Below is a list of required and key recommended textbooks, and additional books and articles for further study.
Main Textbook
Masujima, M. Applied Mathematical Methods of Theoretical Physics - Integral Equations and Calculus of Variations. Weinheim, Germany: Wiley-VCH, 2005. ISBN: 3527405348.
Recommended Textbooks
Stakgold, I. Green’s Functions and Boundary-value Problems. New York, NY: Wiley, 1998. ISBN: 0471610224.
Kanwal, R. P. Linear Integral Equations: Theory and Technique. Boston, MA: Birkhauser, 1996. ISBN: 0817639403.
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
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
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.
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.
Pipkin, A. C. A Course on Integral Equations. New York, NY: Springer-Verlag, 1991. ISBN: 0387975578.
Hochstadt, H. Integral Equations. New York, NY: Wiley, 1973. ISBN: 047140165X, 0471504041.
Weinstein, A., and W. Stenger. Methods of Intermediate Problems for Eigenvalues. New York, NY: Academic Press, 1972. ISBN: 0127424504.
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
Carrie r, G. F., M. Krook, and C. E. Pearson. Functions of a Complex Variable: Theory and Technique. Ithica, NY: Hod Books, 1983. ISBN: 0070100896.
Whittaker, E. T., and G. N. Watson. A Course of Modern Analysis. Cambridge, UK: Cambridge University Press, 1992. ISBN: 0521588073.
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.
———. 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
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).
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
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.
Muskhelishvili, N. I. Singular Integral Equations. New York, NY: Dover, 1992. ISBN: 0486668932.
Gakhov, F. D. Boundary-value Problems. New York, NY: Dover, 1990. ISBN: 0486662756.
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
Broberg, K. B. Cracks and Fracture. San Diego, CA: Academic Press, 1999. ISBN: 0121341305.
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
Hirth, J. P., and J. Lothe. Theory of Dislocations. New York, NY: Wiley, 1982, esp. chapter 8. ISBN: 0471091251.
Integral Equations in Microwave Engineering
King, R. W. P. The Theory of Linear Antennas. Cambridge, MA: Harvard University Press, 1956. ASIN: B0006AUHPW
Tyras, G. Radiation and Propagation of Electromagnetic Waves. New York, NY: Academic Press, 1969. ISBN: 0127056505.
Collin, R. E. Field Theory of Guided Waves. New York, NY: Wiley-IEEE Press, 1990. ISBN: 0879422378.
