Review of Vector Properties

1
Review of Vector Properties

• Scalars and vectors
• Addition and subtraction
• Components and magnitude
• Properties
• Unit vectors
• Rectangular coordinate system in 3-d
• Dot product
• Cross product
• Lines and planes
• Vector spaces

2
Vector Functions - Differentiation

• Vector-valued functions
• Derivative of vector function
• Rules of differentiation
• Tangent, curvature, normal
• Functions of several variables
• Gradient
• Divergence
• Curl

3
Vector formulas and Coordinate system

• Summary of vector formulas
• Orthogonal curvilinear coordinates
• Rectangular coordinates
• Cylindrical coordinates
• Spherical coordinates
• Various vector operations

4
Vector Functions - Integration

• Line integrals
• Double integrals
• Greens theorem
• Surface integrals
• Stokes theorem
• Triple integrals
• Divergence theorem
• Change of variables in multiple integrals