this article makes use of the language and notation of vectors and matrices to explain matters in multivariable calculus. obtainable to a person with a great heritage in single-variable calculus, it provides extra linear algebra than frequently present in a multivariable calculus publication. Colley balances this with very transparent and expansive exposition, many figures, and diverse, wide-ranging routines. teachers will savor Colley’s writing type, mathematical precision, point of rigor, and entire collection of themes 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 different Variables: Functions of a number of Variables; Graphing Surfaces. Limits. The spinoff. houses; Higher-Order Partial Derivatives; Newton’s procedure. The Chain Rule. Directional Derivatives and the Gradient. Vector-Valued capabilities: 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 different Variables: Differentials and Taylor's Theorem. Extrema of capabilities. Lagrange Multipliers. a few purposes of Extrema. a number of Integration: Introduction: parts and Volumes. Double Integrals. altering the Order of Integration. Triple Integrals. swap 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. extra Vector research; Maxwell's Equations. Vector research in larger Dimensions: An creation to Differential types. Manifolds and Integrals of k-forms. The Generalized Stokes's Theorem.
For all readers attracted to multivariable calculus.