Mudanças entre as edições de "Análise Numérica"
De WikiLICC
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(→Livros) |
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=== Floating point arithmetic=== | === Floating point arithmetic=== | ||
| − | M.J. Overton, Numerical Computing and the IEEE Floating Point Standard, SIAM, 2001 (Very readable and systematic presentation.) | + | * 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. | See also Chaps. 1 and 2 of the book by N.J. Higham listed below. | ||
=== Numerical linear algebra === | === Numerical linear algebra === | ||
| − | 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.) |
| − | B.N. Parlett: The Symmetric Eigenvalue Problem, Prentice-Hall, 1980 (Best available account of Lanczos-type methods.) | + | * 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.) | + | * 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.) | + | * 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 - | + | * 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.) | + | * 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=== | ||
| − | I. Daubechies: Ten Lectures on Wavelets, SIAM, 1992. (Bestselling introduction to this topic.) | + | * 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.) | + | * 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.) | + | * 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. | + | * G. Nürnberger: Approximation by Spline Functions, Springer, 1989. |
| − | M.J.D. Powell: Approximation Theory and Methods, Cambridge, 1981. (Broad introductory text.) | + | * 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. | + | * J.C. Mason and D.C. Handscomb: Chebyshev Polynomials, Chapman & Hall, 2003. |
===Optimisation and solution of algebraic equations=== | ===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.) | + | * 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.) | + | * 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.) | + | * 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.) | + | * J. Nocedal and S.J. Wright: Numerical Optimization, 2nd ed., Springer, 2006. (The leading general text.) |
===Applied functional analysis=== | ===Applied functional analysis=== | ||
| − | V.C.L. Hutson & J. S. Pym: Applications of Functional Analysis and Operator Theory, Academic Press, 1980. (Introductory.) | + | * 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.) | + | * 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.) | + | * A. Pazy: Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, 1983. (Advanced.) |
| − | W. Rudin: Functional Analysis, McGraw-Hill, 1973. (Advanced.) - 2 - | + | * W. Rudin: Functional Analysis, McGraw-Hill, 1973. (Advanced.) - 2 - |
| − | R.E. Showalter: Hilbert Space Methods for Partial Differential Equations, Pitman, 1977. (Introductory.) | + | * R.E. Showalter: Hilbert Space Methods for Partial Differential Equations, Pitman, 1977. (Introductory.) |
| − | P.D. Lax: Functional Analysis, Wiley, 2002. | + | * P.D. Lax: Functional Analysis, Wiley, 2002. |
===Mathematical Analysis and Complex Analysis=== | ===Mathematical Analysis and Complex Analysis=== | ||
| − | R. Adams: Sobolev Space, Academic Press, 1975. (Advanced.) | + | * 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.) | + | * 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) | + | * A.N. Kolmogorov & S.V. Fomin: Introductory Real Analysis, Dover, 1970. (Introductory) |
| − | W. Rudin: Real and Complex Analysis, McGraw-Hill, 1977. (Introductory but challenging.) | + | * 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.) | + | * E.H. Lieb and M. Loss, Analysis, AMS, 1997. (Very nice introductory text.) |
| − | J. Jost: Postmodern Analysis, Springer, 2003 (Excellent 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. | + | * 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. | + | * H.A. Priestley, Introduction to Complex Analysis, Oxford University Press, 2003. |
| Linha 69: | Linha 70: | ||
===Ordinary differential equations (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 |
| − | J.C. Butcher: Numerical Analysis of Ordinary Differential Equations, Wiley, 1985. (Extensive advanced treatment.) | + | * 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.) |
| − | H. B. Keller: Numerical Solution of Two-Point Boundary-Value Problems, SIAM, 1976. (Brief but lucid.) | + | * 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.) | + | * 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.) | + | * 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 - | + | * 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=== | ===Partial differential equations - Theory=== | ||
| − | F. John: Partial Differential Equations, Springer, 4th rev. ed. 1991. (Outstanding introduction.) | + | * 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.) | + | * 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.) |
| − | G. Folland: Introduction to Partial Differential Equations, Princeton, 2nd ed. 1995. (Very elegant introduction.) | + | * G. Folland: Introduction to Partial Differential Equations, Princeton, 2nd ed. 1995. (Very elegant introduction.) |
| − | P.R. Garabedian: Partial Differential Equations, Wiley, 1964. (Classic.) | + | * P.R. Garabedian: Partial Differential Equations, Wiley, 1964. (Classic.) |
| − | D. Gilbarg & N.S. Trudinger: Elliptic Partial Differential Equations of Second Order, Springer, 1977. (Advanced.) | + | * 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.) | + | * M.E. Taylor: Partial Differential equations: Basic Theory, Springer, 1996. (Very nice textbook by the author of “the” multivolume treatise on PDE.) |
| − | L.C. Evans: Partial Differential Equations, AMS, 1998. (Excellent textbook, especially good on nonlinear PDE.) | + | * 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.) | + | * 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. |
| − | B. Fornberg: A Practical Guide to Pseudospectral Methods, Cambridge University Press, 1996. | + | * 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. | + | * 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) | + | * R.D. Richtmeyer & K. W. Morton: Difference Methods for Initial-Value Problems, (2nd ed.), Krieger, 1994 (a classic) |
| − | 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 - Finite element methods=== |
| − | 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=== | ===Fluid dynamics - Theoretical=== | ||
| − | 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.) |
| − | G.K. Batchelor: An Introduction to Fluid Dynamics, Cambridge, 1970. (Classic, incompressible flow.) | + | * 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.) | + | * 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.) | + | * H.W. Liepmann & A. Roshko: Elements of Gas Dynamics, Wiley, 1957. (Classic.) |
| − | 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=== | ===Fluid dynamics - Computational=== | ||
| − | 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.) |
| − | 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 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. | + | * 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 | + | * R.J. LeVeque: Finite volume Methods for Hyperbolic Problems, Cambridge, 2002 |
| − | R.J. LeVeque: Numerical Methods for Conservation Laws, Birkhäuser. (Earlier, shorter introductory text, very readable.) | + | * 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 |
Edição das 21h09min de 1 de abril de 2009
Esta linha de pesquisa trata da investigação, desenvolvimento, análise e implementação de algoritmos para a resolução de problemas matemáticos. As soluções podem ser algébricas ou numéricas e visam não só a eficiência dos procedimentos, utilizando paralelismo e computação de alto desempenho, mas também a obtenção de novas teorias matemáticas, através das ferramentas da Álgebra Computacional.
Índice
- 1 Jornais
- 2 Livros
- 2.1 Floating point arithmetic
- 2.2 Numerical linear algebra
- 2.3 Approximation theory
- 2.4 Optimisation and solution of algebraic equations
- 2.5 Applied functional analysis
- 2.6 Mathematical Analysis and Complex Analysis
- 2.7 Ordinary differential equations (theory and numerical solution)
- 2.8 Partial differential equations - Theory
- 2.9 Partial differential equations - Finite difference and spectral methods
- 2.10 Partial differential equations - Finite element methods
- 2.11 Fluid dynamics - Theoretical
- 2.12 Fluid dynamics - Computational
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.
Numerical linear algebra
- 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
- 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.)
- 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.)
- 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.
- 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)
- 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
- 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
