Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
  1. Home
  2. Books
  3. Advanced Mathematics for Applications
  • Cited by 29
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
2011
Online ISBN:
9780511777530
DOI:
https://doi.org/10.1017/CBO9780511777530
Subjects:
Mathematics, Engineering, Mathematical Modeling and Methods, Engineering Mathematics and Programming
Information

Book description

The partial differential equations that govern scalar and vector fields are the very language used to model a variety of phenomena in solid mechanics, fluid flow, acoustics, heat transfer, electromagnetism and many others. A knowledge of the main equations and of the methods for analyzing them is therefore essential to every working physical scientist and engineer. Andrea Prosperetti draws on many years' research experience to produce a guide to a wide variety of methods, ranging from classical Fourier-type series through to the theory of distributions and basic functional analysis. Theorems are stated precisely and their meaning explained, though proofs are mostly only sketched, with comments and examples being given more prominence. The book structure does not require sequential reading: each chapter is self-contained and users can fashion their own path through the material. Topics are first introduced in the context of applications, and later complemented by a more thorough presentation.

Reviews

'This carefully written book by a well-known expert in the area is also an excellent guide to the present literature, recommended as well to graduate students as to experts in the area. This volume will help the reader in getting acquainted with some mathematical aspects of the modern theory of linear and non-linear phenomena arising in relevant applications to mathematical physics.'

Source: Zentralblatt MATH

'A truly wonderful book … The author succeeded in creating a new type of book, that many will put on their desks, and they should: beginners, physicists, advanced learners, instructors, users of maths in the sciences … A modern work, showing new ways, unusually multi-layered, applicable in many contexts and at many levels, an exciting book.'

Siegfried Großmann - Philipps-Universität Marburg

'This book admirably lays down physical and mathematical groundwork, provides motivating examples, gives access to the relevant deep mathematics, and unifies components of many mathematical areas. This sophisticated topics text, which interweaves and connects subjects in a meaningful way, gives readers the satisfaction and the pleasure of putting two and two together.'

Laura K. Gross Source: SIAM Review

Refine List

Actions for selected content:

Select all | Deselect all
  • View selected items
  • Export citations
  • Download PDF (zip)
  • Save to Kindle
  • Save to Dropbox
  • Save to Google Drive

Save Search

You can save your searches here and later view and run them again in "My saved searches".

