Introduction to Partial Differential Equations

  • Hassan Ugail


This chapter provides an introduction to partial differential equations (PDEs) with the aim of introducing the reader with the mathematical concepts that are used in further chapters. The chapter first introduces the general concept of PDEs and discusses various types of PDEs. Special emphasis is given to elliptic PDEs since this type of equations form the basis for the development of geometric design techniques throughout this book.


Finite Element Method Partial Differential Equation Heat Equation Finite Difference Method Boundary Element Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Axler S, Bourdon P, Ramey W (2001) Harmonic function theory. Springer, Berlin MATHGoogle Scholar
  2. 2.
    Castro CG, Ugail H, Willis P, Palmer I (2008) A survey of partial differential equations in geometric design. Vis Comput 24(3):213–225. doi: 10.1007/s00371-007-0190-z CrossRefGoogle Scholar
  3. 3.
    Evans G, Blackledge J, Yardley P (1999) Analytic methods for partial differential equations. Springer, Berlin CrossRefGoogle Scholar
  4. 4.
    Fornberg B (1996) A practical guide to pseudospectral methods. Cambridge University Press, Cambridge MATHGoogle Scholar
  5. 5.
    Gladwell I (1980) Survey of numerical methods for partial differential equations. Oxford University Press, London Google Scholar
  6. 6.
    Gottlieb D, Orzag S (1977) Numerical analysis of spectral methods: theory and applications. SIAM, Philadelphia MATHCrossRefGoogle Scholar
  7. 7.
    Farlow SJ (1999) Partial differential equations for scientists and engineers. Dover, New York Google Scholar
  8. 8.
    Jang CL (2011) Partial differential equations: theory, analysis and applications. Nova Publ., New York Google Scholar
  9. 9.
    Johnson C (2009) Numerical solution of partial differential equations by the finite element method. Dover, New York MATHGoogle Scholar
  10. 10.
    Machura M, Sweet RA (1980) A survey of software for partial differential equations. ACM Trans Math Softw 6(4):461–488. doi: 10.1145/355921.355922 MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Sapiro G (2001) Geometric partial differential equations and image analysis. Cambridge University Press, Cambridge MATHCrossRefGoogle Scholar
  12. 12.
    Smith GD (1985) Numerical solution of partial differential equations: finite difference methods. Clarendon, Oxford MATHGoogle Scholar
  13. 13.
    Zachmanoglou EC, Thoe DW (1988) Introduction to partial differential equations with applications. Dover, New York Google Scholar

Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.University of BradfordBradfordUK

Personalised recommendations