Skip to main content
SpringerLink
Log in

Partial Differential Equations of Second and Higher Order

  • Chapter
Handbook of Applied Mathematics

Abstract

We will use the abbreviation PDE for partial differential equation and ODE for ordinary differential equation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ahlfors, L. V., “Conformality with Respect to Riemannian Metrics,” Ann. Acad. Sci. Fenn., Series Al, No. 206, 1955.

    Google Scholar 

  2. Courant, R., and Hilbert, D., Methods of Mathematical Physics, vols. 1–2, Wiley-Interscience, New York, 1962.

    Google Scholar 

  3. Garabedian, P. R., Partial Differential Equations, Wiley, New York, 1964.

    Google Scholar 

  4. Petrovsky, I. G., Lectures on Partial Differential Equations, Wiley-Interscience, New York, 1954.

    Google Scholar 

  5. Marguerre, K., “Ansätze zur Lösung der Grundgleichungen der Elastizitätstheorie,” Z.A.M.M., 35, 242, 1955.

    Google Scholar 

  6. Pearson, C., Theoretical Elasticity, Harvard University Press, Cambridge, Mass., 1959.

    Google Scholar 

  7. Morse, P., and Feshbach, H., Methods of Theoretical Physics, vols. 1–2, McGraw-Hill, New York, 1953.

    Google Scholar 

  8. Carslaw, H. J., and Jaeger, J. C., Conduction of Heat in Solids, Oxford University Press, New York, 1959.

    Google Scholar 

  9. Carrier, G., Króok, M., and Pearson, C., Functions of a Complex Variable, McGraw-Hill, New York, 1966.

    Google Scholar 

  10. Kober, H., Dictionary of Conformal Representations, Dover, New York, 1952.

    Google Scholar 

  11. Milne-Thomson, L. M., Theoretical Hydrodynamics, Macmillan, New York, 1960.

    Google Scholar 

  12. Muskhelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Groningen, Netherlands, 1953.

    Google Scholar 

  13. Carathéodory, C., Conformal Representation, Cambridge University Press, Cambridge, 1932.

    Google Scholar 

  14. Schwarz, L., Théorie des Distributions, vols. 1–2, Hermann et Cie, Paris, 1950.

    Google Scholar 

  15. Sommerfield, A., Partial Differential Equations in Physics, Academic Press, New York, 1949.

    Google Scholar 

  16. Tricorni, F. G., Integral Equations, Wiley-Interscience, New York, 1957.

    Google Scholar 

  17. Kellogg, O. D., Foundations of Potential Theory, Dover, New York, 1953.

    Google Scholar 

  18. Protter, M. H., and Weinberger, H. F., Maximum Principles in Differential Equations, Prentice-Hall, New Jersey, 1967.

    Google Scholar 

  19. Hutchinson, J. W., and Niordson, F. I., Designing Vibrating Membranes, Report No. 12, 1971, DCAMM, Technical University of Denmark.

    Google Scholar 

  20. Polya, G., and Szegö, G., “Isoperimetric Inequalities in Mathematical Physics,” Ann. of Math. Studies, No. 27, Princeton University Press, Princeton, 1951.

    Google Scholar 

  21. Courant, R., and Friedrichs, K. O., Supersonic Flow and Shock Waves, WileyInterscience, New York, 1948.

    Google Scholar 

  22. Stoker, J. J., Water Waves, Wiley-Interscience, New York, 1957.

    Google Scholar 

  23. Kantorovich, L., and Krylov, V., Approximate Methods in Higher Analysis, Wiley-Interscience, New York, 1958.

    Google Scholar 

  24. Mikhlin, S., Variational Methods in Mathematical Physics, Pergamon, New York, 1964.

    Google Scholar 

  25. Strang, G., and Fix, G., An Analysis of the Finite Element Method, Prentice-Hall, New Jersey, 1973.

    Google Scholar 

  26. Carrier, G. F., and Pearson, C. E., Partial Differential Equations, Academic Press, New York, 1976.

    Google Scholar 

  27. Richtmeyer, R. D., and Morton, K. W., Difference Methods for Initial Value Problems, 2 ed., Wiley, New York, 1967.

    Google Scholar 

  28. Varga, R. S., Matrix Iterative Analysis, Prentice-Hall, New Jersey, 1962.

    Google Scholar 

  29. Brikhoff, G., The Numerical Solution of Elliptic Equations, SIAM Regional Conference Series No. 1, 1971.

    Google Scholar 

  30. Strang, G., and Fix, G., An Analysis of the Finite Element Method, Prentice-Hall, New Jersey, 1973.

    Google Scholar 

  31. Mitchell, A. R., and Wait, R., The Finite Element Method in Partial Differential Equations, Wiley, New York, 1977.

    Google Scholar 

  32. Zienkiewicz, O. C., The Finite Element Method in Engineering Science, McGraw-Hill, London, 1971.

    Google Scholar 

  33. Huebner, K. H., The Finite Element Method for Engineers, Wiley, New York, 1975.

    Google Scholar 

  34. Smith, G. D., Numerical Solution of Partial Differential Equations: Finite Difference Methods, 2 ed., Oxford University Press, Oxford, 1978.

    Google Scholar 

  35. Wirz, H. J., and Smolderen, J. J. (eds.), Numerical Methods in Fluid Dynamics, McGraw-Hill, New York, 1978.

    Google Scholar 

  36. Orszag, S., Numerical Simulation of Incompressible Flows, Studies in Applied Math, 50, 1971, p. 293.

    Google Scholar 

  37. Mitchell, A. R., and Griffiths, D. F., The Finite Difference Method in Partial Differential Equations, Wiley, New York, 1980.

    Google Scholar 

  38. Bauer, F., Betancourt, O., and Garabedian, P., A. Computational Method in Plasma Physics, Springer-Verlag, New York, 1978.

    Google Scholar 

  39. Gottlieb, D., and Orszag, S. A., Numerical Analysis of Spectral Methods, SIAM Regional Conference No. 26, 1977.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dep’ts. of Aeronautics and Astronautics, and of Applied Mathematics, University of Washington, Seattle, Wash., USA

    Prof. Carl E. Pearson

Authors
  1. Prof. Carl E. Pearson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Washington, USA

    Carl E. Pearson (Professor of Applied Mathematics) (Professor of Applied Mathematics)

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Van Nostrand Reinhold

About this chapter

Cite this chapter

Pearson, C.E. (1990). Partial Differential Equations of Second and Higher Order. In: Pearson, C.E. (eds) Handbook of Applied Mathematics. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-1423-3_9

Download citation

  • DOI: https://doi.org/10.1007/978-1-4684-1423-3_9

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-0-442-00521-4

  • Online ISBN: 978-1-4684-1423-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation