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Pretace Acknowledgements About the anthors l Mathematical techniques 1.1 Theory 1.1.1 Dot and cross product 1.1.2 Separation vector 1.1.3 Transformation matrix 1.1.4 Gradient 1.1.5 Divergence 1.1.6 Curl 1.1.7 Laplacian 1.1.8 Line integral 1.1.9 Surface integral 1.1.10 Volume integral 1.1.1 l Fundamental theorem for gradients 1.1.1 2 Fundamental theorem for divergences Gauss's theorem Green's theorem£¬divergence theorem) 1.1.1 3 Fundamental theorelll for CUrls fStoke'S theorem.curl theorem 1.1.1 4 Cylindrical polar coordinates 1.1.1 5 Spherical polar coordinates 1.1.1 6 One.dimensional Dirac delta function 1.1.17 Theory of vector fields 1.2 Problems and solutions Bibliography 2 Electrostatics 2.1 Theory 2.1.1 Coulomb'S law 2.1.2 Electric field 2.1.3 Gauss'S law 2.1.4 Curl ofE 2.1.5 Energy of a point charge distribution 2¡£1.6 Energy of a continuous distribution 2.1.7 Energy per unit volume 2.2 Problems and solutions Bibliography 3 Electric potential 3.1 Theory 3.1.1 Laplace'S equation 3.1.2 Solving Laplace'S equation 3.1.3 General solutions 3£¬1.4 Method of images 3.1.5 Potential due to a dipole 3.1.6 Multiple expansion 3.1.7 Monopole moment 3.2 Problems and solutions Bibliography 4 Magnetostatics 4.1 Theory 4.1.1 Magnetic force 4.1 ¡£2 Force on a current carrying wire