinate Systems. Differentiation in Several Variables: Functions of Several Variables; Graphing Surfaces. Limits. The Derivative. Properties; Higher-Order Partial Derivatives; Newtons Method. The Chain Rule. Directional Derivatives and the Gradient. Vector-Valued Functions: Parametrized Curves and Keplers Laws. Arclength and Differential Geometry. Vector Fields: An Introduction. Gradient Divergence Curl and the Del Operator. Maxima and Minima in Several Variables: Differentials and Taylors Theorem. Extrema of Functions. Lagrange Multipliers. Some Applications of Extrema. Multiple Integration: Introduction: Areas and Volumes. Double Integrals. Changing the Order of Integration. Triple Integrals. Change of Variables. Applications of Integration. Line Integrals: Scalar and Vector Line Integrals. Greens Theorem. Conservative Vector Fields. Surface Integrals and Vector Analysis: Parametrized Surfaces. Surface Integrals. Stokess and Gausss Theorems. Further Vector Analysis; Maxwells Equations. Vector Analysis in Higher Dimensions: An Introduction to Differential Forms. Manifolds and Integrals of k-forms. The Generalized Stokess Theorem. For all readers interested in multivariable calculus.