MATH 132B: Partial Differential Equations and Integral Equations
Spring quarter, 2005
Instructor: Bo Li
Referenes
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Integral Equations: Theory, Numerical Methods, and Applications
Basics: Mainly about Linear Theory
- C. Chen, Z. Hou, and M. Li, Theory of Integral Equations and its Applications,
Shanghai Science and Technology Publisher, 1987 (in Chinese).
- H. Hochstadt, Integral Equations, Wiley, 1989.
- A. Jerri, Introduction to Integral Equations with Applications,
2nd ed., Wiley, 1999.
- R. Kress, Linear Integral Equations, 2nd ed., Springer, 1999.
- A. C. Pipkin, A Course on Integral Equations, Springer, 1991.
- D. Porter and D. S. G. Stirling, Integral Equations, Cambridge University Press, 1990.
- F. Smithies, Integral equations, Cambridge University Press, 1958.
- F. G. Tricomi, Integral Equations, Dover, 1985.
Singular Integral Equations
- R. Estrada and R. P. Kanwal, Singular Integral Equations, Birkhäuser, 1999.
- E. G. Ladopoulos, Singular Integral Equations:
Linear and Non-linear Theory and its Applications in
Science and Engineering, Springer, 2002.
- N.I. Muskhelishvili, Singular Integral Equations: Boundary Problems
of Function Theory and Their Applications to Mathematical Physics, 2nd ed., Dover, 1992.
Numerics
- K. E. Atkinson,
The Numerical Solution of Integral Equations of the Second Kind,
Cambridge University Press, 1997.
- C. T. H. Baker, The Numerical Treatment of Integral Equations,
Oxford University Press, 1977.
- L. M. Delves and J. L. Mohamed, Computational Methods for Integral Equations,
Cambridge University Press, 1988.
- W. Hackbusch, Integral Equations: Theory and Numerical Treatment,
Birkhäuser, 1995.
A Review Article
- A. T. Lonseth, Sources and applications of integral equations, SIAM Review, 19(2),
241-278, 1977.
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Functional Analysis and Theory of Operators
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Introduction of Functional Analysis
- Y. Eidelman, V. Milman, and A. Tsolomitis, Functional Analysis:
An Introduction, American Mathematical Society, 2004.
- D. H. Griffel, Applied Functional Analysis, Dover, 2002.
- F. Hirsch and G. Lacombe, Elements of Functional Analysis, Springer, 1999.
- A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions
and Functional Analysis, Dover, 1999.
- G. E. Shilov, Elementary Functional Analysis, Dover, 1996.
More Functional Analysis
- J. B. Conway, A Course in Functional Analysis, 2nd ed., Springer, 1997.
- R. E. Edwards, Functional Analysis: Theory and Applications,
Dover, 1995.
- E. Kreyszig, Introductory Functional Analysis with Applications, Wiley, 1989.
- P. Lax, Functional Analysis, Wiley, 2002.
- F. Riesz and B. Sz.-Nagy, Functional Analysis, Dover, 1990.
- W. Rudin, Functional Analysis, 2nd ed., McGraw-Hill, 1991.
- M. Schechter, Principles of Functional Analysis, 2nd ed.,
American Mathematical Society, 2001.
- K. Yosida, Functional Analysis, 5th ed., Springer, 1978.
- E. Zeidler, Applied Functional Analysis: Main Principles and Their Applications,
Springer, 1995.
- E. Zeidler, Applied Functional Analysis: Applications to Mathematical Physics,
Springer, 1999.
Operator Theory
- N. I. Akhiezer and I. M. Glazman, Theory of Linear Operators in Hilbert Space,
Dover, 1993.
- S. K. Berberianm, Lectures in Functional Analysis and Operator Theory, Springer, 1974.
- N. Dunford and J. T. Schwartz, Linear Operators: Part I. General Theory, Wiley, 1988.
- N. Dunford and J. T. Schwartz, Linear Operators:
Part II. Spectral Theory, Wiley, 1988.
- N. Dunford and J. T. Schwartz, Linear Operators: Part III. Spectral Operators,
Wiley, 1988.
- G. Helmberg, Introduction to Spectral Theory in Hilbert Space, North-Holland, 1969.
- T. Kato, Perturbation Theory for Linear Operators, Springer, 1995.
- J. Weidmann, Linear Operators in Hilbert Spaces, Springer, 1980.
Last updated by Bo Li on May 3, 2005.