Introduction to Calculus and Analysis II/2

Relations Between Surface and Volume Integrals: Connection Between Line Integrals and Double Integrals in the Plane; Vector Form of the Divergence Theorem. Stokes's Theorem; Formula for Integration by Parts in Two Dimensions: Green's Theorem; The Divergence Theorem Applied to the Transformation of Double Integrals; Area Differentiation; Interpretation of the Formulae of Gauss and Stokes by Two-Dimensional Flows; Orientation of Surfaces; Integrals of Differential Forms and of Scalars over Surfaces; Gauss's and Green's Theorems in Space; Appendix: General Theory of Surfaces and of Surface Integrals.-
Differential Equations: The Differential Equations for the Motion of a Particle in Three Dimensions; The General Linear Differential Equation of the First Order; Linear Differential Equations of Higher Order; General Differential Equations of the First Order; Systems of Differential Equations and Differential Equations of Higher Order; Integration by the Method of Undermined Coefficients; The Potential of Attracting Charges and Laplace's Equation; Further Examples of Partial Differential Equations from Mathematical Physics .-
Calculus of Variations: Functions and Their Extreme Values of a Functional; Generalizations; Problems Involving Subsidiary Conditions. Lagrange Multipliers.-
Functions of a Complex Variable: Complex Functions Represented by Power Series; Foundations of the General Theory of Functions of a Complex Variable; The Integration of Analytic Functions; Cauchy's Formula and Its Applications; Applications to Complex Integration (Contour Integration); Many-Valued Functions and Analytic Extension.- List of Biographical Dates
Index