Gerhard Freiling Prof. Dr. rer. nat.

Member of department Differentialgleichungen

Research interests

PDE: Completely integrable systems of PDE

Ordinary differential equations:

Matrix Riccati equations and generalized Riccati equations and their applications in Differential Games and Systems&Control

Asymptotics of solutions of differential equations with respect to parameters

Problems with turning points

Singular perturbations

Spectral theory:

Direct spectral problems: Expansion theorems, completeness and basis properties of eigenfunctions

Inverse spectral problems: Sturm-Liouville problems with singularities and turning points, inverse problems for systems and pencils

Sampling: Sampling theorems connected with eigenvalue problems

Publications

1. Über Konvergenz und Summierbarkeit von Birkhoffreihen. Marburg 1971 (Diplomarbeit).

2. (with W. Eberhard) Nicht-S-hermitesche Rand- und Eigenwertprobleme. Math. Z. 133, 187-202 (1973).

3. (with W. Eberhard) Das Verhalten der Greenschen Matrix und der Entwicklungen nach Eigenfunktionen N-regulärer Eigenwertprobleme. Math Z. 136, 13-30 (1974).

4. Über das asymptotische Verhalten der Lösungen der linearen Differentialgleichung $M(y)\;=\;\lambda N(y)$ im Intervall $(0,\infty)$ bzw. $(-\infty,\infty)$ und die Darstellung von Funktionen durch eine Klasse von zugeordneten Integraltransformationen. Marburg 1975 (Dissertation).

5. Nichtselbstadjungierte Differentialoperatoren im nichtkompakten Fall. Math. Z. 149, 267- 279 (1976).

6. Ein Äquikonvergenzsatz für eine Klasse von singulären Differentialoperatoren. Math. Z. 153, 255-265 (1977).

7. (with W. Eberhard) Stone-reguälre Eigenwertprobleme. Math Z. 160, 139-161 (1978)

8. Reguläre Eigenwertprobleme mit Mehrpunkt-Integral-Randbedingungen. Math. Z. 171, 113-131 (1980).

9. Irreguläre Mehrpunkt-Eigenwertprobleme mit zerfallenden Randbedingungen. Duisburg 1979 (Habilitationsschrift).

10. Irregular multipoint eigenvalue problems. Math. Meth. in the appl. Sci. 3, 88-103 (1981).

11. Expansion problems with irregular multipoint conditions. Proceedings A of the Royal Soc. Edinb. 88, 235-246 (1981).

12. Singular perturbations of multipoint eigenvalue problems. Archive for Rational Mech. and Anal. 86, 197-210 (1984).

13. Zur Vollständigkeit des Systems der Eigenfunktionen irregulärer Eigenwertprobleme mit $\lambda$-abhängigen Randbedingungen. Zeitschr. f. Analysis und ihre Anw. 3, 263-269 (1984).

14. On the completeness of eigenfunctions of irregular multipoint eigenvalue problems. Journal für die reine und ang. Mathematik 346, 36-47 (1984)

15. Über die mehrfache Vollständigkeit des Systems der Eigenfunktionen und assoziierten Funktionen irregulärer Operatorenbüschel. ZAMM 65, T336-T338 (1984).

16. Zur Vollständigkeit des Systems der Eigenfunktionen und Hauptfunktionen irregulärer Operatorenbüschel. Math. Z. 188, 55- 68 (1984).

17. Necessary conditions for the uniform convergence and Abel-summability of eigenfunction expansions with irregular ordinary differential bundles. Zeitschr. f. Analysis und ihre Anw. 5, 543-554 (1986).

18. Necessary conditions for the $L^2$-convergence of series in eigenfunctions of irregular eigenvalue problems. Journal of Math Anal. and its Appl. 114, 503-511 (1986).

19. On the behaviour of eigenfunction expansions in the complex domain. Proceedings A of the Royal Soc. Edinb., 104, 73-91 (1986).

20. (with G. Bacharach) Reguläre Quasi-Newton Verfahren. (16 Seiten), Schriftenreihe des FB Mathematik der Universität-GH Duisburg Nr. 88 (1986).

21. Boundary value problems associated with multiple roots of the characteristic equation. Results in Mathematics 11, 44-62 (1987).

