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Lynch, D.R.  Numerical Partial Differential Equations for Environmental Scientists and Engineers -- A First Practical Course.  Springer, 2004.

General Numerical Background

Burden R.L. and J.D. Faires, Numerical Analysis Brooks Cole; 9th edition (August 9, 2010).

Hornbeck, R.W., Numerical Methods, Quantum, 1975.

Vemuri, V. and W.J. Karplus, Digital Computer Treatment of Partial Differential Equations, Prentice-Hall, 1981 (FD and FE methods).

Johnson, L.W. and R.D. Riess, Numerial Analysis, 2nd Ed., Addison-Wesley, 1982.

Stoer, J. and R. Burlirsch, Introduction to Numerical Analysis, 2nd Ed., Prindle Weber & Schmidt, 1981.

Churchhouse, R.F., Numerical Methods, Vol. 111 of Handbook of Applicable Mathematics, W. Ledermann, Ed., Wiley, 1981.

Press, W.H., B.P. Flannery, S.A. Teukolsky, W.T. Vetterling, Numerical Recipes: The Art of Scientific Computing. Cambridge Univ. Press, 1986 or latest.

Finite Difference Methods

Smith, G.D., Numerical Solution of Partial Differential Equations, Oxford University Press, 1975.[Roughly equivalent to Morton/Mayers]

Morton, K.W. and D.F. Mayers. Numerical Solution of Partial Differential Equations. Cambridge University Press, 1994.[Roughly equivalent to Smith.]

Ames, W.F., Numerical Methods for Partial Differential Equations, Academic Press, 1977.

Mitchell, A.R. and D.F. Griffiths, Finite Difference Method in Partial Differential Equations, John Wiley & Sons, 1980.

Finite Element Methods

Zienkiewicz, O.C. The Finite Element Method in Engineering Science, McGraw-Hill, 1986 (third ed.), or latest ed.

Zienkiewicz, O.C. and R.L. Taylor.  The Finite Element Method, McGraw-Hill, 1987 (fourth ed.), or latest edition.

Zienkiewicz, O.C. and R.L. Taylor.  The Finite Element Method. Butterworth-Heinemann, 5th ed. 2000

            Volume I:  The Basis

            Volume II:  Solid Mechanics. 

            Volume III:  Fluid Dynamics. 

Strang, G. and G.J. Fix, An Analysis of the Finite Element Method, Prentice-Hall, 1973.

Pinder, G.F. and W.G. Gray, Finite Element Simulation in Surface and Subsurface Hydrology, Academic Press, 1977.

Finalyson, B., Methods of Weighted Residuals and Variational Principles, Academic Press, 1972.

Lewis, R.W., K. Morgan and O.C. Zienkiewicz, Numerical Methods in Heat Transfer, John Wiley, 1982 (includes some FD material also).

Chari and Silvester, Finite Elements in Electrical and Magnetic Field Problems, Wiley 1980.

Mitchell, A.R. and R. Wait, Finite Element Method in Partial Differential Equations, John Wiley & Sons, 1977.

Schwartz, H.R., Finite Element Methods. Academic Press, 1988.

Segerlind, L.J., Applied Finite Element Analysis. Wiley, 1984 or later.

Numerical PDE's (FD + FE)

Lapidus, L. and G.F. Pinder, Numerical Solution of Partial Differential Equations in Science and Engineering, Wiley, latest edition.

Linear Algebra

Golub, G.H. and C. F. Van Loan, Matrix Computations, 1983 or latest edition.

Trefethen, L.N. and D. Bau, III: Numerical Linear Algebra.  SIAM, 1997.

Demmel, J. W. , Applied Numerical Linear Algebra.  SIAM, 1997.

Hildebrand, F.B., Methods of Applied Mathematics, Ch. 1 2nd Ed., Prentice-Hall, 1985.

Westlake, J., Handbook of Numerical Matrix Inversion and Solution of Linear Equations, Krieger, 1975.

Wait, Numerical Solution of Algebraic Equations, Wiley, 1979.

Householder, A.S., The Theory of Matrices in Numerical Analysis, Dover, 1964.

Gourlay, A.R. and G.A. Watson, Computational Methods for Matrix Eigenproblems, Wiley, 1973.

Anderson, E; Bai, Z, et al.  LAPACK Users' Guide.  SIAM, 1995.  http://www.netlib.org/lapack/lug

Weiss, R, Parameter-Free Iterative Linear Solvers.  Akademie Verlag, Mathematical Research Vol 97; 217 pp, 1996

Special Functions, etc.

Abramowitz and Stegun: AMS55, Handbook of Mathematical Functions, National Bureau of Standards.

Hildebrand, F.B. Advanced Calculus for Applications, Prentice-Hall 1962.

Data Assimilation

Bennett, A.F.  Inverse Modeling of the Ocean and Atmosphere.  Cambridge Univ. Press, 2002.

Cressie, N. A.C.  Statistics for Spatial Data.  J. Wiley, New York, 1991.

Wunsch, C.  The Ocean Circulation Inverse Problem.  Cambridge Univ. Press, 1996.