Please provide a title, maximum of 40 characters.
Cancel
×

Contents

Page 2 of 2

Contents

Page 2 of 2

References
References
References
Ablowitz, M. J. & Fokas, A. S. 1997 Complex Variables. Cambridge Google Scholar: Cambridge University Press.
Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Washington Google Scholar: National Bureau of Standards, reprinted by Dover, New York, 1965. See also Oliver W. J. et al. 2010 NIST Handbook of Mathematical Functions. Cambridge: Cambridge University Press.
Adams, R. A. & Fournier, J. J. F. 2003 Sobolev Spaces, 2nd edn. New York Google Scholar: Academic Press.
Ahlfors, L. V. 1979 Complex Analysis. New York Google Scholar: McGraw-Hill.
Ahlfors, L. V. 1987 Lectures on Quasiconformal Mappings. Monterey CA Google Scholar: Wadsworth & Brooks.
Akhiezer, N. I. & Glazman, I. M. 1961 Theory of Linear Operators in Hilbert Space. New York Google Scholar: Ungar, reprinted by Dover, New York, 1993.
Apostol, T. M. 1974 Mathematical Analysis, 2nd edn. Reading Google Scholar: Addison-Wesley.
Arendt, W., Batty, C. J. K., Hieber, M. & Neubrander, F. 2001 Vector-Valued Laplace Transforms and Cauchy Problems. Basel CrossRef | Google Scholar: Birkhäuser.
Barber, J. R. 1992 Elasticity. Dordrecht CrossRef | Google Scholar: Kluwer.
Bary, N. K. 1964 A Treatise on Trigonometric Series. New York Google Scholar: Pergamon Press.
Batchelor, G. K. 1999 An Introduction to Fluid Mechanics, 2nd edn. Cambridge Google Scholar: Cambridge University Press.
Bender, C. M. & Orszag, S. A. 2005 Advanced Mathematical Methods for Scientists and Engineers. New York Google Scholar: Springer.
Beltrami, E. J. & Wohlers, M. R. 1966 Distributions and the Boundary Values of Analytic Functions. New York Google Scholar: Academic Press.
Berezanski, Y. M., Sheftel, Z. G. & Us, G. F. 1996 Functional Analysis. Basel Google Scholar: Birkhäuser.
Bieberbach, L. 1953 Conformal Mapping. New York Google Scholar: Chelsea Publishing Co., reprinted by AMS Chelsea Publishing, New York, 2000.
Bleistein, N. & Handelsman, R. A. 1975 Asymptotic Expansion of Integrals. Orlando FL Google Scholar: Holt, Reinhart & Winston, reprinted by Dover, New York, 1986.
Boas, R. P. 1987 Invitation to Complex Analysis. New York Google Scholar: Random House.
Boccara, N. 1990 Functional Analysis. Boston Google Scholar: Academic Press.
Bracewell, R. N. 1986 The Fourier Transform and Its Applications. New York Google Scholar: McGraw-Hill.
Bremermann, H. 1965 Distributions, Complex Variables and Fourier Transforms. Reading Google Scholar: Addison-Wesley.
Bromwich, T. J. l'A. 1926 Introduction to the Theory of Infinite Series, 2nd edn. London Google Scholar: Macmillan & Co., reprinted by Chelsea Publishing Co., New York, 1991.
de Bruijn, N. G. 1958 Asymptotic Methods in Analysis. Amsterdam Google Scholar: North-Holland, reprinted by Dover, New York, 1981.
Burckel, R. B. 1979 An Introduction to Classical Complex Analysis. New York CrossRef | Google Scholar: Academic Press.
Canuto, C., Hussaini, M. Y., Quarteroni, A. & Zang, T. A. 1988 Spectral Methods in Fluid Dynamics. Berlin CrossRef | Google Scholar: Springer.
Carmichael, R. D. & Mitrović, D. 1989 Distributions and Analytic Functions. Harlow Google Scholar: Longman.
Chaikin, P. M. & Lubensky, T. C. 1995 Principles of Condensed Matter Physics. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Champeney, D. C. 1987 A Handbook of Fourier Theorems. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Chandrasekhar, S. 1961 Hydrodynamic and Hydromagnetic Stability. Oxford Google Scholar: Clarendon Press, reprinted by Dover, New York, 1981.
