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Note: Each chapter concludes with Review Exercises and P.S. Problem Solving | |
Vectors and the Geometry of Space | |
Vectors in the Plane | |
Space Coordinates and Vectors in Space | |
The Dot Product of Two Vectors | |
The Cross Product of Two Vectors in Space | |
Lines and Planes in Space Section Project: Distances in Space | |
Surfaces in Space | |
Cylindrical and Spherical Coordinates | |
Vector-Valued Functions | |
Vector-Valued Functions Section Project: Witch of Agnesi | |
Differentiation and Integration of Vector-Valued Functions | |
Velocity and Acceleration | |
Tangent Vectors and Normal Vectors | |
Arc Length and Curvature | |
Functions of Several Variables | |
Introduction to Functions of Several Variables | |
Limits and Continuity | |
Partial Derivatives Section Project: Moireacute; Fringes | |
Differentials | |
Chain Rules for Functions of Several Variables | |
Directional Derivatives and Gradients | |
Tangent Planes and Normal Lines Section Project: Wildflowers | |
Extrema of Functions of Two Variables | |
Applications of Extrema of Functions of Two Variables Section Project: Building a Pipeline | |
Lagrange Multipliers | |
Multiple Integration | |
Iterated Integrals and Area in the Plane | |
Double Integrals and Volume | |
Change of Variables: Polar Coordinates | |
Center of Mass and Moments of Inertia Section Project: Center of Pressure on a Sail | |
Surface Area Section Project: Capillary Action | |
Triple Integrals and Applications | |
Triple Integrals in Cylindrical and Spherical Coordinates Section Project: Wrinkled and Bumpy Spheres | |
Change of Variables: Jacobians | |
Vector Analysis | |
Vector Fields | |
Line Integrals | |
Conservative Vector Fields and Independence of Path | |
Green's Theorem Section Project: Hyperbolic and Trigonometric Functions | |
Parametric Surfaces | |
Surface Integrals Section Project: Hyperboloid of One Sheet | |
Divergence Theorem | |
Stoke's Theorem Section Project: The Planimeter | |
Appendices | |
Additional Topics in Differential Equations | |
Proofs of Selected Theorems | |
Integration Tables | |
Precalculus Review | |
Rotation and the General Second-Degree Equation | |
Complex Numbers | |
Business and Economic Applications | |
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