22. General boundary eigenvalue problems for systems of differential equations with multiple roots of the characteristic equation. Proc. Royal. Soc. Edingburgh 108, 45-56 (1988).

23. On the completeness and minimality of the derived chains of eigen- and associated functions of boundary eigenvalue problems non- linearly dependent on the parameter. Results in Mathematics 14, 64-83 (1988).

24. (with W. Eberhard and T. Stoeber) Ein indefinites Eigenwertproblem mit einem Vorzeichenwechsel in der Gewichtsfunktion.(59 Seiten), Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 148 (1989).

25. (with W. Eberhard and P. Koch) Über eine Klasse von indefiniten Eigenwertproblemen mit stückweise stetiger Gewichtsfunktion.(69 Seiten), Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 169 (1989).

26. (with W. Eberhard and A. Schneider) On the distribution of the eigenvalues of a class of indefinite eigenvalue problems. J. Diff. Int. Equ. 3, 1167-1179 (1990).

27. (with W. Eberhard and A. Schneider) Expansion theorems for a class of regular indefinite eigenvalue problems. J. Diff. Int. Equ. 3, 1181-1200 (1990).

28. (with F. J. Kaufmann) On uniform and $L^p$-convergence of eigenfunction expansions for indefinite eigenvalue problems. Integral Equations and Operator Theory Vol. 13, 193-215 (1990).

29. Multiple expansions in series of eigen- and associated functions of boundary eigenvalue problems nonlinearly dependent on the spectral parameter; Part I. Results in Mathematics 17, 83-99 (1990).

30. Multiple expansions in series of eigen- and associated functions of boundary eigenvalue problems nonlinearly dependent on the spectral parameter; Part II. Results in Mathematics 17, 241-255 (1990).

31. (with W. Eberhard) Necessary conditions for the convergence and summability of eigenfunction expansions in the complex domain. J. Diff. Int. Equ. 4, (1991).

32. (with G. Jank) Matrix Riccati Equations. Schriftenreihe des FB Mathematik, Universität Duisburg, SM-DU-198 (1991).

33. (with W. Eberhard) Zur Eigenwertasymptotik indefiniter Sturm-Liouvillescher Randwertprobleme. Schriftenreihe des Fachbereichs Mathematik SM-DU-193, 22 p., Duisburg, 1991.

34. (with W.Eberhard and A. Schneider) Note on a paper of E. M. E. Zayed and S. F. M. Ibrahim. Internat. J. Math. and Math. Sci. 15, 809-811 (1992).

35. (with W. Eberhard) The distribution of the eigenvalues for second order eigenvalue problems in the presence of an arbitrary number of turning points. Results in Mathematics 18, 24-41 (1992).

36. (with H. Abou-Kandil and G. Jank) Asymptotic behaviour of Leader-Follower Control: Application to Flexible Structures. In: Proceedings of the second European Control Conference, ECC 93, 1014-1019, Groningen, 1993.

37. (with H. Abou-Kandil and G. Jank) Necessary conditions for constant solutions of coupled Riccati equations in Nash games. Systems and Control Letters 21, 295-306 (1993).

38. (with W. Eberhard) An expansion theorem for eigenvalue problems with several turning points. Analysis 13, 301-308 (1993).

39. (with W. Eberhard and A. Schneider) Connection formulas for second order differential equations with a complex parameter and having an arbitrary number of turning points. Math. Nachrichten 165, 205-229 (1994).

40. (with G. Jank) Nonsymmetric Riccati Equations. In the Proceedings of MTNS 93: Systems and Networks: Mathematical Theory and Applications, Vol. II, Helmke et al. Eds., pp.119-122, Akademie Verlag, Berlin 1994. pdf

41. (with H. Abou-Kandil and G. Jank) Solution and asymptotic behavior of coupled Riccati equations in jump-linear systems. IEEE Trans. Automatic Control 39, 1631-1636 (1994). pdf

42. (with G. Jank) Non-symmetric Riccati Equations. Zeitschr. f. Analysis und ihre Anwendungen 14, 259-284 (1995). pdf

43. (with V. Rykhlov) On a general class of Birkhoff-regular eigenvalue problems. J. Diff. Int. Equ. 8, 2157-2176 (1995).

