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(21 revisões intermediárias pelo mesmo usuário não estão sendo mostradas)
Linha 20: Linha 20:
 
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 ===
+
=== [[Álgebra Linear Numérica]]  ===
  
* G.H. Golub & C. Van Loan: Matrix Computations, 3rd ed. Johns Hopkins, 1996 (The most comprehensive introduction to the subject.)
+
*[[Imagem:InstitutoMatematica.jpg]] 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.)
+
*[[Imagem:InstitutoMatematica.jpg]] 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.)
+
*[[Imagem:InstitutoMatematica.jpg]] 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.)
+
*[[Imagem:InstitutoMatematica.jpg]] 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 -
+
*[[Imagem:InstitutoMatematica.jpg]] N.J. Higham: Accuracy and Stability of Numerical Algorithms, SIAM, 1996. (An exceptionally careful and up-to-date study of error analysis.)
 
* 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.)
+
 
 
===Approximation theory===
 
===Approximation theory===
  
Linha 55: Linha 55:
 
* P.D. Lax: Functional Analysis, Wiley, 2002.
 
* P.D. Lax: Functional Analysis, Wiley, 2002.
 
   
 
   
===Mathematical Analysis and Complex Analysis===
+
===[[Análise Real e Análise Complexa]]===
  
 
* R. Adams: Sobolev Space, Academic Press, 1975. (Advanced.)
 
* R. Adams: Sobolev Space, Academic Press, 1975. (Advanced.)
Linha 66: Linha 66:
 
* H.A. Priestley, Introduction to Complex Analysis, Oxford University Press, 2003.
 
* H.A. Priestley, Introduction to Complex Analysis, Oxford University Press, 2003.
  
 
+
===[[Equações Diferenciais Ordinárias]] (theory and numerical solution)===
 
===Ordinary differential equations (theory and numerical solution)===
 
  
 
* G. Birkhoff & G.-C. Rota: Ordinary Differential Equations, Ginn, 1962
 
* G. Birkhoff & G.-C. Rota: Ordinary Differential Equations, Ginn, 1962
[[Imagem:InstitutoMatematica.jpg]] J.C. Butcher: Numerical Analysis of Ordinary Differential Equations, Wiley, 1985. (Extensive advanced treatment.)
+
*[[Imagem: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, 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.)
 
* 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.)
Linha 79: Linha 77:
 
* 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 -
 
* 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===
+
===[[Equações Diferenciais Parciais]] - Teoria===
  
* F. John: Partial Differential Equations, Springer, 4th rev. ed. 1991. (Outstanding introduction.)
+
*[[Imagem:InstitutoMatematica.jpg]] 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.)
+
*[[Imagem:InstitutoMatematica.jpg]] 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.)
[[Imagem:InstitutoMatematica.jpg]] G. Folland: Introduction to Partial Differential Equations, Princeton, 2nd ed. 1995. (Very elegant introduction.)
+
*[[Imagem: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.)
+
*[[Imagem:InstitutoMatematica.jpg]] P.R. Garabedian: Partial Differential Equations, Wiley, 1964. (Classic.)
* D. Gilbarg & N.S. Trudinger: Elliptic Partial Differential Equations of Second Order, Springer, 1977. (Advanced.)
+
*[[Imagem:InstitutoMatematica.jpg]] 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.)
+
*[[Imagem:InstitutoMatematica.jpg]] M.E. Taylor: Partial Differential equations: Basic Theory, Springer, 1996. (Very nice textbook by the author of “the” multivolume treatise on PDE.)
[[Imagem:InstitutoMatematica.jpg]] L.C. Evans: Partial Differential Equations, AMS, 1998. (Excellent textbook, especially good on nonlinear PDE.)
+
*[[Imagem: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.
 
* 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.)
+
*[[Imagem:InstitutoMatematica.jpg]] J. Smoller: Shock Waves and Reaction-Diffusion Equations, Springer, 1983. (Introductory.)
  
