Introduction to Calculus and Analysis (Volume - 2)

0.0

Table of Contents 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