© 2018

Handbook of Mathematical Geodesy

Functional Analytic and Potential Theoretic Methods

  • Willi Freeden
  • M. Zuhair Nashed


  • Shows how modern mathematics acts as a key technology in today’s geodesy

  • Bridges “real world” observational as well as satellite techniques and “virtual world” modeling as well as simulation

  • Comprises high-level contributions from worldwide recognized researchers in mathematics and geodesy


Part of the Geosystems Mathematics book series (GSMA)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Matthias Augustin, Sarah Eberle, Martin Grothaus
    Pages 165-199
  3. Martin Grothaus, Thomas Raskop
    Pages 491-516
  4. Matthias Augustin, Willi Freeden, Helga Nutz
    Pages 517-560
  5. Willi Freeden, Helga Nutz, Michael Schreiner
    Pages 561-604
  6. Willi Freeden, M. Zuhair Nashed
    Pages 641-685
  7. C. Blick, W. Freeden, H. Nutz
    Pages 687-751
  8. Willi Freeden, Volker Michel, Frederik J. Simons
    Pages 753-819
  9. Christian Gerhards
    Pages 821-853
  10. Christian Gerhards, Sergiy Pereverzyev Jr., Pavlo Tkachenko
    Pages 855-882
  11. Sarah Leweke, Volker Michel, Roger Telschow
    Pages 883-919
  12. Back Matter
    Pages 921-932

About this book


Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.


constructive approximation determination of the shape of the Earth gravitational field determination inference theory and geodetic networks inverse problems satellite methods

Editors and affiliations

  • Willi Freeden
    • 1
  • M. Zuhair Nashed
    • 2
  1. 1.Geomathematics GroupTU KaiserslauternKaiserslauternGermany
  2. 2.Department of MathematicsUniversity of Central FloridaOrlandoUSA

About the editors

Willi Freeden is Professor of Geomathematics at the Technical University of Kaiserslautern, Germany

Zuhair Nahed is Professor at the University of Central Florida, Orlando, USA

Bibliographic information

  • Book Title Handbook of Mathematical Geodesy
  • Book Subtitle Functional Analytic and Potential Theoretic Methods
  • Editors Willi Freeden
    M. Zuhair Nashed
  • Series Title Geosystems Mathematics
  • Series Abbreviated Title Geosystems Math.
  • DOI
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Birkhäuser, Cham
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-319-57179-9
  • Softcover ISBN 978-3-030-09622-9
  • eBook ISBN 978-3-319-57181-2
  • Series ISSN 2510-1544
  • Series E-ISSN 2510-1552
  • Edition Number 1
  • Number of Pages XIV, 932
  • Number of Illustrations 79 b/w illustrations, 76 illustrations in colour
  • Topics Abstract Harmonic Analysis
    Partial Differential Equations
  • Buy this book on publisher's site


“The Handbook of Mathematical Geodesy presents for the mathematicians a wealth of applications and for the geodesists a solid embedding of the fundamental concepts of physical geodesy into approximation theory.” (Karl-Rudolf Koch, Journal of Geodesy, Vol. 93, 2019)

“The Handbook of Mathematical Geodesy presents a remarkable achievement. The book bridges the gap between the abstract work of the mathematicians and the practically oriented measurements of the geodesists. … the book is broadly planned, and it presents the present state of knowledge.” (Karl-Rudolf Koch, International Journal on Geomathematics GEM, Vol. 10, 2019)