44. (with H. Abou-Kandil and G. Jank) On the solution of discrete-time Markovian jump linear quadratic control problems. Automatica 31, 765-768 (1995). pdf

45. (with H. Abou-Kandil, G. Jank and S. R. Lee) On the global existence of solutions for game Riccati differential equations. In: Proceedings of the third European Control Conference, ECC 95, 2597-2602, Rome, 1995. pdf

46. (with H. Abou-Kandil, O. De Smet and G. Jank) Flow Control in a Failure-prone Multi-machine Manufacturing System. In: Proceedings of the IEEE/INRIA Conference EFTA '95, pp. , 575-583, Paris, 1995. pdf

47. (with S. R. Lee) Stackelberg strategies and illustrative examples. In: Proceedings of the 20th anniversary conference of the Korean scientists and engineers association in the UK, 489-496, London 1995.

48. (with H. Abou-Kandil and G. Jank) Generalized Riccati difference and differential equations. Lin. Algebra and its Appl. 241-242, 291-303 (1996). pdf

49. (with H. Abou-Kandil, S.-R. Lee and G. Jank) On the Dependence of the Solutions of Algebraic and Differential Game Riccati Equations on the Parameter $\mu$. European Journal of Control 2, 69-78 (1996). pdf

50. (with H. Abou-Kandil and G. Jank) On Global Existence of Solutions to Coupled Matrix Riccati Equations in Closed Loop Nash Games. IEEE Trans. Automatic Control 41, 264-269 (1996). pdf

51. (with H. Abou-Kandil, S.-R. Lee and G. Jank) On the behavior of the solutions of game (or $H_\infty$-type) Riccati differential equations. In: Proceedings of the World Korean Scientists Conference, Seoul, 158-165, 1996.

52. (with G. Jank, S.- R. Lee and A. Sarychev) Sufficient conditions for the existence of open loop Nash and Stackelberg strategies. In: Proceedings of Controlo 96, Porto, pp. 121-126, 1996. pdf

53. (with G. Jank) Existence and Comparison Theorems for Algebraic and Continuous-time Riccati Differential and Difference Equations. Journal of Dynamical and Control Systems, 2, 529-547, 1996. pdf

54. (with V. Rykhlov) Pointwise convergence of eigenfunction expansions for a general class of regular eigenvalue problems. Methods of Functional Analysis and Topology 3, 27-45 (1997).

55. (with G. Jank and A. Sarychev) Lyapunov Functions and Invariant Sets for Riccati-type Matrix Differential Equations. In: Proceedings of ECC 97, Brüssel, 1997. pdf

56. (with H. Abou-Kandil and G. Jank) Discrete Time Riccati Equations in Open Loop Nash and Stackelberg Games. In: Proceedings of ECC 97, Brüssel, 1997. pdf

57. (with V. Ionescu) Time-varying discrete Riccati equation: Some monotonicity results (and existence of the stabilizing solution) Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 388 (1997). pdf

58. (with V. Yurko) Inverse problems for differential equations with turning points. Inverse Problems 13, 1247-1263 (1997). pdf

59. (with I. Yu. Trooshin) Summability of eigenfunction expansions of three-point boundary value problems. Math. Nachrichten 191, 129-148 (1998). pdf

60. (with V. Yurko) Expansion theorems for boundary value problems with a singularity, Analysis 18, 25-39 (1998).

61. (with V. Yurko) On constructing differential equations with singularities from incomplete spectral information. Inverse problems 14, 1131-1150 (1998). pdf

62. (with V. Yurko) Inverse Sturm-Liouville problems. Lecture Notes, 36 p., Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 409 (1998).

63. (with G. Jank) Existence of Open Loop Stackelberg Equilibria In: Proceedings of MTNS 98, Padova, 1998. pdf

64. (with V. Ionescu) Monotonicity and convexity results for time-varying Riccati equations In: Proceedings of MTNS 98, Padova, 1998. pdf

65. (with V. Yurko) Introduction to the inverse Sturm-Liouville theory. Lecture Notes, 64p., Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 427 (1998).

