Vectors and Geometry in Two and Three Dimensions
	Points
	Vectors
		Addition of Vectors and Multiplication of a Vector by a Scalar
		The Dot Product
		(Optional) Using Dot Products to Resolve Forces — The Pendulum
		(Optional) Areas of Parallelograms
		The Cross Product
		(Optional) Some Vector Identities
		(Optional) Application of Cross Products to Rotational Motion
		(Optional) Application of Cross Products to Rotating Reference Frames
	Equations of Lines in 2d
	Equations of Planes in 3d
	Equations of Lines in 3d
	Curves and their Tangent Vectors
		Derivatives and Tangent Vectors
	Sketching Surfaces in 3d
		Level Curves and Surfaces
	Cylinders
	Quadric Surfaces
Partial Derivatives
	Limits
		Optional — A Nasty Limit That Doesn't Exist
	Partial Derivatives
	Higher Order Derivatives
		Optional — The Proof of Theorem 2.3.4
		Optional — An Example of 2 fxy(x0,y0) 2 fyx(x0,y0)
	The Chain Rule
		Memory Aids for the Chain Rule
		Chain Rule Examples
		Review of the Proof of ddtf(to.x(t))to. = dfdx(to.x(t))to. dxdt(t)
		Proof of Theorem 2.4.1
	Tangent Planes and Normal Lines
		Surfaces of the Form z=f(x,y).
		Surfaces of the Form G(x,y,z)=0.
	Linear Approximations and Error
		Quadratic Approximation and Error Bounds
		Optional — Taylor Polynomials
	Directional Derivatives and the Gradient
	A First Look at Partial Differential Equations
		Optional — Solving the Advection and Wave Equations
		Really Optional — Derivation of the Wave Equation
	Maximum and Minimum Values
		Absolute Minima and Maxima
	Lagrange Multipliers
		(Optional) An Example with Two Lagrange Multipliers
Multiple Integrals
	Double Integrals
		Vertical Slices
		Horizontal Slices
		Volumes
		Examples
		Optional — More about the Definition of Rf(x,y) dxdy
		Even and Odd Functions
	Double Integrals in Polar Coordinates
		Polar Coordinates
		Polar Curves
		Integrals in Polar Coordinates
		Optional— Error Control for the Polar Area Formula
	Applications of Double Integrals
	Surface Area
	Triple Integrals
	Triple Integrals in Cylindrical Coordinates
		Cylindrical Coordinates
		The Volume Element in Cylindrical Coordinates
		Sample Integrals in Cylindrical Coordinates
	Triple Integrals in Spherical Coordinates
		Spherical Coordinates
		The Volume Element in Spherical Coordinates
		Sample Integrals in Spherical Coordinates
	Optional— Integrals in General Coordinates
		Optional — Dropping Higher Order Terms in du,dv
Trigonometry
	Trigonometry — Graphs
	Trigonometry — Special Triangles
	Trigonometry — Simple Identities
	Trigonometry — Add and Subtract Angles
	Inverse Trigonometric Functions
Powers and Logarithms
	Powers
	Logarithms
Table of Derivatives
Table of Integrals
Table of Taylor Expansions
3d Coordinate Systems
	Cartesian Coordinates
	Cylindrical Coordinates
	Spherical Coordinates
ISO Coordinate System Notation
	Polar Coordinates
	Cylindrical Coordinates
	Spherical Coordinates
Conic Sections and Quadric Surfaces