Vector Calculus (3rd Edition)

Vector Calculus (3rd Edition)

<p style="margin: 0px;"> <b> </b> 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 Colley€s writing style, mathematical precision, level of rigor, and full selection of topics treated.</p> <p style="margin: 0px;"> </p> <p style="margin: 0px;"> <b> </b> <b>Vectors: </b>Vectors in Two and Three Dimensions. More About Vectors. The Dot Product. The Cross Product. Equations for Planes; Distance Problems. Some <i>n</i>-Dimensional Geometry. New Coordinate Systems. <b>Differentiation in Several Variables: </b>Functions of Several Variables; Graphing Surfaces. Limits. The Derivative. Properties; Higher-Order Partial Derivatives; Newton€s Method. The Chain Rule. Directional Derivatives and the Gradient.<b> Vector-Valued Functions: </b>Parametrized Curves and Kepler's Laws. Arclength and Differential Geometry. Vector Fields: An Introduction. Gradient, Divergence, Curl, and the Del Operator.<b> Maxima and Minima in Several Variables: </b>Differentials and Taylor's Theorem. Extrema of Functions. Lagrange Multipliers. Some Applications of Extrema.<b> Multiple Integration: </b>Introduction: Areas and Volumes. Double Integrals. Changing the Order of Integration. Triple Integrals. Change of Variables. Applications of Integration.<b> Line Integrals: </b>Scalar and Vector Line Integrals. Green's Theorem. Conservative Vector Fields.<b> Surface Integrals and Vector Analysis: </b>Parametrized Surfaces. Surface Integrals. Stokes's and Gauss's Theorems. Further Vector Analysis; Maxwell's Equations.<b> Vector Analysis in Higher Dimensions: </b>An Introduction to Differential Forms. Manifolds and Integrals of <i>k</i>-forms. The Generalized Stokes's Theorem. </p> <p style="margin: 0px;">  <br> </p> <b> </b> For all readers interested in multivariable calculus.