.01

.02

.03

• Introduction to vectors

  • Vector from two points

  • Combinations of vectors

  • Sum of two vectors

  • Copying vectors and using them to find combinations

  • Unit vector in the direction of the given vector

  • Angle between a vector and the x-axis

  • Magnitude and angle of the resultant force

• Dot products

  • Dot product of two vectors

  • Angle between two vectors

  • Orthogonal, parallel, or neither

  • Acute angle between the lines

  • Acute angle between the curves

  • Direction cosines and direction angles

  • Scalar equation of a line

  • Scalar equation of a plane

  • Scalar and vector projections

• Cross products

  • Cross product of two vectors

  • Vector orthogonal to the plane

  • Volume of the parallelepiped given vectors

  • Volume of the parallelepiped given adjacent edges

  • Scalar triple product for coplanar vectors

• Vector functions and space curves

  • Domain of the vector function

  • Limit of the vector function

  • Sketching the vector equation

  • Projections of the curve

  • Vector and parametric equations of a line segment

  • Vector function for the curve of intersection of two surfaces

• Derivatives and integrals of vector functions

  • Derivative of a vector function

  • Unit tangent vector

  • Parametric equations of the tangent line

  • Integral of a vector function

• Arc length and curvature

  • Arc length

  • Reparametrizing the curve

  • Unit tangent vectors and unit normal vectors

  • Curvature

  • Maximum curvature

  • Normal and osculating planes

• Velocity and acceleration

  • Velocity and acceleration vectors

  • Velocity, acceleration and speed, given position

  • Velocity and position given acceleration and initial conditions

  • Tangential components and normal components of acceleration

• Line integrals

  • Line integral of a curve

  • Line integral of a vector function

  • Conservative vector fields

  • Potential function of a conservative vector field

  • Independence of path

  • Work done by the force field

  • Open, connected, and simply-connected regions

• Green's theorem

  • Green's theorem with one region

  • Green's theorem with two regions

• Curl and divergence

  • Curl and divergence of a vector field

  • Potential function of a conservative vector field

• Parametric surfaces and areas

  • Points on the surface

  • Surface of the vector equation

  • Parametric representation of the surface

  • Tangent plane to the parametric surface

  • Area of the surface

• Surface integrals

  • Surface integrals

• Stokes' and divergence theorem

  • Stokes theorem

  • Divergence theorem

.04

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