Useful References for Math 331-004: Introduction to PDE

General Introductory Textbooks

• Applied Partial Differential Equations with Fourier Series and Boundary Value Problems 4th ed., by Richard Haberman, Prentice Hall, 2004. The main text for our class.

• Partial Differential Equations, Theory and Technique 2nd ed., by G.F. Carrier and C.E. Pearson, Academic Press, 1988. A very nice book at a similar level to Haberman, with more of an emphasis on solution techniques other than separation of variables. See pp. 75-90 for information about the classification of second order equations.

• Partial Differential Equations for Scientists and Engineers, by S.J. Farlow, Dover Edition, 1993. An inexpensive introductory text which stresses separation of variables. See pp. 174-182 and 331-339 for information about the classification of second order equations.

Ordinary Differential Equations

• Your favorite ordinary differential equations textbook.

• Elementary Differential Equations with Boundary Value Problems, 4th ed., by Edwards and Penney, Prentice Hall. The textbook used in Math 222, a prerequisite to Math 331.

Calculus

• Your favorite calculus textbook.

• Calculus, 6th ed., by Edwards and Penney, Prentice Hall. The textbook used in the calculus sequence which is a prerequisite to Math 222.

• div, grad, curl and all that: an informal text on vector calculus 2nd ed., by H.M. Schey, W.W. Norton, 1992. Applications in electrostatics are used to motivate the basics of vector calculus.

Fourier Analysis

• Fourier Series, by G.P. Tolstov, Dover Edition, 1976. Inexpensive classic text.

• A First Course in Fourier Analysis, by D.W. Kammler, Prentice Hall, 2000. A modern introduction to Fourier Analysis. Chapter 9 has some interesting comments on efficiently animating solutions to partial differential equations.

Applications

• Transport Phenomena, 2nd ed., by R.B. Bird, W.E. Stewart, and E.N. Lightfoot, John Wiley and Sons, 2002. Full of physical insights, with many worked problems in mass, momentum, and heat transter.

• Elementary Fluid Dynamics, by D.J. Acheson, Oxford University Press, 1990. Full of physical insights, with many good problems with answers and hints.

• The Mathematics of Financial Derivatives: A Student Introduction, by P. Wilmott, S. Howison, and J. Dewynne, Cambridge University Press, 1995. Readable introduction to the subject. Shows how many problems can be reduced to solving partial differential equations after some analysis.

Related Classes in the Math Department

• Several people in the class expressed an interest in numerical methods. You can get a good introduction in Math 340: Applied Numerical Methods and Optimization. A more advanced class which concentrates on numerical techniques for partial differential equations is Math 440: Advanced Applied Numerical Methods.

• Several people in the class expressed an interest in chaos. You can get an introduction to this subject in Math 473: Intermediate Differential Equations.

• You can get more information about the classes mentioned above by visiting the Math Department's compendium of online syllabi (go to math.njit.edu/Undergraduate/undergraduate.html and click on Course Descriptions and Syllabi)