Differential and Integral Calculus, Volume 2

Partial table of contents:

Preliminary Remarks on Analytical Geometry and Vector Analysis:Rectangular Coordinates and Vectors, Affine Transformations and theMultiplication of Determinants.

Functions of Several Variables and Their Derivatives: Continuity,The Total Differential of a Function and Its GeometricalMeaning.

Developments and Applications of the Differential Calculus:Implicit Functions, Maxima and Minima.

Multiple Integrals: Transformation of Multiple Integrals, ImproperIntegrals.

Integration over Regions in Several Dimensions: Surface Integrals,Stokes's Theorem in Space.

Differential Equations: Examples on the Mechanics of a Particle,Linear Differential Equations.

Calculus of Variations: Euler's Differential Equation in theSimplest Case, Generalizations.

Functions of a Complex Variable: The Integration of AnalyticFunctions, Cauchy's Formula and Its Applications.

Appendixes.

Index.