Multivariable Calculus with Matrices

For standard undergraduate Calculus courses. Multivariable Calculus now has a full chapter of material on matrices and eigenvalues up front. All of Multivariable Calculus has been rewritten with matrix notation.* NEW-Linear algebra and matrices-Found in Semester III. Linear systems and matrices through determinants and eigenvalues are now introduced in Chapter 11. The subsequent multivariable chapters now integrate matrix methods and terminology with traditional multivariable calculus (e.g., the chain rule in matrix form). * NEW-CD-ROM/WWW learning resources fully integrated throughout-The CD-ROM accompanying the book contains a student-usable, functional array of fully integrated learning resources linked to individual sections of the text. Most text examples are animated with 'What-If' scenarios. The whole text is available in interactive Maple notebooks. * NEW-320 End-of-section Concepts/Questions and Discussion -Adds beginning conceptual questions that can serve as the basis for either writing assignments or for individual and group discussion. Also added are higher-end problems at the ends of problem sets. * NEW-True/False Study Guide-Ten author-written true/false questions (with hints) review each section. These 1080 new questions are not printed in the book, but the icon takes you to them on the CD-ROM. * NEW-Computer projects-At the end of each section. Now briefer, with the deletion of in-text technology details. Maple/Mathematica/Matlab/Calculator resources for each Project are included on the CD-ROM. * A lively and accessible writing style. * The most extensively visual text in the market-Highlighted by hundreds of Mathematica and MATLAB generated figures throughout the book. * More than 795 new problems-Almost all of these are in the intermediate range of difficulty, neither highly theoretical nor computationally routine. Some reflect an emphasis on new technology by encouraging the use of technology ranging from a graphing calculator to a computer algebra system. * Website available to users-With student help center staffed by graduate students available on Sunday evenings. Site includes animations of most text examples with 'what-if' scenarios, challenging applications that require the user to have some type of number crunching software, self-paced quizzes, and internet links of additional calculus material.

Table of Contents:
10. Infinite Series. Introduction. Infinite Sequences. Infinite Series and Convergence. Taylor Series and Taylor Polynomials. The Integral Test. Comparison Tests for Positive-Term Series. Alternating Series and Absolute Convergence. Power Series. Power Series Computations. Series Solutions of Differential Equations. 11. Vectors and Matrices. Vectors in the Plane. Three-Dimensional Vectors. The Cross Product of Vectors. Lines and Planes in Space. Linear Systems and Matrices. Matrix Operations. Eigenvalues and Rotated Conics. 12. Curves and Surfaces in Space. Curves and Motion in Space. Curvature and Acceleration. Cylinders and Quadric Surfaces. Cylindrical and Spherical Coordinates. 13. Partial Differentiation. Introduction. Functions of Several Variables. Limits and Continuity. Partial Derivatives. Multivariable Optimization Problems. Linear Approximation and Matrix Derivatives. The Multivariable Chain Rule. Directional Derivatives and Gradient Vectors. Lagrange Multipliers and Constrained Optimization. Critical Points of Multivariable Functions. 14. Multiple Integrals. Double Integrals. Double Integrals over More General Regions. Area and Volume by Double Integration. Double Integrals in Polar Coordinates. Applications of Double Integrals. Triple Integrals. Integration in Cylindrical and Spherical Coordinates. Surface Area. Change of Variables in Multiple Integrals. 15. Vector Calculus. Vector Fields. Line Integrals. The Fundamental Theorem and Independence of Path. Green's Theorem. Surface Integrals. The Divergence Theorem. Stokes' Theorem. Appendices. Answers. Index.