 
===Partial differential equations - Finite difference and spectral methods===
 
===Partial differential equations - Finite difference and spectral methods===
  
 
* R.J. LeVeque: Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007.
 
* R.J. LeVeque: Finite Difference Methods for Ordinary and Partial Differential Equations, SIAM, 2007.
[[Imagem:InstitutoMatematica.jpg]] B. Fornberg: A Practical Guide to Pseudospectral Methods, Cambridge University Press, 1996.
+
* [[Imagem: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.
+
* [[Imagem:InstitutoMatematica.jpg]] 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) [[Imagem:InstitutoMatematica.jpg]] 1967
 
* R.D. Richtmeyer & K. W. Morton: Difference Methods for Initial-Value Problems, (2nd ed.), Krieger, 1994 (a classic) [[Imagem: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: 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.)
 
* L.N. Trefethen: Spectral Methods in MATLAB, SIAM, 2000. (Basis of our MSc course.)
  
===Partial differential equations - Finite element methods===
+
===Partial differential equations - [[Elementos Finitos|Método dos Elementos Finitos]]===
 
* S.C. Brenner and L.R. Scott: The Mathematical Theory of Finite Element Methods, Springer, 2nd edition, 2002.
 
* 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.)
 
* 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!)
 
* 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.)
 
* 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.  
+
* G. Strang & G.J. Fix: An Analysis of the finite Element Method, Prentice-Hall, 1973.
+
 
===Fluid dynamics - Theoretical===
+
===[[Dinâmica de Fluidos]] - Teórica===
  
 
* D.A. Anderson: Modern Compressible Flow, McGraw-Hill, 2nd ed., 1990. (A modern treatment, very readable.)
 
* D.A. Anderson: Modern Compressible Flow, McGraw-Hill, 2nd ed., 1990. (A modern treatment, very readable.)
Linha 115: Linha 113:
 
* I.J. Sobey: Introduction to Interactive Boundary Layer Theory, OUP, 2000.
 
* I.J. Sobey: Introduction to Interactive Boundary Layer Theory, OUP, 2000.
  
===Fluid dynamics - Computational===
+
===[[Dinâmica de Fluidos Computacional]]===
  
 
* D.A. Anderson, J.C. Tannehill & R.A. Pletcher: Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, 1984. (Good introductory book.)
 
* D.A. Anderson, J.C. Tannehill & R.A. Pletcher: Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, 1984. (Good introductory book.)
Linha 123: Linha 121:
 
[[Imagem:InstitutoMatematica.jpg]] R.J. LeVeque: Numerical Methods for Conservation Laws, Birkhäuser. (Earlier, shorter introductory text, very readable.)
 
[[Imagem: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
 
* R. Peyret & T.D. Taylor: Computational Methods for Fluid Flow, Springer, 1983
 +
 +
==Mais algumas referências==
 +
Cálculo Numérico Clássico:
 +
 +
:) Burden, Richard L..  Faires, J. Douglas. Análise numérica.
 +
:) Franco, Neide Bertoldi.  Cálculo numérico,  2006
 +
:? Sperandio, Décio. Mendes,  Silva,. Cálculo numérico:
 +
 +
Mecânica de Fluidos
 +
 +
:) Brunetti, Franco.  Mecânica dos fluidos, 2007
 +
:?  Cattani, Mauro Sergio D..  Elementos de mecânica dos fluidos. 2005.
 +
:| Etkin, Bernard. Dynamics of atmospheric flight.  (Antigo, talvez algumas idéias e comparações do mundo real.)
 +
 +
Referência em Matlab:
 +
:) Gilat, Amos. Matlab com aplicações em engenharia.
 +
 +
 +
Elementos Finitos (muito básico)
 +
:( Assan, Aloisio Ernesto. Método dos elementos finitos : primeiros passos.
 +
 +
Prova de Teoremas
 +
:) Cupillari, Antonella. The nuts and bolts of proofs. c2005.
 +
:) Velleman, Daniel J..How to prove it : a structured approach.
 +
 +
Introducao teoria economica dos jogos, 26 coloquio brasileiro matematica. Humberto BOrtolossi, Gilmar garbaggio e Brigida Sartini.
 +
 +
Nonlinear Parabolic Equations and Hyperbolic-parabolic Coupled Systems, Songmu Zheng, Publicado por CRC Press, 1995
 +
ISBN 0582244889, 9780582244887
 +
 +
Malcolm Adams e Victor Guillemin, Measure Theory and probability

