Coordinates in Geodesy

1. Introduction.- 2. General Fundamentals of Surface Coordinates.- 2.1 Fundamentals of the Theory of Surfaces.- 2.2 Fundamentals of Complex Analysis.- 3. Representing the Transformation Equations Between Surface Coordinates by Power Series.- 3.1 Constructing Surface Coordinates.- 3.2 Representing Power Series.- 3.3 Transformations Between Geodesic Polar Coordinates and Arbitrary Surface Coordinates.- 3.4 Transformations Between Geodesic Parallel Coordinates and Arbitrary Surface Coordinates.- 3.5 Transformations Between Isothermal Surface Coordinates and Arbitrary Surface Coordinates.- 4. Surface Coordinates on Ellipsoids of Revolution.- 4.1 Preliminary Remarks.- 4.2 Ellipsoids of Revolution and Their Representation Using Geographic Coordinates.- 4.3 Transformations Between Geodesic Polar Coordinates and Geographic Coordinates.- 4.4 Transformations Between Soldner's Parallel Coordinates and Geographic Coordinates.- 4.5 Defining Isothermal Surface Coordinates in the Geographic Coordinate System.- 4.6 Transformations Between Isothermal Geographic Coordinates and Geographic Coordinates.- 4.7 Transformations Between Gaussian Isothermal Coordinates and Geographic Coordinates.- 4.8 Transformations Between Gaussian Isothermal Coordinates and Geodesic Polar Coordinates.- 4.9 Transformations Between Two Systems of Gaussian Isothermal Coordinates.- 4.10 Transformations Between Isothermal Stereographic Coordinates and Geographic Coordinates.- 5. Three-Dimensional Coordinates.- 5.1 Preliminary Remarks.- 5.2 Fundamentals of Three-Dimensional Euclidean Geometry.- 5.3 Surface-Normal Coordinates.- 5.4 Geodetic Coordinates.- 5.5 Transformations Between Geographically Geodetic Coordinates.