Ciarlet, P. G. 1989 Introduction to Numerical Linear Algebra and Optimization. Cambridge Google Scholar: Cambridge University Press.
Coddington, E. A. & Levinson, N. 1955 Theory of Ordinary Differential Equations. New York Google Scholar: McGraw-Hill.
Constanda, C. 2000 Direct and Indirect Boundary Integral Equation Methods. Boca Raton Google Scholar: Chapman & Hall/CRC.
Conway, J. B. 1978 Functions of One Complex Variable, 2nd edn. New York CrossRef | Google Scholar: Springer.
Conway, J. B. 1985 A Course in Functional Analysis. New York CrossRef | Google Scholar: Springer.
Copson, E. T. 1955 An Introduction to the Theory of Functions of a Complex Variable. Oxford Google Scholar: Clarendon Press.
Courant, R. & Hilbert, D. 1953 Methods of Mathematical Physics. New York Google Scholar: Interscience, reprinted by Wiley, 1991.
Cullen, C. G. 1972 Matrices and Linear Transformations, 2nd edn. Reading Google Scholar: Addison-Wesley.
Dassios, G. & Kleinman, R. E. 1989 On Kelvin inversion and low-frequency scattering. SIAM Review 31 CrossRef | Google Scholar, 565–585.
Davis, H. F. 1963 Fourier Series and Orthogonal Functions. Boston Google Scholar: Allyn & Bacon, reprinted by Dover, New York, 1989.
Davies, B. 2002 Integral Transforms and their Applications, 3rd edn. New York CrossRef | Google Scholar: Springer.
Davies, E. B. 1995 Spectral Theory and Differential Operators. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Debnath, L. 1995 Integral Transforms and Their Applications. Boca Raton Google Scholar: CRC Press.
Debnath, L. & P., Mikusiński. 1990 Introduction to Hilbert Spaces with Applications. Boston Google Scholar: Academic Press.
Doetsch, G. 1943 Theorie und Anwendung der Laplace-Transformation. New York Google Scholar: Dover.
Doetsch, G. 1950 Handbuch der Laplace-Transformation. Basel CrossRef | Google Scholar: Birkhäuser.
Doetsch, G. 1974 Introduction to the Theory and Applications of the Laplace Transformation. New York CrossRef | Google Scholar: Springer.
Doob, J. L. 1994 Measure Theory. New York CrossRef | Google Scholar: Springer.
Driscoll, T. A. & Trefethen, L. N. 2002 Schwarz-Christoffel Mapping. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Dunford, N. & Schwartz, J. T. 1963 Linear Operators. New York Google Scholar: Wiley-Interscience.
Edmunds, D. E. & Evans, W. D. 1987 Spectral Theory and Differential Operators. Oxford Google Scholar: Clarendon Press.
Erdélyi, A., Magnus, W. & Oberhettinger, F. 1953 Higher Transcendental Functions. New York Google Scholar: McGraw-Hill.
Erdélyi, A. 1956 Asymptotic Expansions. New York Google Scholar: Dover.
Erdélyi, A., Magnus, W., Oberhettinger, F. & Tricomi, F. G. 1954 Tables of Integral Transforms. New York Google Scholar: McGraw-Hill.
Farkas, H. M. & Kra, I. 1980 Riemann Surfaces, 2nd edn. Berlin CrossRef | Google Scholar: Springer.
Fedoriouk, M. 1987 Méthodes Asymptotiques pour les Équations Différenielles Ordinaires Linéaires. Moscow Google Scholar: Mir.
Fornberg, B. 1996 A Practical Guide to Pseudospectral Methods. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Forsyth, A. R. 1956 A Treatise on Differential Equations, 6th edn. London Google Scholar: McMillan & Co., reprinted by Dover, New York, 1996.
Friedlander, G. & Joshi, M. 1998 Introduction to the Theory of Distributions, 2nd edn. Cambridge Google Scholar: Cambridge University Press.
Friedman, B. 1956 Principles and Techniques of Applied Mathematics. New York Google Scholar: Wiley.
