Here are detailed solutions to the optional (but highly encouraged) exercises for MATH 2263: Multivariable Calculus. I want there to be solutions that explain what the problem solver is thinking and doing.
Worksheets #
Solutions #
Chapter 12: Vectors and the Geometry of Space #
12.1: Three-Dimensional Coordinate Systems
12.2: Vectors
12.3: The Dot Product
12.4: The Cross Product
12.5: Equations of Lines and PlanesChapter 14: Partial Derivatives #
14.1: Functions of Several Variables
14.2: Limits and Continuity
14.3: Partial Derivatives
14.4: Tangent Planes and Linear Approximations
14.5: The Chain Rule
14.6: Directional Derivatives and the Gradient Vector
14.7: Maximum and Minimum Values
14.8: Lagrange MulitpliersChapter 15: Multiple Integrals #
15.1: Double Integrals over Rectangles
15.2: Double Integrals over General Regions