Readings

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

Main Textbook

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

Recommended Textbooks

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

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

Buy at Amazon 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

Buy at Amazon 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

Buy at Amazon 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.

Buy at Amazon 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.

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

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

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

Buy at Amazon 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

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

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

Buy at Amazon 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.

Buy at Amazon ———. 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

Buy at Amazon 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).

Buy at Amazon 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

Buy at Amazon 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.

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

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

Buy at Amazon 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

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

Buy at Amazon 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

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

Integral Equations in Microwave Engineering

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

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

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