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(Ordinary differential equations (theory and numerical solution))
(Numerical linear algebra)
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See also Chaps. 1 and 2 of the book by N.J. Higham listed below.
 
See also Chaps. 1 and 2 of the book by N.J. Higham listed below.
  
=== Numerical linear algebra ===
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=== [[Álgebra Linear Numérica]]  ===
  
 
* G.H. Golub & C. Van Loan: Matrix Computations, 3rd ed. Johns Hopkins, 1996 (The most comprehensive introduction to the subject.)
 
* G.H. Golub & C. Van Loan: Matrix Computations, 3rd ed. Johns Hopkins, 1996 (The most comprehensive introduction to the subject.)
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* A. Greenbaum: Iterative Methods for Solving Linear Systems, SIAM 1997. (Excellent survey of Krylov subspace iterations.)
 
* A. Greenbaum: Iterative Methods for Solving Linear Systems, SIAM 1997. (Excellent survey of Krylov subspace iterations.)
 
* H.C. Elman, D.J. Silvester, A.J. Wathen, Finite Elements And Fast Iterative Solvers, Oxford University Press, 2005 (Major new book at the interface of finite elements and matrix iterations.)
 
* H.C. Elman, D.J. Silvester, A.J. Wathen, Finite Elements And Fast Iterative Solvers, Oxford University Press, 2005 (Major new book at the interface of finite elements and matrix iterations.)
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===Approximation theory===
 
===Approximation theory===
  

Edição das 22h21min de 24 de maio de 2009

Segue uma lista de livros úteis para o estudo de Análise Numérica.

Jornais

  • Acta Numerica
  • SIAM Review Journal of Computational Physics
  • SIAM Journal on Numerical Analysis
  • SIAM Journal on Matrix Analysis & Applications
  • SIAM Journal on Scientific Computing
  • BIT Numerical Mathematics
  • Numerische Mathematik
  • IMA Journal of Numerical Analysis
  • Mathematics of Computation
  • Foundations of Computational Mathematics

Livros

Floating point arithmetic

  • M.J. Overton, Numerical Computing and the IEEE Floating Point Standard, SIAM, 2001 (Very readable and systematic presentation.)

See also Chaps. 1 and 2 of the book by N.J. Higham listed below.

Álgebra Linear Numérica

  • G.H. Golub & C. Van Loan: Matrix Computations, 3rd ed. Johns Hopkins, 1996 (The most comprehensive introduction to the subject.)
  • B.N. Parlett: The Symmetric Eigenvalue Problem, Prentice-Hall, 1980 (Best available account of Lanczos-type methods.)
  • L.N. Trefethen & D. Bau: Numerical Linear Algebra, 1997 (General graduate-level text, including Krylov subspace iterations.)
  • J.W. Demmel: Applied Numerical Linear Algebra, SIAM, 1997. (Best up-to-date source on recent algorithms such as divide-and-conquer.)
  • N.J. Higham: Accuracy and Stability of Numerical Algorithms, SIAM, 1996. (An exceptionally careful and up-to-date study of error analysis.) - 1 -
  • A. Greenbaum: Iterative Methods for Solving Linear Systems, SIAM 1997. (Excellent survey of Krylov subspace iterations.)
  • H.C. Elman, D.J. Silvester, A.J. Wathen, Finite Elements And Fast Iterative Solvers, Oxford University Press, 2005 (Major new book at the interface of finite elements and matrix iterations.)

Approximation theory

  • I. Daubechies: Ten Lectures on Wavelets, SIAM, 1992. (Bestselling introduction to this topic.)
  • G. Strang & T. Nguyen: Wavelets and Filter Banks, Wellesley-Cambridge Press, 1996. (Fascinating presentation of wavelets from the linear algebra point of view.)
  • P.J. Davies: Interpolation and Approximation, Blaisdell, 1963, reprinted by Dover, 1975. (Old, but extremely well written as an introduction to most aspects of the subject.)
  • G. Nürnberger: Approximation by Spline Functions, Springer, 1989.
  • M.J.D. Powell: Approximation Theory and Methods, Cambridge, 1981. (Broad introductory text.)
  • J.C. Mason and D.C. Handscomb: Chebyshev Polynomials, Chapman & Hall, 2003.

