Calculus Multivariable

The ninth edition continues to provide engineers with an accessible resource for learning calculus. The book includes carefully worked examples and special problem types that help improve comprehension. New applied exercises demonstrate the usefulness of the mathematics. Additional summary tables with step-by-step details are also incorporated into the chapters to make the concepts easier to understand. The Quick Check and Focus on Concepts exercises have been updated as well. Engineers become engaged in the material because of the easy-to-read style and real-world examples.

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Ch 11 Three-Dimensional Space; Vectors 11.1 Rectangular Coordinates in 3-Space; Spheres; Cylindrical Surfaces 11.2 Vectors 11.3 Dot Product; Projections 11.4 Cross Product 11.5 Parametric Equations of Lines 11.6 Planes in 3-Space 11.7 Quadric Surfaces 11.8 Cylindrical and Spherical Coordinates Ch 12 Vector-Valued Functions 12.1 Introduction to Vector-Valued Functions 12.2 Calculus of Vector-Valued Functions 12.3 Change of Parameter; Arc Length 12.4 Unit Tangent, Normal, and Binormal Vectors 12.5 Curvature 12.6 Motion Along a Curve 12.7 Kepler's Laws of Planetary Motion Ch 13 Partial Derivatives 13.1 Functions of Two or More Variables 13.2 Limits and Continuity 13.3 Partial Derivatives 13.4 Differentiability, Differentials, and Local Linearity 13.5 The Chain Rule 13.6 Directional Derivatives and Gradients 13.7 Tangent Planes and Normal Vectors 13.8 Maxima and Minima of Functions of Two Variables 13.9 Lagrange Multipliers Ch 14 Multiple Integrals 14.1 Double Integrals 14.2 Double Integrals over Nonrectangular Regions 14.3 Double Integrals in Polar Coordinates 14.4 Surface Area; Parametric Surfaces} 14.5 Triple Integrals 14.6 Triple Integrals in Cylindrical and Spherical Coordinates 14.7 Change of Variable in Multiple Integrals; Jacobians 14.8 Centers of Gravity Using Multiple Integrals Ch 15 Topics in Vector Calculus 15.1 Vector Fields 15.2 Line Integrals 15.3 Independence of Path; Conservative Vector Fields 15.4 Green's Theorem 15.5 Surface Integrals 15.6 Applications of Surface Integrals; Flux 15.7 The Divergence Theorem 15.8 Stokes' Theorem Appendix [order of sections TBD] A Graphing Functions Using Calculators and Computer Algebra Systems B Trigonometry Review C Solving Polynomial Equations D Mathematical Models E Selected Proofs Web Appendices F Real Numbers, Intervals, and Inequalities G Absolute Value H Coordinate Planes, Lines, and Linear Functions I Distance, Circles, and Quadratic Functions J Second-Order Linear Homogeneous Differential Equations; The Vibrating String K The Discriminant ANSWERS PHOTOCREDITS INDEX

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