66. (with G. Jank and S.-R. Lee) Coupled matrix Riccati equations in minimal cost variance control problems. IEEE Trans. Automatic Control 44, 556-560 (1999). pdf

67. (with V. Ionescu) Time-varying discrete Riccati equation: Some monotonicity results. Lin. Algebra and its Appl. 286, 135-148 (1999). pdf

68. (with V. Yurko) Inverse spectral problems for differential equations on the half-line with turning points. Journal of Differential Equations 154, 419-453 (1999). pdf

69. (with V. Ionescu) Nonsymmetric discrete-time difference and algebraic Riccati equations: Some representation formulae and comments. Dynamic Systems and Applications 8, 421-437 (1999). pdf

70. (with H. Abou-Kandil and G. Jank) Discrete Time Riccati Equations in Open Loop Nash and Stackelberg Games. European Journal of Control 5, 56-69 (1999). pdf

71. (with V. Yurko) Reconstructing parameters of a medium from incomplete spectral information. Results in Mathematics 35, 228-249 (1999). pdf

72. (with A. Hochhaus) Existence and convergence results for periodic Riccati differential equations. 6 pages. In: Proceedings of the European Control Conference, Karlsruhe, 1999.

73. (with V. Yurko) Inverse spectral problems for second-order differential operators. Part 1. 118 pages. Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 458 (1999).

74. (with V. Yurko) Inverse spectral problems for second-order differential operators. Part 2. 66 pages. Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 464 (2000).

75. (with V. Yurko) Inverse spectral problems for second-order differential operators. Part 3. 36 pages. Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 464 (2000).

76. (with G. Jank and A. Sarychev) Non - Blow - Up Conditions for Riccati - type Matrix Differential and Difference Equations. Results in Mathematics 37, 84-103 (2000). pdf

77. (with M. Annaby) Sampling for integrodifferential transforms arising from second order differential operators. Mathematische Nachrichten 216, 25-43 (2000).

78. (with M. Annaby) Sampling expansions associated with Kamke problems. Math. Zeitschrift 234, 163-189 (2000). pdf

79. On the existence of hermitian solutions of general algebraic Riccati equations. Schriftenreihe des FB Mathematik der Universität-GH-Duisburg Nr. 446 (1999); a short version appeared in: Proceedings of MTNS 2000, Perpignan, Juni 2000.

80. (with V. Yurko) Reconstructing parameters of a medium from incomplete spectral information. In: Proceedings of MTNS 2000, Perpignan, Juni 2000. pdf

81. (with V. Ionescu) Monotonicity and convexity properties of matrix Riccati equations. IMA Journal Math. Control & Inf. 18, 61-72 (2001). pdf

82. (with W. Eberhard and K. Wilcken-Stoeber) Indefinite eigenvalue problems with several singular points and turning points. Math. Nachrichten 229, 51-57, (2001). pdf

83. (with S. R. Lee and G. Jank) Open loop Stackelberg equilibria in linear-quadratic differential games. Journal of Optimization Theory 110, 515-544, (2001). pdf

84. (with A. Hochhaus) Basic properties of a class of rational matrix differential equations. Proceedings of the European Control Conference, Porto, 2001. pdf

85. (with V. Mehrmann and H. Xu) Existence, Uniqueness and Parametrization of Lagrangian Invariant Subspaces. SIAM J. Matrix Anal. Appl. 23, 1045-1069, (2002). pdf

86. (with V. Yurko) On the determination of differential equations with singularities and turning points. Results in Mathematics 41, 275-290 (2002). pdf

87. (with A. Hochhaus) Convergence and existence results for continuous- and discrete-time Riccati equations. Results in Mathematics, 42, 252-276, 2002. pdf

88. (with V. Yurko) Inverse spectral problems for singular non-selfadjoint differential operators with discontinuities in an interior point. Inverse Problems 18, 1-17 (2002). pdf

89. A survey of nonsymmetric Riccati equations. Lin. Algebra and its Appl. 251-252, 243-270 (2002). pdf

90. (with V. Rykhlov and V. Yurko) Spectral analysis for an indefinite Sturm-Liouville problem. Applicable Analysis 81, 1283-1305 (2002). pdf

91. (with A. Hochhaus) Properties of the solutions of rational matrix difference equations. Computers and Mathematics with Applications 45, Special issue on Advances in Difference equations VI, 1137-1154, (2003). pdf

92. (with M. Vietri and V. Yurko) Full- and half-range expansions for an indefinite singular Sturm-Liouville problem connected with an astrophysical problem of particle acceleration around a shock. Letters in Math. Phys. 64, 65-73 (2003). pdf

