APPENDIX 1

References

Software see at the beginning of Chaps. 19 and 24.

General References

[GenRef1] Abramowitz, M. and I. A. Stegun (eds.), Handbook of Mathematical Functions. 10th printing, with corrections. Washington, DC: National Bureau of Standards. 1972 (also New York: Dover, 1965). See also [W1]

[GenRef2] Cajori, F., History of Mathematics. 5th ed. Reprinted. Providence, RI: American Mathematical Society, 2002.

[GenRef3] Courant, R. and D. Hilbert, Methods of Mathematical Physics. 2 vols. Hoboken, NJ: Wiley, 1989.

[GenRef4] Courant, R., Differential and Integral Calculus. 2 vols. Hoboken, NJ: Wiley, 1988.

[GenRef5] Graham, R. L. et al., Concrete Mathematics. 2nd ed. Reading, MA: Addison-Wesley, 1994.

[GenRef6] Ito, K. (ed.), Encyclopedic Dictionary of Mathematics. 4 vols. 2nd ed. Cambridge, MA: MIT Press, 1993.

[GenRef7] Kreyszig, E., Introductory Functional Analysis with Applications. New York: Wiley, 1989.

[GenRef8] Kreyszig, E., Differential Geometry. Mineola, NY: Dover, 1991.

[GenRef9] Kreyszig, E. Introduction to Differential Geometry and Riemannian Geometry. Toronto: University of Toronto Press, 1975.

[GenRef10] Szegö, G., Orthogonal Polynomials. 4th ed. Reprinted. New York: American Mathematical Society, 2003.

[GenRef11] Thomas, G. et al., Thomas’ Calculus, Early Transcendentals Update. 10th ed. Reading, MA: Addison-Wesley, 2003.

Part A. Ordinary Differential Equations (ODEs) (Chaps. 1–6)

See also Part E: Numeric Analysis

[A1] Arnold, V. I., Ordinary Differential Equations. 3rd ed. New York: Springer, 2006.

[A2] Bhatia, N. P. and G. P. Szego, Stability Theory of Dynamical Systems. New York: Springer, 2002.

[A3] Birkhoff, G. and G.-C. Rota, Ordinary Differential Equations. 4th ed. New York: Wiley, 1989.

[A4] Brauer, F. and J. A. Nohel, Qualitative Theory of Ordinary Differential Equations. Mineola, NY: Dover, 1994.

[A5] Churchill, R. V., Operational Mathematics. 3rd ed. New York: McGraw-Hill, 1972.

[A6] Coddington, E. A. and R. Carlson, Linear Ordinary Differential Equations. Philadelphia: SIAM, 1997.

[A7] Coddington, E. A. and N. Levinson, Theory of Ordinary Differential Equations. Malabar, FL: Krieger, 1984.

[A8] Dong, T.-R. et al., Qualitative Theory of Differential Equations. Providence, RI: American Mathematical Society, 1992.

[A9] Erdélyi, A. et al., Tables of Integral Transforms. 2 vols. New York: McGraw-Hill, 1954.

[A10] Hartman, P., Ordinary Differential Equations. 2nd ed. Philadelphia: SIAM, 2002.

[A11] Ince, E. L., Ordinary Differential Equations. New York: Dover, 1956.

[A12] Schiff, J. L., The Laplace Transform: Theory and Applications. New York: Springer, 1999.

[A13] Watson, G. N., A Treatise on the Theory of Bessel Functions. 2nd ed. Reprinted. New York: Cambridge University Press, 1995.

[A14] Widder, D. V., The Laplace Transform. Princeton, NJ: Princeton University Press, 1941.

[A15] Zwillinger, D., Handbook of Differential Equations. 3rd ed. New York: Academic Press, 1998.

Part B. Linear Algebra, Vector Calculus (Chaps. 7–10)

For books on numeric linear algebra, see also Part E: Numeric Analysis.

