Vector CalculusNow in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world. 
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The historical sections are fascinating and give a deeper insight into the nature of mathematics. I highly recommend it for anyone wanting a little background on the abstract nature of upper level math.
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Beautiful, wellwritten, clear and not cluttered. Best textbook I have ever used.
Contents
The Geometry of Euclidean Space  1 
Differentiation  94 
HigherOrder Derivatives Maxima and Minima  181 
Double and Triple Integrals  317 
The Change of Variables Formula  368 
Integrals Over Paths and Surfaces  421 
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Common terms and phrases
arc length axis boundary chain rule change of variables closed curve component Compute constant continuous function cos2 critical points cross product curl curvature defined definition denote described determinant df/dx differentiable direction disk divergence double integral dx dy dz elementary region equal equation Evaluate EXAMPLE Exercise Fds field F Find fluid formula Fubini's theorem Gauss geometric given gradient graph gravitational Green's theorem improper integrals iterated integral Lagrange multiplier level curves limit line integral mass mathematical matrix maximum minimum multiplication Newton onetoone onevariable calculus open set oriented orthogonal parallelogram parametrization parametrized surface partial derivatives path integral perpendicular proof prove radius real numbers realvalued function rectangle region D rotation scalar Section Show sin2 SOLUTION sphere spherical coordinates Stokes Suppose surface integral tangent plane triangle unit normal unit vector vector field velocity vector Verify volume xy plane zero
References to this book
Plants in Changing Environments: Linking Physiological, Population, and ... F. A. Bazzaz No preview available  1996 
Numerical Partial Differential Equations: Finite Difference Methods J.W. Thomas Limited preview  1995 