• Forman S. Acton: Numerical Methods That Work, QA297.A83.
• K. Atkinson: An Introduction to Numerical Analysis, 2nd ed., Wiley, 1989.
• P. G. Ciarlet and J. L. Lions (eds.): Handbook of Numerical Analysis, North Holland, 1990.
• S. Conte and C. de Boor: Elementary Numerical Analysis: an algorithmic approach, 3rd ed., McGraw-Hill, 1980. QA297.C65.
• G. Dahlquist and A. Bjorck: Numerical Methods, Prentice Hall, 1974. QA297.D3313 1974.
• G. E. Forsythe et al.: Computer Mathods for Mathematical Computations. QA297.F68.
• W. Gautschi: Numerical Analysis: an introduction, Birkhauser, 1997.
• R. W. Hamming: Numerical Methods for Scientists and Engineers, 2nd ed., Dover 1986.
• Peter Henrici: Applied & Computational Complex Analysis, 3 vols., Wiley, 1974-1977-1986. QA331.H453.
• A. S. Householder: The Numerical Treatment of a Single Nonlinear Equation. QA218.H68.
• E. Isaacson and H. Keller: Analysis of Numerical Methods, Wiley, 1966;  Dover reprint, 1994. QA297.I8.
• D. Kahaner, C. Moler, and S. Nash: Numerical Methods and Software, Prentice-Hall, 1989.
• D. Kincaid and W. Cheney: Numerical Analysis: Mathematics of Scientific Computing, Brooks/Cole, 1996.
• R. Kress: Numerical Analysis, GTM 181, Springer-Verlag, 1998.
• A. Ralston and P. Rabinowitz: A First Course in Numerical Analysis, McGraw-Hill, 1978. QA297.R3 1978.
• L. F. Shampine, R. C. Allen jr., and S. Pruess: Fundamentals of Numerical Computing, Wiley, 1997.
• G. W. Stewart: Afternotes on Numerical Analysis, SIAM, 1996.
• J. Stoer and R. Bulirsch: Introduction to Numerical Analysis, 2nd ed., Springer-Verlag, 1993. QA297.S8213.

• J. L. Buchanan and P. R. Turner: Numerical Mathods and Analysis, McGraw-Hill, 1992.
• R. L. Burden and J. D. Faires: Numerical Analysis, 6th ed., Brooks/Cole, 1997.
• E. W. Cheney and D. Kincaid: Numerical Mathematics and Computing, 3rd ed., Brooks/Cole, 1994.
• L. V. Fausett: Applied Numerical Analysis Using MATLAB, Prentice-Hall, 1999.
• G. H. Golub, ed.: Studies in Numerical Analysis, MAA Studies in Math., v. 24, Mathematical Association of America, 1984. QA297.S83 1984.
• R. W. Hamming: Introduction to Applied Numerical Analysis, McGraw-Hill. QA297.H275.
• F. B. Hildebrand: Introduction to Numerical Analysis, Dover, 1987. QA297.H54 1987,
• L. W. Johnson and R. D. Riess: Numerical Analysis, 2nd ed. QA297.J63 1982.
• G. Lindfield and J. Penny: Numerical Methods Using MATLAB, 2nd ed., Prentice-Hall, 1999.
• J. H. Maindonald: Statistical Computation, Wiley, 1984. QA276.4.M25 1984.
• J. H. Mathews and K. D. Fink: Numerical Methods Using MATLAB, 3rd ed., Prentice-Hall, 1999.
• G. Strang: Introduction to Linear Algebra, 2nd ed., Wellesley-Cambridge, 1998.
• C. Van Loan: Introduction to Scientific Computing: A Matrix-Vector Approach Using MATLAB, 2nd ed.,  Prentice-Hall, 1999.

• N. I. Achieser: Theory of Approximation, Dover, 1992.
• J. H. Ahlberg et al.: The Theory of Splines and Their Applications, Math. in Sci. and Eng. 38, Acad. Press, 1967. QA3.M38 v.38.
• E. W. Cheney: Approximation Theory, 2nd ed., Chelsea, 1982.
• Philip J. Davis: Interpolation and Approximation, Dover, 1963. QA221.D3.
• C. de Boor: A Practical Guide to Splines, Appl. Math. Sci. 27, Springer-Verlag, 1978. QA1.A647 v.27.
• G. G. Lorentz: Approximation of Functions, 2nd ed., Chelsea, 1986.
• G. G. Lorentz: Bernštein Polynomials, 2nd ed., 1986.
• P. P. Petrushev and V. A. Popov: Rational Approximation of Real Functions, Encyc. Math & App. 28, Cambridge, 1987.
• T. J. Rivlin: An Introduction to the Approximation of Functions, Dover [reprint], 1981. QA221.R3 1978.
• A. F. Timan: Theory of Approximation of Functions of a Real Variable, Dover, 1993.
• H. S. Wilf: Mathematics for the Physical Sciences,¹ Dover, 1978. QA401.W68

• J. C. Butcher: The Numerical Analysis of Ordinary Differential Equations: Runge-Kutta and general linear methods, Wiley, 1987.
• K. Dekker and J. G. Verwer: Stability of Runge-Kutta methods for stiff nonlinear differential equations, North Holland, 1984.
• S. O. Fatunla: Numerical Methods for Initial Value Problems in Ordinary Differential Equations, Academic Press, 1988.
• C. W. Gear: Numerical Initial Value Problems in Ordinary Differential Equations, Prentice Hall, 1971. QA 372.G4.
• E. Hairer, S. P. Norsett, and G. Wanner: Solving Ordinary Differential Equations, Springer-Verlag; I: nonstiff problems (1993), II (1991).
• Peter Henrici: Discrete Variable Methods in Ordinary Differential Equations, Wiley, 1962.
• I. Iserles: A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996.
• J. D. Lambert: Numerical Methods for Ordinary Differential Systems: The Initial Value Problem, Wiley, 1991.
• J. Lambert: Computational Methods in Ordinary Differential Equations,
• W. E. Milne: Numerical Solutions of Differential Equations, 2nd ed. Dover, 1970 QA371.M57 1970.
• L. Shampine: Numerical solution of ordinary differential equations, Chapman & Hall, 1994.
• L. Shampine and M. Gordon: Computer Solution of Ordinary Differential Equations, Freeman, 1975. QA372.S416.