Friedman, A. 1963 Generalized Functions and Partial Differential Equations. Englewood Cliffs NJ Google Scholar: Prentice-Hall.
Gantmacher, F. R. 1959 Matrix Theory. New York Google Scholar: Chelsea Publishing Co.
Garabedian, P. R. 1964 Partial Differential Equations. New York Google Scholar: Wiley, reprinted by AMS Chelsea Publishing, New York, 1998.
Gelfand, I. M. & Shilov, G. E. 1964 Generalized Functions, vol. 1. New York Google Scholar: Academic Press.
Godunov, S. K. 1998 Modern Aspects of Linear Algebra. Providence CrossRef | Google Scholar: American Mathematical Society.
Golub, G. H. & van Loan, C. F. 1989 Matrix Computations, 2nd edn. Baltimore Google Scholar: Johns Hopkins University Press.
Goldstein, H. 1980 Classical Mechanics, 2nd edn. Reading Google Scholar: Addison-Wesley.
González, M. O. 1991 Complex Analysis – Selected Topics. New York Google Scholar: Dekker.
Gradshteyn, I. S., Ryzhik, I. M., Jeffrey, A. & Zwillinger, D., eds. 2007 Table of Integrals, Series, and Products, 7th edn. Orlando Google Scholar: Academic Press.
Griffel, D. H. 2002 Applied Functional Analysis. Mineola Google Scholar: Dover.
Gurtin, M. E. 1984 The linear theory of elasticity. In Mechanics of Solids (ed. C., Truesdell), vol. 2, pp. 1–295. Berlin Google Scholar: Springer.
Haaser, N. B. & Sullivan, J. A. 1971 Real Analysis. New York Google Scholar: Van Nostrand/Reinhold, revised edition reprinted by Dover, New York, 1991.
Hadamard, J. 1923 Lectures on Cauchy's Problem in Linear Partial Differential Equations. New Haven Google Scholar: Yale University Press, reprinted by Dover, New York, 1952.
Hajmirzaahmad, M. & Krall, A. M. 1992. Singular second-order operators: the maximal and minimal operators, and selfadjoint operators in between. SIAM Rev. 34 CrossRef | Google Scholar, 614–634.
Hajnal, A. & Hamburger, P. 1999 Set Theory. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Halmos, P. R. 1958 Finite-Dimensional Vector Spaces. Princeton Google Scholar: van Nostrand, reprinted by Springer, 1993.
Halmos, P. R. 1960 Naive Set Theory. Princeton Google Scholar: Van Nostrand.
Halmos, P. R. 1974 Measure Theory. New York Google Scholar: Van Nostrand.
Hardy, G. H. 1956 Divergent Series. Oxford Google Scholar: Clarendon Press.
Hardy, G. H. & Rogosinski, W. W. 1956 Fourier Series. Cambridge Google Scholar: Cambridge University Press.
Helmberg, G. 1969 Introduction to Spectral Theory in Hilbert Space. Amsterdam Google Scholar: North-Holland.
Henrici, P. 1974 Applied and Computational Complex Analysis, vol. 1. New York Google Scholar: Wiley, reprinted, 1993.
Henrici, P. 1986 Applied and Computational Complex Analysis, vol. 3. New York Google Scholar: Wiley.
Hetnarski, R. B. & Ignaczak, J. 2004 Mathematical Theory of Elasticity. New York Google Scholar: Taylor & Francis.
Hille, E. 1959 Analytic Function Theory. New York Google Scholar: Ginn & Co., reprinted by Chelsea Publishing Co., New York, 1982.
Hille, E. & Phillips, R. S. 1965 Functional Analysis and Semi-Groups, revised edition edn. Providence Google Scholar: American Mathematical Society
Hinch, E. J. 1991 Perturbation Methods. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Hobson, E. W. 1931 The Theory of Spherical and Ellipsoidal Harmonics. Cambridge Google Scholar: Cambridge University Press, reprinted by Chelsea Publishing Co., New York, 1965.
Hochstadt, H. 1971 The Functions of Mathematical Physics. New York Google Scholar: Wiley-Interscience, reprinted by Dover, New York, 1987.
