Mathematical Foundation of Geodesy

Kai Borre has been a professor of geodesy at Aalborg University since 1976. His professional interests are geodesy and satellite based positioning and navigation. He is the (co)author of seven textbooks and has published numerous scientific reviewed papers. He is also an editor of GPS Solutions. Dr. Borre is renowned for having written several hundred Matlab scripts for positioning. He is honorary doctor of the Vilnius Gediminas Technical University.

• Linear Equations.- The Adjustment Procedure in Tensor Form.- The Theory of Rounding Errors in the Adjustment by Elements of Geodetic Networks.- A Contribution to the Mathematical Foundation of Physical Geodesy.- A Remark on Approximation of T by Series in Spherical Harmonics.- On the Geometry of Adjustment.- Remarks to the Discussion Yesterday.- Letters on Molodenskiy’s Problem.- On the Spectrum of Geodetic Networks.- Mathematical Geodesy.- Foundation of a Theory of Elasticity for Geodetic Networks.- Integrated Geodesy.- On Potential Theory.- La Formule de Stokes Est-Elle Correcte?.- Some Remarks About Collocation.- Apropos Some Recent Papers by Willi Freeden on a Class of Integral Formulas in the Mathematical Geodesy.- S-Transformation or How to Live Without the Generalized Inverse—Almost.- Integrated Geodesy.- A Measure for Local Redundancy—A Contribution to the Reliability Theory for Geodetic Networks.- A Convergence Problem in Collocation Theory.- Non-Linear Adjustment and Curvature.- Mechanics of Adjustment.- Angelica Returning or The Importance of a Title.- Evaluation of Isotropic Covariance Functions of Torsion Balance Observations.- Contribution to the Geometry of the Helmert Transformation.- Letter on a Problem in Collocation Theory.- Approximation to The Earth Potential From Discrete Measurements.- An Old Procedure for Solving the Relative Orientation in Photogrammetry.

From the reviews:"The papers were written in the period 1962-1998 and present a wide range of significant topics in the mathematical foundation of geodesy. … All the articles are mathematically well founded and scientifically relevant. The book will be of interest to mathematicians and geodesists as well as to students and historians." (Alexander Denisjuk, Mathematical Reviews, Issue 2007 i)"Torben Krarup is one of the most outstanding theoretical geodesists … of the last 50 years. … written many small informal papers which circulated among friends and exerted considerable influence, not only in the geodetic community, but also, e.g. on the well-known mathematician L. Hörmander … . The present book comprises most of such … informal papers. … It is a must to all people, working in physical geodesy, to read this book … ." (Helmut Moritz, Zentralblatt MATH, Vol. 1162, 2009)