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Below is a list of required and key recommended textbooks, and additional books and articles for further study.



Main Textbook


Amazon logo Masujima, M. Applied Mathematical Methods of Theoretical Physics - Integral Equations and Calculus of Variations. Weinheim, Germany: Wiley-VCH, 2005. ISBN: 3527405348.



Recommended Textbooks


Amazon logo Stakgold, I. Green's Functions and Boundary-value Problems. New York, NY: Wiley, 1998. ISBN: 0471610224.

Amazon logo Kanwal, R. P. Linear Integral Equations: Theory and Technique. Boston, MA: Birkhauser, 1996. ISBN: 0817639403.

Amazon logo Drazin, P. G., and R. S. Johnson. Solitons: An Introduction. Cambridge, UK: Cambridge University Press, 1989. ISBN: 052133389X; 0521336554 (paperback).



Green's Functions and Boundary-value Problems


Amazon logo Jereys, H., and B. S. Jereys. Methods of Mathematical Physics. Cambridge, UK: Cambridge University Press, 2000. ISBN: 0521664020.

Coddington, E. A., and N. Levinson. Theory of Ordinary Differential Equations. New York, NY: McGraw-Hill, 1955.

Hellwig, G. Partial Differential Equations. New York, NY: Blaisdell, 1964.

Bergman, S., and M. Schier. Kernel Functions and Elliptic Differential Equations in Mathematical Physics. New York, NY: Academic Press, 1953.

Kellogg, O. D. Foundations of Potential Theory. New York, NY: Dover, 1954.



Elements of Theory of Fredholm Integral Equations


Amazon logo Courant, R., and D. Hilbert. Methods of Mathematical Physics. Vol. I. New York, NY: Wiley, 1989. ISBN: 0471504475.

Feshbach, H., and P. M. Morse. Methods of Theoretical Physics. New York, NY: McGraw-Hill, 1953.

Amazon logo Tricomi, F. G. Integral Equations. New York, NY: Dover, 1985. ISBN: 0486648281

Mikhlin, S. G. Integral Equations and their Applications to Certain Problems in Mechanics, Mathematical Physics, and Technology. New York, NY: Pergamon, 1957.

Smithies, F. Integral Equations. New York, NY: Cambridge University Press, 1958.

Amazon logo Pipkin, A. C. A Course on Integral Equations. New York, NY: Springer-Verlag, 1991. ISBN: 0387975578.

Amazon logo Hochstadt, H. Integral Equations. New York, NY: Wiley, 1973. ISBN: 047140165X, 0471504041.

Amazon logo Weinstein, A., and W. Stenger. Methods of Intermediate Problems for Eigenvalues. New York, NY: Academic Press, 1972. ISBN: 0127424504.

Amazon logo Dunford, N., and J. T. Schwartz. Linear Operators. Vols. I-III. New York, NY: Wiley, 1988. ISBN: 0470226382.



Theory of Functions of a Complex Variable and Fourier Transforms


Amazon logo Carrier, G. F., M. Krook, and C. E. Pearson. Functions of a Complex Variable: Theory and Technique. Ithica, NY: Hod Books, 1983. ISBN: 0070100896.

Amazon logo Whittaker, E. T., and G. N. Watson. A Course of Modern Analysis. Cambridge, UK: Cambridge University Press, 1992. ISBN: 0521588073.

Amazon logo Sveshnikov, A. G., and A. N. Tikhonov. The Theory of Functions of a Complex Variable. Translated from Russian by G. Yankovsky. Moscow, Russia: Mir Publ., 1974. ASIN: B0007APBKC

Titchmarsh, E. C. The Theory of Functions. New York, NY: Oxford University Press, 1939.

Amazon logo ———. Introduction to the Theory of Fourier Integrals. New York, NY: Chelsea Pub. Co., 1986. ISBN: 0828403244.

Paley, R., and N. Wiener. Fourier Transforms in the Complex Domain. New York, NY: American Mathematical Society, 1934.

Levinson, N. Gap and Density Theorems. New York, NY: American Mathematical Society, 1940.



Wiener-Hopf Integral Equations


Amazon logo Noble, B. Methods based on the Wiener-Hopf Technique for the Solution of Partial Differential Equations. New York, NY: Chelsea Publishing Company, 1988. ISBN: 0828403325.

Weinstein (Vajnshtejn), L. A. The Theory of Diraction and the Factorization Method (Generalized Wiener-Hopf technique). Translated from Russian by P. Beckmann, Golem Press, 1969.

Krein, M. G. Am Math Transl 22, no. 163 (1962).

Reissner, E., J. Math Phys Mass Inst Tech 20, no. 219 (1941).

Hopf, E. Mathematical Problems of Radiative Equilibrium. London, UK: Cambridge University Press, 1933.

Wiener, N., and E. Hopf. S B Preuss Akad Wiss 696, no. 706 (1931).

Levine, H., and J. Schwinger. Phys Rev 73, 383 (1948).



Wiener-Hopf Sum Equations


Krein, M. G. Am Math Transl 22, no. 163 (1962).

Amazon logo McCoy, B., and T. T. Wu. The Two-dimensional Ising Model. Cambridge, MA: Harvard University Press, 1973. ISBN: 0674914406.



The Hilbert Problem and Singular Integral Equations of the Cauchy Type


Amazon logo Carrier, G. F., M. Krook, and C. E. Pearson. Functions of a Complex Variable: Theory and Technique. Ithica, NY: Hod Books, 1983, chapter 8. ISBN: 0070100896.

Amazon logo Muskhelishvili, N. I. Singular Integral Equations. New York, NY: Dover, 1992. ISBN: 0486668932.

Amazon logo Gakhov, F. D. Boundary-value Problems. New York, NY: Dover, 1990. ISBN: 0486662756.

Amazon logo Lu, J.-L. Boundary-value Problems for Analytic Functions. River Edge, NJ: World Scientific, 1993. ISBN: 9810210205.



Modern Applications to Engineering




Wiener-Hopf Method in Elastodynamics of Crack Motion


Amazon logo Broberg, K. B. Cracks and Fracture. San Diego, CA: Academic Press, 1999. ISBN: 0121341305.

Amazon logo Freund, L. B. Dynamic Fracture Mechanics. New York, NY: Cambridge University Press, 1990. ISBN: 0521303303.

———. J Mech Phys Solids 20 (1972): 129-140, 141-152.

Willis, J. R., and A. B. Movchan. J Mech Phys Solids 43 (1995): 319-341.



Singular Integral Equations for Dislocations in Solids


Amazon logo Hirth, J. P., and J. Lothe. Theory of Dislocations. New York, NY: Wiley, 1982, esp. chapter 8. ISBN: 0471091251.



Integral Equations in Microwave Engineering


Amazon logo King, R. W. P. The Theory of Linear Antennas. Cambridge, MA: Harvard University Press, 1956. ASIN: B0006AUHPW

Amazon logo Tyras, G. Radiation and Propagation of Electromagnetic Waves. New York, NY: Academic Press, 1969. ISBN: 0127056505.

Amazon logo Collin, R. E. Field Theory of Guided Waves. New York, NY: Wiley-IEEE Press, 1990. ISBN: 0879422378.


 








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