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Lecturer(s)
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Šprlák Michal, Doc. Ing. PhD.
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Course content
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1. Exterior spherical horizontal boundary value problem. 2. Exterior spherical gradiometric boundary value problem. 3. Gravitational tensor of the third order - differential operators and basic properties. 4. Exterior spherical gravitational curvature boundary value problem. 5. Complete Meissl diagram of spherical integral transformations. 6. Effect of the distant zones for integral transformations. 7. Formulation of practical integral estimators. 8. Error propagation in practical integral estimates - analytical formulas. 9. Direct modelling of the gravitational potential and its first-, second-, and third-order derivatives in the spatial domain. 10. Spherical harmonic expansions of the gravitational potential and its first-, second-, and third-order derivatives. 11. Analytical continuation of spherical harmonic series. 12. Spectral combination of gravitational field quantities.
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Learning activities and teaching methods
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- Practical training (number of hours)
- 26 hours per semester
- Contact hours
- 26 hours per semester
- Preparation for an examination (30-60)
- 50 hours per semester
- Preparation for laboratory testing; outcome analysis (1-8)
- 20 hours per semester
- Preparation for comprehensive test (10-40)
- 10 hours per semester
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| prerequisite |
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| Knowledge |
|---|
| to explain fundamentals of land surveying |
| to explain fundamentals of the adjustment calculus |
| to explain fundamentals of algebra |
| to explain fundamentals of the mathematical analysis |
| to explain fundamental of the tensor calculus |
| to explain fundamentals of the potential theory |
| Skills |
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| programming |
| to make a plot or a map |
| to interpret results and their uncertainties |
| symbolic derivations of equations and algebraic manipulations |
| Competences |
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| N/A |
| N/A |
| learning outcomes |
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| Knowledge |
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| to resolve quantities of the gravitational field and to understand their properties |
| to resolve types of exterior boundary value problems of the potential theory |
| to resolve types of integral transformations for gravitational field modelling |
| Skills |
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| to formulate and solve exterior boundary value problems of the potential theory |
| to practically compute parameters of the gravitational field |
| Competences |
|---|
| N/A |
| N/A |
| N/A |
| teaching methods |
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| Knowledge |
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| Lecture |
| Self-study of literature |
| Practicum |
| Task-based study method |
| Skills |
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| Self-study of literature |
| Practicum |
| Task-based study method |
| Competences |
|---|
| Lecture |
| Self-study of literature |
| Practicum |
| Task-based study method |
| assessment methods |
|---|
| Knowledge |
|---|
| Oral exam |
| Written exam |
| Test |
| Combined exam |
| Skills |
|---|
| Oral exam |
| Written exam |
| Combined exam |
| Test |
| Competences |
|---|
| Oral exam |
| Written exam |
| Combined exam |
| Test |
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Recommended literature
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Arfken,G. Mathematical Metods for Physicists. Oxford, 1970.
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Burša, M. - Kostelecký, J. Kosmická geodézie a kosmická dynamika. MO AČR, 1994.
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Burša, Milan; Pěč, Karel. Tíhové pole a dynamika Země. 1. vyd. Praha : Academia, 1988.
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Hamáčková, Eliška; Šprlák, Michal; Pitoňák, Martin; Novák, Pavel. Non-singular expressions for the spherical harmonic synthesis of gravitational curvatures in a local north-oriented reference frame. Computers and Geosciences ISSN 0098-3004 Vol. 88. 2016.
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Hofmann-Wellenhof, Bernhard; Moritz, Helmut. Physical geodesy. 1st ed. Wien : SpringerWienNewYork, 2005. ISBN 3-211-23584-1.
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Jekeli, Christopher. Spectral methods in geodesy and geophysics. 2017. ISBN 978-1-4822-4525-7.
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Novák, Pavel; Pitoňák, Martin; Šprlák, Michal; Tenzer, Robert. Higher-order gravitational potential gradients for geoscientific applications. Earth-Science Reviews ISSN 0012-8252 Vol. 198 (201. 2019.
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Novák, Pavel; Šprlák, Michal; Tenzer, Robert; Pitoňák, Martin. Integral formulas for transformation of potential field parameters in geosciences. Earth-Science Reviews ISSN 0012-8252 Vol. 164 (201. 2017.
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Šprlák, Michal; Hamáčková, Eliška; Novák, Pavel. Alternative validation method of satellite gradiometric data by integral transform of satellite altimetry data. Journal of Geodesy ISSN 0949-7714 Vol. 89, no. 8 (. 2015.
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Šprlák, Michal; Novák, Pavel. Integral formulas for computing a third-order gravitational tensor from volumetric mass density, disturbing gravitational potential, gravity anomaly and gravity disturbance. Journal of Geodesy ISSN 0949-7714 Vol. 89, no. 2 (. 2015.
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Šprlák, Michal; Novák, Pavel,; Pitoňák, Martin. Spherical harmonic analysis of gravitational curvatures and its implications for future satellite missions. Surveys in Geophysics ISSN 0169-3298 Vol. 37, no. 2016.
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Šprlák, Michal; Novák, Pavel. Spherical gravitational curvature boundary-value problem. Journal of Geodesy ISSN 0949-7714 Vol. 90, no. 8 (. 2016.
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