• J. E. Dennis and J. More: Quasi-Newton methods, motivation, and theory, SIAM Review, vol 19 #1, Jan. 1977.
• J. E. Dennis and R. B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice-Hall, 1983, SIAM, 1996.
• C. T. Kelley: Iterative Methods for Linear and Nonlinear Equations, SIAM, 1995.
• J. Ortega and W. Rheinboldt: Iterative Solution of Nonlinear Equations in Several Variables, Academic Press, 1970.
• J. F. Traub: Iterative Methods for the Solution of Equations, 2nd ed., Chelsea, 1992.

• O. Axelsson: Iterative Solution Methods, Cambridge University Press, 1994.
• P. G. Ciarlet: Introduction to Numerical Linear Algebra and Optimisation, Cambridge, 1988.
• J. W. Demmel: Applied Numerical Linear Algebra, SIAM, 1997.
• G. Forsythe and C. Moler: Computer Solution of Linear Algebraic Systems, Prentice Hall, 1967.
• G. Golub and C. Van Loan: Matrix Computations, 3rd ed., Johns Hopkins University Press, 1996. QA188.G85.
• A. Gourley and G. Watson: Computational Methods for Matrix Eigenproblems, Wiley, 1973.
• W. W. Hager: Applied Numerical Linear Algebra, Prentice-Hall, 1988.
• R. A. Horn and C. R. Johnson: Matrix Analysis, Cambridge, 1990.
• A. S. Householder: The Theory of Matrices in Numerical Analysis, Dover, 1975. QA263.H67.
• G. W. Stewart: Introduction to Matrix Computations, Academic Press, 1973.
• L. N. Trefethen and D. Bau: Numerical Linear Algebra, SIAM, 1997.
• J. H. Wilkinson: The Algebraic Eigenvalue Problem, Oxford, 1988. QA218.W5 1965.
• J. H. Wilkinson: Rounding Errors in Algebraic Processes, Prentice-Hall, 1963; Dover reprint, 1994. QA76.5.W53 1963.
• J. H. Wilkinson and C. Reinsch: Handbook for Automatic Computation. Vol. II: Linear Algebra, Springer-Verlag, 1971.

• B. Szabo and I. Babuška: Finite Element Analysis
• D. Braess: Finite Elements: Theory, fast solvers, and applications in solid mechanics, Cambridge University Press, 1997.
• S. Brenner and L. R. Scott: The Mathematical Theory of Finite Element Methods, Springer-Verlag, 1994.
• P. G. Ciarlet: The Finite Element Method for Elliptic Problems, North Holland, 1980.
• K. Eriksson, D. Estep, P. Hansbo, C. Johnson: Computational Differential Equations, Cambridge University Press, 1996.
• T. J. R. Hughes: The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice Hall, 1987.
• C. Johnson: Numerical Solutions of Partial Differential Equations by the Finite Element Method, Cambridge University Press, 1987.
• J. T. Marti: Introduction to Sobolëv Spaces and Finite Element Solution of Elliptic Boundary Value Problems, Comp. Math. and Apps. 7, Acad. Press, 1986. QA371.M279.
• G. Strang and G. Fix: An Analysis of the Finite Element Method, Prentice-Hall, 1973. TA335.S77 1973.
• O. C. Zienkiewicz and R. L. Taylor: The Finite Element Method, 4th ed., McGraw Hill, 1989.

• W. F. Ames: Numerical Methods for Partial Differential Equations. QA374.A46 1977.
• L. Fox: The Numerical Solution of Two-Point Boundary Problems in Ordinary Differential Equations, Dover, 1990.
• S. K. Godunov and V. S. Ryabenki: Difference Schemes: an introduction to the underlying theory, North Holland, 1987.
• C. Hall and T. Porsching: Numerical Analysis of Partial Differential Equations, Prentice Hall, 1990.
• I. Iserles: A First Course in the Numerical Analysis of Differential Equations, Cambridge University Press, 1996.
• R. J. LeVeque: Numerical methods for conservation laws, Birkhauser Verlag, 1992.
• H. Keller: Numerical Methods for Two-Point Boundary Value Problems, SIAM, 1976; Dover [reprint], 1992.
• R. D. Richtmyer and K. W. Morton: Difference Methods for Initial Value Problems, Wiley-Interscience, 1967.
• G. Sod: Numerical Methods in Fluid Mechanics: Initial and Initial Boundary Value Problems, Cambridge University Press, 1985.
• J. Strikwerda: Finite Difference Schemes and Partial Differential Equations, Wadsworth and Brooks/Cole, 1989.

• William H. Press et al.: Numerical Recipes ... : The Art of Scientific Computing, Cambridge Univ. Press; various dates and languages, e.g., Fortran, C and Pascal. LC numbers include QA297.N866 1986 (Fortran), QA76.73.C15N865 1988 (C), and QA76.73.P2N87 1989 (Pascal).

¹Perhaps the most useful collection of "classical results that every young analyst should know" ever assembled. If amazon.com is to be believed, it is (still) out of print as of the date below. Dover Publications ought to be bombarded with mail until that situation is rectified.