Holmes, M. H. 1995 Introduction to Perturbation Methods. New York CrossRef | Google Scholar: Springer.
Hörmander, L. 1983 The Analysis of Linear Partial Differential Operators. Berlin Google Scholar: Springer.
Horn, R. A. & Johnson, C. R. 1994 Topics in Matrix Analysis. Cambridge Google Scholar: Cambridge University Press.
Hoskins, R. F. 1999 Delta Functions. Chichester Google Scholar: Horwood Publishing.
Hrbacek, K. & Jech, T. 1999 Introduction to Set Theory, 3rd edn. New York Google Scholar: Dekker.
Ince, E. L. 1926 Ordinary Differential Equations. London Google Scholar: Longmans, Green and Co., reprinted by Dover, New York, 1956.
Isaacson, E. & Keller, H. B. 1966 Analysis of Numerical Methods. New York Google Scholar: Wiley, reprinted by Dover, New York, 1994.
Ivanov, V. I. & Trubetskov, M. K. 1995 Handbook of Conformal Mapping with Computer Aided Visualization. Boca Raton Google Scholar: CRC Press.
Jackson, J. D. 1998 Classical Electrodynamics, 3rd edn. New York Google Scholar: Wiley.
Jeffreys, H. 1962 Asymptotic Approximations. Oxford Google Scholar: Clarendon Press.
Jeffreys, H. & Jeffreys, B. 1999 Methods of Mathematical Physics, 3rd edn. Cambridge Google Scholar: Cambridge University Press.
Jerry, A. J. 1998 The Gibbs Phenomenon in Fourier Analysis, Splines and Wavelet Approxmations. Dordrecht CrossRef | Google Scholar: Kluwer.
John, F. 1955 Plane Waves and Spherical Means Applied to Partial Differential Equations. New York Google Scholar: Interscience.
Jones, D. S. 1966 Generalised Functions. New York Google Scholar: McGraw-Hill.
Jost, J. 2006 Compact Riemann Surfaces. Berlin CrossRef | Google Scholar: Springer.
Kanwal, R. P. 2004 Generalized Functions, 3rd edn. Boston CrossRef | Google Scholar: Birkhäuser.
Kellogg, O. D. 1967 Foundations of Potential Theory. Berlin CrossRef | Google Scholar: Springer.
Kemmer, N. 1977 Vector Analysis: A Physicist's Guide to the Mathematics of Fields in Three Dimensions. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Kharazishvili, A. B. 2006 Strange Functions in Real Analysis. Boca Raton Google Scholar: Chapman & Hall.
Knopp, K. 1966 Theory and Applications of Infinite Series. New York Google Scholar: Hafner, reprinted by Dover, New York 1990.
Kober, H. 1957 Dictionary of Conformal Representations. New York Google Scholar: Dover.
Kolmogorov, A. N. & Fomin, S. V. 1957 Elements of the Theory of Functions and Functional Analysis. Rochester NY Google Scholar: Graylock Press, reprinted by Dover, 1999.
Korevaar, J. 2004 Tauberian Theory: A Century of Development. Berlin CrossRef | Google Scholar: Springer.
Körner, T. W. 1989 Fourier Analysis. Cambridge Google Scholar: Cambridge University Press.
Krantz, S. G. 1999 Handbook of Complex Variables. Basel CrossRef | Google Scholar: Birkhäuser.
Kress, R. 1989 Linear Integral Equations. Berlin CrossRef | Google Scholar: Springer.
Kubrusly, C. A. 2001 Elements of Operator Theory. Boston CrossRef | Google Scholar: Birkhäuser.
Kythe, P. K. 1998 Computational Conformal Mapping. Boston CrossRef | Google Scholar: Birkhäuser.
Ladyzhenskaya, O. A. 1985 The Boundary Value Problems of Mathematical Physics. New York CrossRef | Google Scholar: Springer.
Lamb, H. 1932 Hydrodynamics, 6th edn. Cambridge Google Scholar: Cambridge University Press, reprinted 1993.
Lancaster, P. & Tismenetsky, M. 1985 The Theory of Matrices Google Scholar, 2nd edn. Academic Press.
Lanczos, C. 1970 The Variational Principles of Mechanics. Toronto Google Scholar: University of Toronto Press, reprinted by Dover, New York, 1986.
