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Class Notes

Part 1: Vectors in Space and Vector-Valued Functions

Section 2.1: Vectors in the Plane

Section 2.2: Vectors in Three Dimensions

Section 2.3: The Dot Product

Section 2.4: The Cross Product

Section 2.5: Equations of Lines and Planes in Space

Section 2.6: Cylindrical & Quadric Surfaces

Section 3.1: Vector-Valued Functions and Space Curves

Section 3.2: Calculus of Vector-Valued Functions

Section 3.3: Arc Length and Curvature

Section 3.4: Motion in Space

Part 2: Multivariable Functions

Section 4.1: Functions of Several Variables

Section 4.3: Partial Derivatives

Section 4.4: Tangent Planes and Linear Approximations

Section 4.5: The Chain Rule

Section 4.6: Directional Derivatives and the Gradient

Section 4.7: Maxima/Minima Problems

Section 4.8: Lagrange Multipliers