## Table of Contents

**1. Coordinate and Vector Geometry.**

Rectangular Coordinates and Distance. Graphs of Functions of Two Variables. Quadric Surfaces. Cylindrical and Spherical Coordinates. Vectors in Three-Dimensional Space. The Dot Product, Projection, and Work. The Cross Product and Determinants. Planes and Lines in R3. Vector-Valued Functions. Derivatives and Motion.

**2. Geometry and Linear Algebra in R**

^{n}.

Vectors and Coordinate Geometry in Rn. Matrices. Linear Transformations. Geometry of Linear Transformations. Quadratic Forms.

**3. Differentiation.**

Graphs, Level Sets, and Vector Fields: Geometry. Limits and Continuity. Open Sets, Closed Sets, and Continuity. Partial Derivatives. Differentiation and the Total Derivative. The Chain Rule.

**4. Applications of Differentiation.**

The Gradient and Directional Derivative. Divergence and Curl. Taylor's Theorem. Local Extrema. Constrained Optimization and Lagrange Multipliers.

**5. Integration.**

Paths and Arclength. Line Integrals. Double Integrals. Triple Integrals. Parametrized Surfaces and Surface Area. Surface Integrals. Change of Variables in Double Integrals. Change of Variables in Triple Integrals.

**6. Fundamental Theorems.**

The Fundamental Theorem for Path Integrals. Green's Theorem. The Divergence Theorem. Stokes's Theorem.

**7. Laboratory Writing Projects.**

Plotting Parameterized Surfaces. Making a Movie. A Mechanical Linkage. The Frenet Frame. Bézier Curves. Filling a Lake. Calculating Volume by Changing Coordinates. Predicting Eclipses.

**Bibliography.**

**Answers to Selected Exercises.**

**Index.**

### These online resources are available at no cost.

Companion Website-Barr, 2nd Edition