Landau, L. D. & Lifshitz, E. M. 1981 Quantum Mechanics: Non-Relativistic Theory, 3rd edn. New York Google Scholar: Pergamon, reprinted by Butterworth-Heineman, Oxford, 2003.
Landau, L. D. & Lifshitz, E. M. 1987 a Fluid Mechanics, 2nd edn. New York Google Scholar: Pergamon, reprinted by Butterworth-Heineman, Oxford, 2003.
Landau, L. D. & Lifshitz, E. M. 1987 b Theory of Elasticty, 3rd edn. Oxford Google Scholar: Pergamon.
Lang, S. 1983 Real Analysis, 2nd edn. Reading Google Scholar: Addison-Wesley.
Lang, S. 1985 Complex Analysis, 2nd edn. New York CrossRef | Google Scholar: Springer.
Lebedev, N. N. 1965 Special Functions and Their Applications. Englewood Cliffs NJ Google Scholar: Prentice-Hall, reprinted by Dover, New York, 1972.
Levitan, B. M. & Sargsjan, I. S. 1975 Introduction to Spectral Theory: Selfadjoint Ordinary Differential Operators. Providence CrossRef | Google Scholar: American Mathematical Society.
Levitan, B. M. & Sargsjan, I. S. 1991 Sturm-Liouville and Dirac Operators. Dordrecht CrossRef | Google Scholar: Kluwer.
Lieb, E. H. & Loss, M. 1997 Analysis. Providence Google Scholar: American Mathematical Society.
Lighthill, M. J. 1958 Fourier Analysis and Generalised Functions. Cambridge Google Scholar: Cambridge University Press.
Lighthill, M. J. 1978 Waves in Fluids. Cambridge Google Scholar: Cambridge University Press.
Liseikin, V. D. 1999 Grid Generation Methods. New York CrossRef | Google Scholar: Springer.
Liseikin, V. D. 2007 A Computational Differential Geometry Approach to Grid Generation. Berlin Google Scholar: Springer.
Liusternik, L. & Sobolev, V. 1961 Elements of Functional Analysis. New York Google Scholar: Ungar.
Locker, J. 2000 Spectral Theory of Non-Self-Adjoint Two-Point Differential Operators. Providence Google Scholar: American Mathematical Society.
Love, A. E. H. 1927 A Treatise on the Mathematical Theory of Elasticity, 4th edn. Cambridge Google Scholar: Cambridge University Press, reprinted by Dover, New York, 1944.
MacCluer, C. R. 2004 Boundary Value Problems and Fourier Expansions. New York Google Scholar: Dover.
Markusevich, A. I. 1965 Theory of Functions, 2nd edn. New York Google Scholar: Chelsea Publishing Co.
Mathews, J. & Walker, R. L. 1971 Mathematical Methods of Physics, 2nd edn. Meno Park Google Scholar: Benjamin.
Medvedev, F. A. 1991 Scenes from the History of Real Functions. Basel CrossRef | Google Scholar: Birkhäuser.
Mitrinović, D. S. & Kečkić, J. D. 1984 The Cauchy Method of Residues. Theory and Applications. Dordrecht CrossRef | Google Scholar: Reidel.
Mlak, W. 1991 Hilbert Spaces and Operator Theory. Dordrecht Google Scholar: Kluwer.
Moler, C. & van Loan, C. F. 1978 19 dubious ways to compute exponential of a matrix. SIAM Rev. 20 CrossRef | Google Scholar, 801–836.
Moon, P. & Spencer, D. E. 1961 Field Theory Handbook. Berlin CrossRef | Google Scholar: Springer.
Morse, P. M. & Feshbach, H. 1953 Methods of Theoretical Physics. New York Google Scholar: McGraw-Hill.
Murdock, J. A. 1991 Perturbations. New York Google Scholar: Wiley.
Naimark, M. A. 1967 Linear Differential Operators. New York Google Scholar: Ungar.
Narasimhan, R. & Nievergelt, Y. 2001 Complex Analysis in One Variable, 2nd edn. Boston CrossRef | Google Scholar: Birkhäuser.
Natanson, I. P. 1961 Theory of Functions of a Real Variable. New York Google Scholar: Ungar.
Naylor, A. W. & Sell, G. R. 2000 Linear Operator Theory in Engineering and Science, 2nd edn. New York Google Scholar: Springer.
Nussenzweig, H. M. 1972 Causality and Dispersion Relations. New York Google Scholar: Academic Press.