Optimisation and solution of algebraic equations

  • J.E. Dennis & R.B. Schnabel: Numerical Methods for Unconstrained Optimization and Nonlinear Equations, Prentice Hall, 1983. (Excellent textbook introduction to quasi-Newton methods, including systems of equations as well as optimisation.)
  • R. Fletcher: Practical Methods of Optimisation, Wiley, 1987. (Very good general account of methods in this area, with strong practical bias.)
  • S. Wright: Primal-Dual Interior Methods, SIAM 1996 (Exceptionally well written introduction to primal-dual methods in mathematical programming.)
  • J. Nocedal and S.J. Wright: Numerical Optimization, 2nd ed., Springer, 2006. (The leading general text.)

Applied functional analysis

  • V.C.L. Hutson & J. S. Pym: Applications of Functional Analysis and Operator Theory, Academic Press, 1980. (Introductory.)
  • E. Kreyszig: Introduction to Functional Analysis and its Applications, Wiley, 1978. (Introductory.)
  • A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983. (Advanced.)
  • W. Rudin: Functional Analysis, McGraw-Hill, 1973. (Advanced.) - 2 -
  • R.E. Showalter: Hilbert Space Methods for Partial Differential Equations, Pitman, 1977. (Introductory.)
  • P.D. Lax: Functional Analysis, Wiley, 2002.

Mathematical Analysis and Complex Analysis

  • R. Adams: Sobolev Space, Academic Press, 1975. (Advanced.)
  • C.M. Bender & S. A. Orszag: Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, 1978. (Classic book on ODES, asymptotics, and much more.)
  • A.N. Kolmogorov & S.V. Fomin: Introductory Real Analysis, Dover, 1970. (Introductory)
  • W. Rudin: Real and Complex Analysis, McGraw-Hill, 1977. (Introductory but challenging.)
  • E.H. Lieb and M. Loss, Analysis, AMS, 1997. (Very nice introductory text.)
  • J. Jost: Postmodern Analysis, Springer, 2003 (Excellent introductory text.)
  • L.V. Ahlfors, Complex Analysis: An introduction to the theory of analytic functions of one complex variable, McGraw-Hill, 1966.
  • H.A. Priestley, Introduction to Complex Analysis, Oxford University Press, 2003.


Ordinary differential equations (theory and numerical solution)

  • G. Birkhoff & G.-C. Rota: Ordinary Differential Equations, Ginn, 1962

InstitutoMatematica.jpg J.C. Butcher: Numerical Analysis of Ordinary Differential Equations, Wiley, 1985. (Extensive advanced treatment.)

  • E. Hairer, S.P. Norsett & G. Wanner: Solving Ordinary Differential Equations I: Nonstiff Problems, Springer, 2nd rev. ed. 1993, Corr. 2nd printing, 2000. (Delightfully readable advanced account, full of personality.)
  • E. Hairer & G. Wanner: Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, Springer, 2nd rev. ed. 1996. 3rd printing, 2004. (Second volume of above.)
  • H. B. Keller: Numerical Solution of Two-Point Boundary-Value Problems, SIAM, 1976. (Brief but lucid.)
  • J. D. Lambert: Numerical Methods for Ordinary Differential Equations: The Initial Value Problem (2nd ed.), Wiley, 1991. (A standard reference.)
  • L. F. Shampine: Numerical Solution of Ordinary Differential Equations, Chapman & Hall, 1994. (Includes many practical illustrations.)
  • U.M. Ascher and L.R. Petzold: Computer Methods for Ordinary Differential Equations and Differential-Algebraic Equations, SIAM, 1998. (Accessible text including DAE’S.) - 3 -

Partial differential equations - Theory

  • F. John: Partial Differential Equations, Springer, 4th rev. ed. 1991. (Outstanding introduction.)
  • R. Courant & D. Hilbert: Methods of Mathematical Physics, I (1935), II (1962), Interscience. (Old, but well written as an introduction to partial differential equations of mathematical physics.)

