Multivariable Calculus

<div class="c-un-numbered-headers-and-contents-list__container"> <ol start="10"> <li><strong>Sequences and Infinite Series</strong> <ul> <li>10.1 An Overview</li> <li>10.2 Sequences</li> <li>10.3 Infinite Series</li> <li>10.4 The Divergence and Integral Tests</li> <li>10.5 Comparison Tests</li> <li>10.6 Alternating Series</li> <li>10.7 The Ratio and Root Tests</li> <li>10.8 Choosing a Convergence Test</li> </ul> <ul> <li>Review Exercises</li> </ul></li> <li><strong>Power Series</strong> <ul> <li>11.1 Approximating Functions with Polynomials</li> <li>11.2 Properties of Power Series</li> <li>11.3 Taylor Series</li> <li>11.4 Working with Taylor Series</li> </ul> <ul> <li>Review Exercises</li> </ul></li> <li><strong>Parametric and Polar Curves</strong> <ul> <li>12.1 Parametric Equations</li> <li>12.2 Polar Coordinates</li> <li>12.3 Calculus in Polar Coordinates</li> <li>12.4 Conic Sections</li> </ul> <ul> <li>Review Exercises</li> </ul></li> <li><strong>Vectors and the Geometry of Space</strong> <ul> <li>13.1 Vectors in the Plane</li> <li>13.2 Vectors in Three Dimensions</li> <li>13.3 Dot Products</li> <li>13.4 Cross Products</li> <li>13.5 Lines and Planes in Space</li> <li>13.6 Cylinders and Quadric Surfaces</li> </ul> <ul> <li>Review Exercises</li> </ul></li> <li><strong>Vector-Valued Functions</strong> <ul> <li>14.1 Vector-Valued Functions</li> <li>14.2 Calculus of Vector-Valued Functions</li> <li>14.3 Motion in Space</li> <li>14.4 Length of Curves</li> <li>14.5 Curvature and Normal Vectors</li> </ul> <ul> <li>Review Exercises</li> </ul></li> <li><strong>Functions of Several Variables</strong> <ul> <li>15.1 Graphs and Level Curves</li> <li>15.2 Limits and Continuity</li> <li>15.3 Partial Derivatives</li> <li>15.4 The Chain Rule</li> <li>15.5 Directional Derivatives and the Gradient</li> <li>15.6 Tangent Planes and Linear Approximation</li> <li>15.7 Maximum/Minimum Problems</li> <li>15.8 Lagrange Multipliers</li> </ul> <ul> <li>Review Exercises</li> </ul></li> <li><strong>Multiple Integration</strong> <ul> <li>16.1 Double Integrals over Rectangular Regions</li> <li>16.2 Double Integrals over General Regions</li> <li>16.3 Double Integrals in Polar Coordinates</li> <li>16.4 Triple Integrals</li> <li>16.5 Triple Integrals in Cylindrical and Spherical Coordinates</li> <li>16.6 Integrals for Mass Calculations</li> <li>16.7 Change of Variables in Multiple Integrals</li> </ul> <ul> <li>Review Exercises</li> </ul></li> <li><strong>Vector Calculus</strong> <ul> <li>17.1 Vector Fields</li> <li>17.2 Line Integrals</li> <li>17.3 Conservative Vector Fields</li> <li>17.4 Green’s Theorem</li> <li>17.5 Divergence and Curl</li> <li>17.6 Surface Integrals</li> <li>17.7 Stokes’ Theorem</li> <li>17.8 Divergence Theorem</li> </ul> <ul> <li>Review Exercises</li> </ul></li> </ol> <ul> <li><strong>D2 Second-Order Differential Equations ONLINE</strong> <ul> <li>D2.1 Basic Ideas</li> <li>D2.2 Linear Homogeneous Equations</li> <li>D2.3 Linear Nonhomogeneous Equations</li> <li>D2.4 Applications</li> <li>D2.5 Complex Forcing Functions</li> </ul> <ul> <li>Review Exercises</li> </ul></li> </ul> <h3>Appendices</h3> <ul> <li>A. Proofs of Selected Theorems</li> <li>B. Algebra Review ONLINE</li> <li>C. Complex Numbers ONLINE</li> </ul> <ul> <li>Answers</li> <li>Index</li> <li>Table of Integrals</li> </ul> </div>