Ortega, J. M. 1987 Matrix Theory, A Second Course. New York CrossRef | Google Scholar: Plenum.
Paliouras, J. D. & Meadows, D. S. 1990 Complex Variables for Scientists and Engineers, 2nd edn. New York Google Scholar: Macmillan.
Pandey, J. N. 1996 The Hilbert Transform of Schwartz Distributions and Applications. New York Google Scholar: Wiley.
Panofsky, W. K. H. & Phillips, M. 1956 Classical Electricity and Magnetism. Reading Google Scholar: Addison Wesley.
Pathak, R. S. 1997 Integral Transforms of Generalized Functions and Their Applications. Amsterdam Google Scholar: Gordon & Breach.
Pease, M. C. 1965 Methods of Matrix Algebra. New York Google Scholar: Academic Press.
Pécseli, H. L. 2000 Fluctuations in Physical Systems. Cambridge Google Scholar: Cambridge University Press.
Piziak, R. & Odell, P. L. 2007 Matrix Theory: From Generalized Inverses to Jordan Form. Boca Raton Google Scholar: Chapman & Hall.
Pomp, A. 1998 The Boundary-Domain Integral Method for Elliptic Systems. New York CrossRef | Google Scholar: Springer.
Pozrikidis, C. 1992 Boundary Integral and Singularity Methods for Linearized Viscous Flow. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Rao, M. M. 2004 Measure Theory and Integration, 2nd edn. New York Google Scholar: Dekker.
Renardy, M. & Rogers, R. C. 1993 An Introduction to Partial Differential Equations. New York Google Scholar: Springer.
Richards, I. & Youn, H. K. 1990 Theory of Distributions: A Non-Technical Introduction. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Richtmyer, R. D. 1978 Principles of Advanced Mathematical Physics. Berlin CrossRef | Google Scholar: Springer.
Riesz, F. & Sz.-Nagy, B. 1955 Functional Analysis. New York Google Scholar: Ungar, reprinted by Dover, New York, 1990.
Robinson, J. C. 2001 Infinite-Dimensional Dynamical Systems. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Roman, P. 1975 Some Modern Mathematics for Physicists and Other Outsiders. New York Google Scholar: Pergamon Press.
Roos, B. W. 1969 Analytic Functions and Distributions in Physics and Engineering. New York Google Scholar: Wiley.
Rudin, W. 1987 Real and Complex Analysis. New York Google Scholar: McGraw-Hill.
Saichev, A. I. & Woyczyński, W. A. 1997 Distributions in the Physical and Engineering Sciences. Boston Google Scholar: Birkhäuser.
Sakurai, J. J. 1994 Modern Quantum Mechanics, revised edn. Reading Google Scholar: Addison-Wesley.
Samko, S. G., Kilbas, A. A. & Marichev, O. I. 1993 Fractional Integrals and Derivatives. Amsterdam Google Scholar: Gordon & Breach.
Sansone, G. 1959 Orthogonal Functions. New York Google Scholar: Interscience, reprinted by Dover, New York, 1991.
Schinzinger, R. & Laura, P. A. A. 1991 Conformal Mapping: Methods and Applications. Amsterdam Google Scholar: Elsevier, reprinted by Dover, New York.
Schwartz, L. 1966a Mathematics for the Physical Sciences. Reading Google Scholar: Addison-Wesley.
Schwartz, L. 1966b Théorie des Distributions. Paris Google Scholar: Hermann.
Schwartz, L. 1970 Analyse. Paris Google Scholar: Hermann.
Smirnov, V. I. 1964 A Course of Higher Mathematics. Oxford Google Scholar: Pergamon Press.
Smith, M. G. 1966 Laplace Transform Theory. London Google Scholar: van Nostrand.
Sneddon, I. N. 1951 Fourier Transforms. New York Google Scholar: McGraw-Hill, reprinted by Dover, New York, 1995.
Sneddon, I. N. 1955 Functional analysis. In Encyclopedia of Physics (ed. S., Flügge), vol. 2, pp. 198–348. Berlin Google Scholar: Springer.