InstitutoMatematica.jpg G. Folland: Introduction to Partial Differential Equations, Princeton, 2nd ed. 1995. (Very elegant introduction.)

  • P.R. Garabedian: Partial Differential Equations, Wiley, 1964. (Classic.)
  • D. Gilbarg & N.S. Trudinger: Elliptic Partial Differential Equations of Second Order, Springer, 1977. (Advanced.)
  • M.E. Taylor: Partial Differential equations: Basic Theory, Springer, 1996. (Very nice textbook by the author of “the” multivolume treatise on PDE.)

InstitutoMatematica.jpg L.C. Evans: Partial Differential Equations, AMS, 1998. (Excellent textbook, especially good on nonlinear PDE.)

  • H.O. Kreiss & J. Lorenz: Initial Boundary Value Problems and the Navier-Stokes Equations, Academic Press, 1989.
  • J. Smoller: Shock Waves and Reaction-Diffusion Equations, Springer, 1983. (Introductory.)

Partial differential equations - Finite difference and spectral methods

  • R.J. LeVeque: Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007.

InstitutoMatematica.jpg B. Fornberg: A Practical Guide to Pseudospectral Methods, Cambridge University Press, 1996.

  • B. Gustaffson, H.-O. Kreiss & J. Oliger: Time Dependent Problems and Difference Methods, Wiley, 1995.
  • R.D. Richtmeyer & K. W. Morton: Difference Methods for Initial-Value Problems, (2nd ed.), Krieger, 1994 (a classic) InstitutoMatematica.jpg 1967
  • L.N. Trefethen: Finite Difference and Spectral Methods for Ordinary and Partial Differential Equations, freely available online. (Trefethen’s text from courses taught at MIT and Cornell.)
  • L.N. Trefethen: Spectral Methods in MATLAB, SIAM, 2000. (Basis of our MSc course.)

Partial differential equations - Finite element methods

  • S.C. Brenner and L.R. Scott: The Mathematical Theory of Finite Element Methods, Springer, 2nd edition, 2002.
  • D.Braess: Finite Elements, Cambridge University Press, 2001. (A very accessible account of the theory of finite element methods.)
  • P.G. Ciarlet: The Finite Element Method for Elliptic Problems, North-Holland, 1978. (Difficult to find a copy!)
  • C. Johnson: Numerical Solution of Partial Differential Equations by the Finite Element Method, Cambridge, 1987. (Introductory.)
  • G. Strang & G.J. Fix: An Analysis of the finite Element Method, Prentice-Hall, 1973.

Fluid dynamics - Theoretical

  • D.A. Anderson: Modern Compressible Flow, McGraw-Hill, 2nd ed., 1990. (A modern treatment, very readable.)
  • G.K. Batchelor: An Introduction to Fluid Dynamics, Cambridge, 1970. (Classic, incompressible flow.)
  • T. Cebeci & P. Bradshaw: Momentum Transfer in Boundary Layers, McGraw-Hill, 1977. (Theory and computation of boundary layers.)
  • H.W. Liepmann & A. Roshko: Elements of Gas Dynamics, Wiley, 1957. (Classic.)
  • I.J. Sobey: Introduction to Interactive Boundary Layer Theory, OUP, 2000.

Fluid dynamics - Computational

  • D.A. Anderson, J.C. Tannehill & R.A. Pletcher: Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, 1984. (Good introductory book.)
  • C. Hirsch: Numerical Computation of Internal and External Flows 1: Fundamentals of Numerical Discretisation, Wiley 1989.
  • C. Hirsch: Numerical Computation of Internal and External Flows 2: Computational Methods for Inviscid and Viscous Flows, Wiley 1990.
  • R.J. LeVeque: Finite volume Methods for Hyperbolic Problems, Cambridge, 2002

InstitutoMatematica.jpg R.J. LeVeque: Numerical Methods for Conservation Laws, Birkhäuser. (Earlier, shorter introductory text, very readable.)

  • R. Peyret & T.D. Taylor: Computational Methods for Fluid Flow, Springer, 1983