1.1 Introduction1.2 Basic Laws of Vector Algebra1.2.1 Vector Equality1.2.2 Vector Addition and Subtraction1.2.3 Position and Distance Vectors1.2.4 Vector Multiplication1.3 Orthogonal Coordinate Systems1.3.1 Rectangular (Cartesian) Coordinates (x, y, z)1.3.2 Cylindrical Coordinates (ρ, φ, z)1.3.3 Spherical Coordinates (r, θ, φ)1.3.4 Transformation between Cylindrical and Spherical Coordinates1.4 Differential Elements of Length, Surface, and Volume1.4.1 Rectangular Coordinate System1.4.2 Cylindrical Coordinate System1.4.3 Spherical Coordinate System1.4.4 Comparison of Differential Elements for Coordinate Systems1.5 Line, Surface, and Volume Integrals1.5.1 Line Integral1.5.2 Surface Integral1.5.3 Volume Integral1.6 Vector Differential Operator1.6.1 Vector Differential Operator ∇ in Cylindrical Coordinates1.6.2 Vector Differential Operator ∇ in Spherical Coordinates1.7 Gradient of a Scalar Field1.8 Divergence of a Vector Field1.9 Divergence Theorem1.10 Curl of a Vector Field1.11 Stokes’s Theorem1.12 Laplacian Operator1.13 Null Identities1.13.1 Identity-I1.13.2 Identity-II1.14 Helmholtz’s TheoremReview Questions