[B1] Bellman, R., Introduction to Matrix Analysis. 2nd ed. Philadelphia: SIAM, 1997.

[B2] Chatelin, F., Eigenvalues of Matrices. New York: Wiley-Interscience, 1993.

[B3] Gantmacher, F. R., The Theory of Matrices. 2 vols. Providence, RI: American Mathematical Society, 2000.

[B4] Gohberg, I. P. et al., Invariant Subspaces of Matrices with Applications. New York: Wiley, 2006.

[B5] Greub, W. H., Linear Algebra. 4th ed. New York: Springer, 1975.

[B6] Herstein, I. N., Abstract Algebra. 3rd ed. New York: Wiley, 1996.

[B7] Joshi, A. W., Matrices and Tensors in Physics. 3rd ed. New York: Wiley, 1995.

[B8] Lang, S., Linear Algebra. 3rd ed. New York: Springer, 1996.

[B9] Nef, W., Linear Algebra. 2nd ed. New York: Dover, 1988.

[B10] Parlett, B., The Symmetric Eigenvalue Problem. Philadelphia: SIAM, 1998.

Part C. Fourier Analysis and PDEs (Chaps. 11–12)

For books on numerics for PDEs see also Part E: Numeric Analysis.

[C1] Antimirov, M. Ya., Applied Integral Transforms. Providence, RI: American Mathematical Society, 1993.

[C2] Bracewell, R., The Fourier Transform and Its Applications. 3rd ed. New York: McGraw-Hill, 2000.

[C3] Carslaw, H. S. and J. C. Jaeger, Conduction of Heat in Solids. 2nd ed. Reprinted. Oxford: Clarendon, 2000.

[C4] Churchill, R. V. and J. W. Brown, Fourier Series and Boundary Value Problems. 6th ed. New York: McGraw-Hill, 2006.

[C5] DuChateau, P. and D. Zachmann, Applied Partial Differential Equations. Mineola, NY: Dover, 2002.

[C6] Hanna, J. R. and J. H. Rowland, Fourier Series, Transforms, and Boundary Value Problems. 2nd ed. New York: Wiley, 2008.

[C7] Jerri, A. J., The Gibbs Phenomenon in Fourier Analysis, Splines, and Wavelet Approximations. Boston: Kluwer, 1998.

[C8] John, F., Partial Differential Equations. 4th edition New York: Springer, 1982.

[C9] Tolstov, G. P., Fourier Series. New York: Dover, 1976.

[C10] Widder, D. V., The Heat Equation. New York: Academic Press, 1975.

[C11] Zauderer, E., Partial Differential Equations of Applied Mathematics. 3rd ed. New York: Wiley, 2006.

[C12] Zygmund, A. and R. Fefferman, Trigonometric Series. 3rd ed. New York: Cambridge University Press, 2002.

Part D. Complex Analysis (Chaps. 13–18)

[D1] Ahlfors, L. V., Complex Analysis. 3rd ed. New York: McGraw-Hill, 1979.

[D2] Bieberbach, L., Conformal Mapping. Providence, RI: American Mathematical Society, 2000.

[D3] Henrici, P., Applied and Computational Complex Analysis. 3 vols. New York: Wiley, 1993.

[D4] Hille, E., Analytic Function Theory. 2 vols. 2nd ed. Providence, RI: American Mathematical Society, Reprint V1 1983, V2 2005.

[D5] Knopp, K., Elements of the Theory of Functions. New York: Dover, 1952.

[D6] Knopp, K., Theory of Functions. 2 parts. New York: Dover, Reprinted 1996.

[D7] Krantz, S. G., Complex Analysis: The Geometric Viewpoint. Washington, DC: The Mathematical Association of America, 1990.

[D8] Lang, S., Complex Analysis. 4th ed. New York: Springer, 1999.

[D9] Narasimhan, R., Compact Riemann Surfaces. New York: Springer, 1996.

[D10] Nehari, Z., Conformal Mapping. Mineola, NY: Dover, 1975.

