Mathematical Foundation of Geodesy: Selected Papers of Torben Krarup / Edition 1

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This volume contains selected papers by Torben Krarup, one of the most important geodesists of the 20th century. The collection includes the famous booklet "A Contribution to the Mathematical Foundation of Physical Geodesy" from 1969, the unpublished "Molodenskij letters" from 1973, the final version of "Integrated Geodesy" from 1978, "Foundation of a Theory of Elasticity for Geodetic Networks" from 1974, as well as trend-setting papers on the theory of adjustment.

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Editorial Reviews

From the Publisher
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)

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Product Details

  • ISBN-13: 9783540337652
  • Publisher: Springer Berlin Heidelberg
  • Publication date: 7/26/2006
  • Edition description: 2006
  • Edition number: 1
  • Pages: 416
  • Product dimensions: 6.30 (w) x 9.40 (h) x 1.10 (d)

Meet the Author

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.

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Table of Contents

1 Linear equations 1
2 The adjustment procedure in tensor form 17
3 The theory of rounding errors in the adjustment by elements 23
4 A contribution to the mathematical foundation of physical geodesy 29
5 A remark on approximation of T by series in spherical harmonics 91
6 On the geometry of adjustment 93
7 Remarks to the discussion yesterday 101
8 Letters on Molodenskiy's problem 105
9 On the spectrum of geodetic networks 135
10 Mathematical geodesy 153
11 Foundation of a theory of elasticity for geodetic networks 159
12 Integrated geodesy 179
13 On potential theory 207
14 La Formule de Stokes Est-Elle Correcte? 257
15 Some remarks about collocation 261
16 Apropos some recent papers by Willi Freeden 273
17 S-transformation 281
18 Integrated geodesy 289
19 A measure for local redundancy 301
20 A convergence problem in collocation theory 309
21 Non-linear adjustment and curvature 323
22 Mechanics of adjustment 333
23 Angelica returning or the importance of a title 341
24 Evaluation of isotropic covariance functions 347
25 Contribution to the geometry of the Helmert transformation 359
26 Letter on a problem in collocation theory 375
27 Approximation to the Earth potential 379
28 Relative orientation in photogrammetry 395
A Bibliography for Torben Krarup 413
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