CONTENT:

COMPLEX NUMBERS AND THEIR ALGEBRA, GEOMETRY OF COMPLEX NUMBERS, POWERS AND ROOTS OF COMPLEX NUMBERS, STEREOGRAPHIC PROJECTION, SUMS OF POINTS, FUNCTIONS OF COMPLEX VARIABLES, LIMITS AND CONTINUITY, DERIVATIVES, CAUCHY-RIEMANN EQUATIONS, ANALYTIC FUNCTIONS, HARMONIC FUNCTIONS, SINGULAR POINTS, EXPONENTIAL FUNCTION, TRIGONOMETRIC FUNCTIONS, HYPERBOLIC FUNCTIONS, LOGARITHMIC FUNCTION, INVERSES OF TRIGONOMETRIC AND HYPERBOLIC FUNCTIONS, ALGEBRAIC FUNCTIONS, ELEMENTARY TRANSFORMATIONS, LINEAR TRANSFORMATION, BILINEAR TRANSFORMATION, EXPONENTIAL TRANSFORMATION, LOGARITHMIC TRANSFORMATION, HYPERBOLIC SINE-COSINE TRANSFORMATION, APPLICATIONS TO OSCILLATING SYSTEMS, COMPLEX LINE INTEGRALS, COMPLEX INTEGRALS OF REAL AND COMPLEX FUNCTIONS AND THEIR RELATIONSHIP, SPACES OF SIMPLE AND MULTIPLE CONTINUITY, CAUCHY INTEGRATION THEOREMS, CAUCHY INTEGRAL FORMULAS AND RELATED THEOREMS, SEQUENCES OF COMPLEX NUMBERS, SERIES OF COMPLEX NUMBERS, SEQUENCES AND SERIES OF FUNCTIONS, ABSOLUTE AND UNIFORM CONVERGENCE, POWER SERIES, IMPORTANT THEOREMS, TAYLOR SERIES, SIGNIFICANT SERIES, LAURENT SERIES, THEOREMS OF INTEGRAL REMAINDERS, TRIGONOMETRIC INTEGRALS, GENERALIZED INTEGRALS OF RATIONAL FUNCTIONS, GENERALIZED INTEGRALS INCLUDING TRIGONOMETRIC FUNCTIONS, DISCONTINUOUS CURVES, INTEGRALS OF FUNCTIONS OF MULTIPLE TYPES, COMPLEX NUMBERS AND THEIR ALGEBRA, CLASSIFICATION OF O.D.E., INITIAL AND BOUNDARY VALUE PROBLEMS, FORMATION OF O.D.E., METHODS OF SOLVING O.D.E., PRACTICAL PROBLEMS AND CREATION OF O.D.E., ALMOST LINEAR FIRST-ORDER O.D.E., SOLUTION PROCESS OF THE ALMOST LINEAR FIRST-ORDER O.D.E., METHODS FOR SOLVING THE CHARACTERISTIC SYSTEM, SOLUTION OF THE LINEAR FIRST-ORDER O.D.E., NORMAL FORM OF O.D.E., EQUATIONS WITH CONSTANT COEFFICIENTS, SPECIAL LINEAR SECOND-ORDER O.D.E. WITH CONSTANT COEFFICIENTS, GENERAL SOLUTION OF SECOND-ORDER O.D.E., SECOND-ORDER O.D.E. IN PHYSICS, SECOND-ORDER O.D.E. WITH TWO OR MORE VARIABLES, BASIC PROPERTIES OF O.D.E. WITH CONSTANT COEFFICIENTS, SOLUTION OF THE LINEAR O.D.E. WITH CONSTANT COEFFICIENTS, THE METHOD OF SEPARATION OF VARIABLES, SEPARATION OF VARIABLES IN A DIFFUSION PROBLEM, SEPARATION OF VARIABLES IN A TEMPERATURE DISTRIBUTION IN A CIRCULAR RING, FOURIER SERIES, INTEGRAL TRANSFORMS, FOURIER TRANSFORMATION, LAPLACE TRANSFORMATION, STURM-LIOUVILLE SYSTEMS, EIGENVALUE AND EIGENFUNCTION THEOREMS, STURM-LIOUVILLE SYSTEM IN HEAT FLOW PROBLEMS, BESSEL FUNCTIONS, SINGULAR STURM-LIOUVILLE SYSTEMS, LEGENDRE EQUATION, NON-HOMOGENEOUS PROBLEMS OF BOUNDARY CONDITIONS, NON-HOMOGENEOUS HEAT TRANSFER PROBLEM, BOUNDARY CONDITION PROBLEMS, D'ALEMBERT'S SOLUTION FOR THE WAVE EQUATION, APPLICATIONS OF D'ALEMBERT'S SOLUTION, THE WAVE EQUATION IN TWO AND THREE DIMENSIONS, NON-HOMOGENEOUS DIRICHLET PROBLEM - GREEN'S FUNCTION.