Calculus, Multivariable: Early Transcendental Functions

Overview

Main description

Students who have used Smith/Minton's Calculus say it was easier to read than any other math book they've used. That testimony underscores the success of the authors’ approach, which combines the best elements of reform with the most reliable aspects of mainstream calculus teaching, resulting in a motivating, challenging book. Smith/Minton also provide exceptional, reality-based applications that appeal to students’ interests and demonstrate the elegance of math in the world around us. New features include: • A new organization placing all transcendental functions early in the book and consolidating the introduction to L'Hôpital's Rule in a single section. • More concisely written explanations in every chapter. • Many new exercises (for a total of 7,000 throughout the book) that require additional rigor not found in the 2nd Edition. • New exploratory exercises in every section that challenge students to synthesize key concepts to solve intriguing projects. • New commentaries (“Beyond Formulas”) that encourage students to think mathematically beyond the procedures they learn. • New counterpoints to the historical notes, “Today in Mathematics,” that stress the contemporary dynamism of mathematical research and applications, connecting past contributions to the present. • An enhanced discussion of differential equations and additional applications of vector calculus.

Table of contents

10 Vectors and the Geometry of Space 10.1 Vectors in the Plane 10.2 Vectors in Space 10.3 The Dot Product Components and Projections10.4 The Cross Product 10.5 Lines and Planes in Space 10.6 Surfaces in Space 11 Vector-Valued Functions 11.1 Vector-Valued Functions 11.2 The Calculus of Vector-Valued Functions 11.3 Motion in Space 11.4 Curvature11.5 Tangent and Normal VectorsTangential and Normal Components of Acceleration Kepler’s Laws11.6 Parametric Surfaces 12 Functions of Several Variables and Partial Differentiation 12.1 Functions of Several Variables 12.2 Limits and Continuity 12.3 Partial Derivatives 12.4 Tangent Planes and Linear ApproximationsIncrements and Differentials12.5 The Chain Rule 12.6 The Gradient and Directional Derivatives 12.7 Extrema of Functions of Several Variables 12.8 Constrained Optimization and Lagrange Multipliers 13 Multiple Integrals 13.1 Double Integrals 13.2 Area, Volume, and Center of Mass 13.3 Double Integrals in Polar Coordinates 13.4 Surface Area 13.5 Triple IntegralsMass and Center of Mass13.6 Cylindrical Coordinates 13.7 Spherical Coordinates 13.8 Change of Variables in Multiple Integrals 14 Vector Calculus 14.1 Vector Fields 14.2 Line Integrals 14.3 Independence of Path and Conservative Vector Fields 14.4 Green's Theorem 14.5 Curl and Divergence 14.6 Surface Integrals14.7 The Divergence Theorem 14.8 Stokes' Theorem 14.9 Applications of Vector Calculus 15 Second-Order Differential Equations15.1 Second-Order Equations with Constant Coefficients 15.2 Nonhomogeneous Equations: Undetermined Coefficients15.3 Applications of Second-Order Differential Equations15.4 Power Series Solutions of Differential EquationsAppendix A: Proofs of Selected TheoremsAppendix B: Answers to Odd-Numbered Exercises