93. (with A. Hochhaus) About a generalized algebraic Riccati equation. In: Analysis and optimization of differential systems. V. Barbu, I. Lasiecka, D. Tiba and C. Varsan, Editors, Kluwer Academic Publishers, Boston, 169-178, 2003. pdf

94. (with G. Jank and D. Kremer) Solvability condition for a nonsymmetric Riccati equations appearing in Stackelberg games. In: Proceedings of the European Control Conference ECC 2003, Cambridge, England, 2003. pdf

95. (with M. Annaby and A.I.Zayed) Discontinuous boundary value problems: expansion and sampling theorems. Journal of Integral Equations and Applications. 16, 1-24 (2004). pdf

96. (with V. Dragan, A. Hochhaus and T. Morozan) A class of nonlinear differential equations on the space of symmetric matrices. Electronic Journal of Differential equations, 96, 48 pages, 2004. pdf, online

97. (with A. Hochhaus) On a class of rational matrix differential equations arising in stochastic control. Lin. Algebra and its Appl. 379, 43-68 (2004). pdf

98. (with A. Hochhaus) On the asymptotic behavior of the solutions of parameter-dependent matrix Riccati differential equations with respect to the parameter. Proceedings of Dynamic Systems and Applications 4, 613-619 (2004), Dynamic Publishers, Inc., Atlanta, USA. pdf

99. (with M. Annaby) A sampling theorem for transformations with discontinuous kernels. Applicable Analysis 83, 1053-1075 (2004). pdf

100. (with V. Yurko) The inverse problem method on the half-line and a nested system of Riccati differential equations. Results in Mathematics 45, 246-253 (2004). pdf

101. (with V. Yurko) Nested Riccati equations connected with a completely integrable system and related topics. In: Proceedings of MTNS 2004, (Editors: B. de Moor et al.), Leuven, Belgien, 9 pages.

102. (with V. Dragan, A. Hochhaus and T. Morozan) An iterative procedure for the computation of the maximal solution of a class of generalized Riccati differential equations. In: Proceedings of MTNS 2004, (Editors: B. de Moor et al.), Leuven, Belgien, 13pages. pdf

103. Discussion on: 'An algorithm for solving a perturbed algebraic Riccati equation' by E.F. Costa and J.B.R. do Val. European J. Control 10, 581-583 (2004) pdf

104. (with V. Yurko)The Weyl-type matrix and the method of spectral mappings in the inverse problem theory. Far East Journal of Appl. Math. 19, 125-146, (2005). pdf

105. (with V. Yurko) Boundary value problems with regular singularities and singular boundary conditions. International Journal of Math. and Math Sci. 9, 1481-1495, (2005). pdf

106. (with W. Eberhard and A. Zettl) Sturm-Liouville problems with non-selfadjoint boundary conditions. Math. Nachrichten 278, 1509-1523, (2005). pdf

107. (with V. Yurko) Inverse problems for differential operators with singular boundary conditions. Math. Nachrichten 278, 1561-1578, (2005). pdf

108. (with T. Damm, V. Dragan and T. Morozan) Differential equations with positive evolutions and some applications. Results in Mathematics 48, 206-236, (2005). pdf

109. (with V. Yurko) Recovering differential operators on graphs with general matching conditions. Schriftenreihe des Instituts für Mathematik der Universitäat-Duisburg-Essen Nr. 618 (2005).

110. (with M. Annaby und I.A. Soliman) Sampling theorems associated with differential operators iterated from lower order ones. Contemporary Mathematics 412, 31-50, AMS, Providence, (2006). pdf

111. (with V. Yurko) Spectral analysis for the non-selfadjoint matrix-Sturm-Liouville equation on the half-line. Schriftenreihe des Instituts für Mathematik der Universität-Duisburg-Essen Nr. 621 (2006).