[D11] Springer, G., Introduction to Riemann Surfaces. Providence, RI: American Mathematical Society, 2001.

Part E. Numeric Analysis (Chaps. 19–21)

[E1] Ames, W. F., Numerical Methods for Partial Differential Equations. 3rd ed. New York: Academic Press, 1992.

[E2] Anderson, E., et al., LAPACK User's Guide. 3rd ed. Philadelphia: SIAM, 1999.

[E3] Bank, R. E., PLTMG. A Software Package for Solving Elliptic Partial Differential Equations: Users’ Guide 8.0. Philadelphia: SIAM, 1998.

[E4] Constanda, C., Solution Techniques for Elementary Partial Differential Equations. Boca Raton, FL: CRC Press, 2002.

[E5] Dahlquist, G. and A. Björck, Numerical Methods. Mineola, NY: Dover, 2003.

[E6] DeBoor, C., A Practical Guide to Splines. Reprinted. New York: Springer, 2001.

[E7] Dongarra, J. J. et al., LINPACK Users Guide. Philadelphia: SIAM, 1979. (See also at the beginning of Chap. 19.)

[E8] Garbow, B. S. et al., Matrix Eigensystem Routines: EISPACK Guide Extension. Reprinted. New York: Springer, 1990.

[E9] Golub, G. H. and C. F. Van Loan, Matrix Computations. 3rd ed. Baltimore, MD: Johns Hopkins University Press, 1996.

[E10] Higham, N. J., Accuracy and Stability of Numerical Algorithms. 2nd ed. Philadelphia: SIAM, 2002.

[E11] IMSL (International Mathematical and Statistical Libraries), FORTRAN Numerical Library. Houston, TX: Visual Numerics, 2002. (See also at the beginning of Chap. 19.)

[E12] IMSL, IMSL for Java. Houston, TX: Visual Numerics, 2002.

[E13] IMSL, C Library. Houston, TX: Visual Numerics, 2002.

[E14] Kelley, C. T., Iterative Methods for Linear and Nonlinear Equations. Philadelphia: SIAM, 1995.

[E15] Knabner, P. and L. Angerman, Numerical Methods for Partial Differential Equations. New York: Springer, 2003.

[E16] Knuth, D. E., The Art of Computer Programming. 3 vols. 3rd ed. Reading, MA: Addison-Wesley, 1997–2009.

[E17] Kreyszig, E., Introductory Functional Analysis with Applications. New York: Wiley, 1989.

[E18] Kreyszig, E., On methods of Fourier analysis in multigrid theory. Lecture Notes in Pure and Applied Mathematics 157. New York: Dekker, 1994, pp. 225–242.

[E19] Kreyszig, E., Basic ideas in modern numerical analysis and their origins. Proceedings of the Annual Conference of the Canadian Society for the History and Philosophy of Mathematics. 1997, pp. 34–45.

[E20] Kreyszig, E., and J. Todd, QR in two dimensions. Elemente der Mathematik 31 (1976), pp. 109–114.

[E21] Mortensen, M. E., Geometric Modeling. 2nd ed. New York: Wiley, 1997.

[E22] Morton, K. W., and D. F. Mayers, Numerical Solution of Partial Differential Equations: An Introduction. New York: Cambridge University Press, 1994.

[E23] Ortega, J. M., Introduction to Parallel and Vector Solution of Linear Systems. New York: Plenum Press, 1988.

[E24] Overton, M. L., Numerical Computing with IEEE Floating Point Arithmetic. Philadelphia: SIAM, 2004.

[E25] Press, W. H. et al., Numerical Recipes in C: The Art of Scientific Computing. 2nd ed. New York: Cambridge University Press, 1992.

[E26] Shampine, L. F., Numerical Solutions of Ordinary Differential Equations. New York: Chapman and Hall, 1994.

[E27] Varga, R. S., Matrix Iterative Analysis. 2nd ed. New York: Springer, 2000.