Edição atual tal como às 13h15min de 5 de junho de 2012

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

  • InstitutoMatematica.jpg G.H. Golub & C. Van Loan: Matrix Computations, 3rd ed. Johns Hopkins, 1996 (The most comprehensive introduction to the subject.)
  • InstitutoMatematica.jpg B.N. Parlett: The Symmetric Eigenvalue Problem, Prentice-Hall, 1980 (Best available account of Lanczos-type methods.)
  • InstitutoMatematica.jpg L.N. Trefethen & D. Bau: Numerical Linear Algebra, 1997 (General graduate-level text, including Krylov subspace iterations.)
  • InstitutoMatematica.jpg J.W. Demmel: Applied Numerical Linear Algebra, SIAM, 1997. (Best up-to-date source on recent algorithms such as divide-and-conquer.)
  • InstitutoMatematica.jpg N.J. Higham: Accuracy and Stability of Numerical Algorithms, SIAM, 1996. (An exceptionally careful and up-to-date study of error analysis.)
  • 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.

Análise Real e Análise Complexa

  • 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.

Equações Diferenciais Ordinárias (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 -

Equações Diferenciais Parciais - Teoria

  • InstitutoMatematica.jpg F. John: Partial Differential Equations, Springer, 4th rev. ed. 1991. (Outstanding introduction.)
  • InstitutoMatematica.jpg 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.)
  • InstitutoMatematica.jpg P.R. Garabedian: Partial Differential Equations, Wiley, 1964. (Classic.)
  • InstitutoMatematica.jpg D. Gilbarg & N.S. Trudinger: Elliptic Partial Differential Equations of Second Order, Springer, 1977. (Advanced.)
  • InstitutoMatematica.jpg 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.
  • InstitutoMatematica.jpg 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.
  • InstitutoMatematica.jpg 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 - Método dos Elementos Finitos

  • 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.

Dinâmica de Fluidos - Teórica

  • 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.

Dinâmica de Fluidos Computacional

  • 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

Mais algumas referências

Cálculo Numérico Clássico:

) Burden, Richard L.. Faires, J. Douglas. Análise numérica.
) Franco, Neide Bertoldi. Cálculo numérico, 2006
? Sperandio, Décio. Mendes, Silva,. Cálculo numérico:

Mecânica de Fluidos

) Brunetti, Franco. Mecânica dos fluidos, 2007
? Cattani, Mauro Sergio D.. Elementos de mecânica dos fluidos. 2005.
| Etkin, Bernard. Dynamics of atmospheric flight. (Antigo, talvez algumas idéias e comparações do mundo real.)

Referência em Matlab:

) Gilat, Amos. Matlab com aplicações em engenharia.


Elementos Finitos (muito básico)

( Assan, Aloisio Ernesto. Método dos elementos finitos : primeiros passos.

Prova de Teoremas

) Cupillari, Antonella. The nuts and bolts of proofs. c2005.
) Velleman, Daniel J..How to prove it : a structured approach.

Introducao teoria economica dos jogos, 26 coloquio brasileiro matematica. Humberto BOrtolossi, Gilmar garbaggio e Brigida Sartini.

Nonlinear Parabolic Equations and Hyperbolic-parabolic Coupled Systems, Songmu Zheng, Publicado por CRC Press, 1995 ISBN 0582244889, 9780582244887

Malcolm Adams e Victor Guillemin, Measure Theory and probability