Sneddon, I. N. 1966 Mixed Boundary Value Problems in Potential Theory. Amsterdam Google Scholar: North-Holland.
Sommerfeld, A. 1950 Partial Differential Equations in Physics. New York Google Scholar: Academic Press.
Srednicki, M. 2007 Quantum Field Theory. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Stakgold, I. 1967 Boundary Value Problems of Mathematical Physics. New York Google Scholar: Macmillan.
Stakgold, I. 1997 Green's Functions and Boundary Value Problems, 2nd edn. New York Google Scholar: Wiley-Interscience.
Strichartz, R. S. 1994 A Guide to Distribution Theory and Fourier Transforms. Boca Raton Google Scholar: CRC Press.
Stroock, D. W. 1999 A Concise Introduction to the Theory of Integration, 3rd edn. Boston Google Scholar: Birkhäuser.
Sveshnikov, A. G. & Tikhonov, A. N. 1978 The Theory Functions of a Complex Variable. Moscow Google Scholar: Mir Publishers.
Taylor, A. E. & Lay, D. C. 1980 Introduction to Functional Analysis. New York Google Scholar: Wiley.
Titchmarsh, A. C. 1948 Introduction to the Theory of Fourier Integrals, 2nd edn. Oxford Google Scholar: Clarendon Press.
Titchmarsh, E. C. 1962 Eigenfunction Expansions. Oxford Google Scholar: Clarendon Press.
Tranter, C. J. 1966 Integral Tranforms in Mathematical Physics, 3rd edn. London Google Scholar: Methuen & Co.
Vallée, PoussinCh.-J., de La 1949 Cours d'Analyse Infinitésimale, 8th edn. Louvain/Paris Google Scholar: Librairie Universitaire/Gauthier-Villars.
van der Pol, B. & Bremmer, H. 1959 Operational Calculus Based on the Two-Sided Laplace Integral. Cambridge Google Scholar: Cambridge University Press.
Vladimirov, V. S. 2002 Methods of the Theory of Generalized Functions. London Google Scholar: Taylor & Francis.
Watson, G. N. 1944 A Treatise on the Theory of Bessel Functions, 2nd edn. Cambridge Google Scholar: Cambridge University Press.
Weinberg, S. 1995 The Quantum Theory of Fields. Cambridge CrossRef | Google Scholar: Cambridge University Press.
Weyl, H. 1964 The Concept of a Riemann Surface. Reading Google Scholar: Addison-Wesley.
Whitham, G. B. 1974 Linear and Nonlinear Waves. New York Google Scholar: Wiley, reprinted, 1999.
Whittaker, E. T. & Watson, G. N. 1927 Modern Analysis, 4th edn. Cambridge Google Scholar: Cambridge University Press.
Widder, D. V. 1946 The Laplace Transform. Princeton Google Scholar: Princeton University Press.
Widder, D. V. 1961 Advanced Calculus, 2nd edn. Englewood Cliff NJ Google Scholar: Prentice-Hall, reprinted by Dover, New York, 1989.
Widder, D. V. 1971 An Introduction to Transform Theory. New York Google Scholar: Academic Press.
Wigner, E. P. 1960 The unreasonable effectiveness of mathematics in the natural sciences. Comm. Pure Appl. Math. 13 CrossRef | Google Scholar, 1–14.
Wilkinson, J. H. 1988 The Algebraic Eigenvealue Problem, 2nd edn. Oxford Google Scholar: Clarendon Press.
Wouk, A. 1979 A Course of Applied Functional Analysis. New York Google Scholar: Wiley.
Zauderer, E. 1989 Partial Differential Equations of Applied Mathematics. New York Google Scholar: Wiley.
Zemanian, A. H.Distribution Theory and Transform Analysis. New York CrossRef | Google Scholar: McGraw-Hill.
Zwillinger, D. 2002 CRC Standard Mathematical Tables and Formulae, 31st edn. Boca Raton CrossRef | Google Scholar: CRC Press.

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 9847 *
Loading metrics...

Book summary page views

Total views: 9635 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 8th April 2025. This data will be updated every 24 hours.

Usage data cannot currently be displayed.