Historical Introduction.- I. Equations and Units.- 1.1. Dimensional and Numerical Equations.- 1.2. The kg-m-sec-amp System of Units.- 1.3. The Definition of the Unit of Electric Current, the Ampere [A].- 1.4. Derived Electrical Units.- 1.5. The Practical (Physical) Units for Electrical Quantities.- 1.6. The Fundamental Electrical Laws.- 1.7. Transformation of Units.- II. Complex Notation and Symbolic Methods.- 2.1. Complex Notation and Rotating Vectors.- 2.2. Computations with Complex Vectors.- 2.2.1. Definitions.- 2.2.2. Addition.- 2.2.3. Subtraction.- 2.2.4. Multiplication.- 2.2.5. Division.- 2.2.6. Logarithm of a Complex Number.- 2.2.7. Raising a Complex Number to a Given Power.- 2.2.8. Differentiation and Integration.- 2.3. Conjugate Complex Vectors and Their Applications.- 2.4. Addition of Harmonic Functions of the Same Frequency.- 2.5. Symbolic Method for Solving Linear Differential Equations.- 2.6. Complex Solution and Boundary Conditions.- 2.7. Computation of Power.- 2.8. Basic Theory of Internal Friction.- III. Analytic Functions: Their Integration and the Delta Function.- 3.1. Analytic Functions.- 3.2. Representation of an Analytic Function by a Power Series.- 3.3. Cauchy's Formula.- 3.4. The Cauchy Integral Formula.- 3.5. Residues.- 3.6. Examples.- 3.6.1. Evaluation of Integrals of the type