[E28] Varga, R. S., Gergorin and His Circles. New York: Springer, 2004.[E29] Wilkinson, J. H., The Algebraic Eigenvalue Problem. Oxford: Oxford University Press, 1988.

Part F. Optimization, Graphs (Chaps. 22–23)

[F1] Bondy, J. A. and U.S.R. Murty, Graph Theory with Applications. Hoboken, NJ: Wiley-Interscience, 1991.

[F2] Cook, W. J. et al., Combinatorial Optimization. New York: Wiley, 1997.

[F3] Diestel, R., Graph Theory. 4th ed. New York: Springer, 2006.

[F4] Diwekar, U. M., Introduction to Applied Optimization. 2nd ed. New York: Springer, 2008.

[F5] Gass, S. L., Linear Programming. Method and Applications. 3rd ed. New York: McGraw-Hill, 1969.

[F6] Gross, J. T. and J. Yellen (eds.), Handbook of Graph Theory and Applications. 2nd ed . Boca Raton, FL: CRC Press, 2006.

[F7] Goodrich, M. T., and R. Tamassia, Algorithm Design: Foundations, Analysis, and Internet Examples. Hoboken, NJ: Wiley, 2002.

[F8] Harary, F., Graph Theory. Reprinted. Reading, MA: Addison-Wesley, 2000.

[F9] Merris, R., Graph Theory. Hoboken, NJ: Wiley-Interscience, 2000.

[F10] Ralston, A., and P. Rabinowitz, A First Course in Numerical Analysis. 2nd ed. Mineola, NY: Dover, 2001.

[F11] Thulasiraman, K., and M. N. S. Swamy, Graph Theory and Algorithms. New York: Wiley-Interscience, 1992.

[F12] Tucker, A., Applied Combinatorics. 5th ed. Hoboken, NJ: Wiley, 2007.

Part G. Probability and Statistics (Chaps. 24–25)

[G1] American Society for Testing Materials, Manual on Presentation of Data and Control Chart Analysis. 7th ed. Philadelphia: ASTM, 2002.

[G2] Anderson, T. W., An Introduction to Multivariate Statistical Analysis. 3rd ed. Hoboken, NJ: Wiley, 2003.

[G3] Cramér, H., Mathematical Methods of Statistics. Reprinted. Princeton, NJ: Princeton University Press, 1999.

[G4] Dodge, Y., The Oxford Dictionary of Statistical Terms. 6th ed. Oxford: Oxford University Press, 2006.

[G5] Gibbons, J. D. and S. Chakraborti, Nonparametric Statistical Inference. 4th ed. New York: Dekker, 2003.

[G6] Grant, E. L. and R. S. Leavenworth, Statistical Quality Control. 7th ed. New York: McGraw-Hill, 1996.

[G7] IMSL, Fortran Numerical Library. Houston, TX: Visual Numerics, 2002.

[G8] Kreyszig, E., Introductory Mathematical Statistics. Principles and Methods. New York: Wiley, 1970.

[G9] O'Hagan, T. et al., Kendall's Advanced Theory of Statistics 3-Volume Set. Kent, U.K.: Hodder Arnold, 2004.

[G10] Rohatgi, V. K. and A. K. MD. E. Saleh, An Introduction to Probability and Statistics. 2nd ed. Hoboken, NJ: Wiley-Interscience, 2001.

Web References

[W1] upgraded version of [GenRef1] online at http://dlmf.nist.gov/. Hardcopy and CD-Rom: Oliver, W. J. et al. (eds.), NIST Handbook of Mathematical Functions. Cambridge; New York: Cambridge University Press, 2010.

[W2] O'Connor, J. and E. Robertson, MacTutor History of Mathematics Archive. St. Andrews, Scotland: University of St. Andrews, School of Mathematics and Statistics. Online at http://www-history.mcs.st-andrews.ac.uk. (Biographies of mathematicians, etc.).