112. (with S. Buterin und M. Annaby) Sampling Theorems Associated with Birkhoff-Regular Problems. In: Proceedings of the conference "Mathematical Analysis and Its Applications", Assiut, Ägypten, 2006. pdf

113. (with T. Damm und V. Dragan) Lyapunov iterations for coupled Riccati differential equations in connection with Nash differential games. Mathematical Reports of the Roumanian Academy 9, 35-46 (2007). pdf

114. (with V. Yurko) Inverse problems for differential operators on trees with general matching conditions. Applicable Analysis 86, 653-667, (2007). pdf

115. (with V. Yurko) Inverse problems for Sturm-Liouville operators on noncompact trees. Results in Mathematics 50, 195-212, (2007). pdf

116. (with T. Mazur und V. Yurko) A numerical algorithm for solving inverse problems for singular Sturm-Liouville operators. Advances in Dynamical Systems and Applications 2, 95-105, (2007). pdf

117. (with G. Galkin und V. Yurko) A numerical algorithm for solving an incomplete inverse problem for stratified media. Schriftenreihe des Instituts für Mathematik der Universität-Duisburg-Essen Nr. 649 (2007), 11 pages.

118. (with V. Yurko) An inverse problems for the non-selfadjoint matrix Sturm-Liouville equation on the half-line. Journal of Inverse and Ill-Posed Problems 15, no.8 (2008), 785-798. pdf

119. (with M. Ignatiev und V. Yurko) An inverse spectral problem for Sturm-Liouville operators with singular potential on star-type graphs. In: Proceedings of Symposia in Pure Mathematics 77 , 397-408 (2008) (Editors: P. Exner et al.), AMS, Providence. pdf

120. (with G. Galkin und V. Yurko) Numerical solution of the inverse synthesis problem for stratified media from incomplete spectral information. Far East Journal of Mathematical Sciences 31, to appear (2008). pdf

121. (with T. Damm und V. Dragan) Coupled Riccati differential equations arising in connection with Nash differential games. In: Proceedings of the IFAC World Congress 2008, pp. 3946-3951, Seoul, Korea, Editors: M.J. Chung, P. Misra, H. Shim. pdf

122. (with V. Dragan,T. Morozan und A. Stoica) Iterative algorithms for stabilizing solution of the game theoretic Riccati equations of stochastic control. Proceedings of the 18th Symposium on Mathematical Theory of Networks & Systems (MTNS), Blacksburg, Virginia, USA, 2008.

123. (with S. Buterin und M. Annaby) Sampling, Hermite-interpolation and Birkhoff-regular problems. J. Austral. Math. Soc. A, to appear.

124. (with V. Yurko) Stability of the solution of inverse problems for Sturm-Liouville operators with non-separated boundary conditions. Schriftenreihe des Instituts für Mathematik der Universität-Duisburg-Essen Nr. 671 (2008), 8 pages.

125. (with A. Chernozhukova) A uniqueness theorem for boundary value problems with nonlinear dependence of the boundary conditions on the spectral parameter. Inverse Problems in Science and Engineering, to appear.

TEXTBOOKS and LECTURE NOTES

1. (with V. Yurko) Inverse Sturm-Liouville Problems and their Applications. NOVA Science Publishers, New York, 2001.

2. (with H. Abou-Kandil, V. Ionescu and G. Jank) Matrix Riccati Equations in Control and Systems Theory. Birkhäusser Verlag, Heidelberg, 2003

3. (with V. Yurko) Introduction in the theory of entire functions. Schriftenreihe des Instituts für Mathematik der Universität-Duisburg-Essen Nr. 546 (2003)

4. (with V. Yurko) Differential equations of mathematical physics. 88 Seiten. Schriftenreihe des Instituts für Mathematik der Universität-Duisburg-Essen Nr. 560 (2003)

5. (with V. Yurko) Exercises for the course: Differential equations of mathematical physics. Schriftenreihe des Instituts für Mathematik der Universität-Duisburg-Essen Nr. 589 (2004), 56 Seiten.

6. (with V. Yurko) Lectures on differential equations of mathematical physics: A first course. NOVA Science Publishers, New York, 2008.

7. Analysis II, Duisburg, 1995/2003.

8. Analysis III, Duisburg, 1996/2003.

9. Analysis IV, Duisburg, 1996/2004.

10. Analysis I, Duisburg, 2002.

11. Funktionentheorie I and II, Duisburg, 2003/2005.

12. Funktionalanalysis, Duisburg, 2003.

13. (with H.-B. Knoop) Mathematik für Informatiker I, Duisburg 2006.

14. (with H.-B. Knoop) Mathematik für Informatiker II, Duisburg 2006.