MAA Reviews

Differential Equations: Introductory Texts

*** Boyce, William E. and DiPrima, Richard C. Elementary Differential Equations and Boundary Value Problems, New York, NY: John Wiley, 1969, 1992. Fifth Edition.

* Braun, Martin. Differential Equations and Their Applications: An Introduction to Applied Mathematics, New York, NY: Springer-Verlag, 1975, 1983. Third Edition.

Burghes, David N. and Borrie, M.S. Modelling with Differential Equations New York, NY: Halsted Press, 1981.

* Coddington, Earl A. An Introduction to Ordinary Differential Equations Mineola, NY: Dover, 1989.

** Edwards, C.H., Jr. and Penney, David E. Elementary Differential Equations with Applications, Englewood Cliffs, NJ: Prentice Hall, 1985, 1989. Second Edition.

Hochstadt, Harry. Differential Equations Mineola, NY: Dover, 1975.

** Hubbard, John H. and West, Beverly H. Differential Equations: A Dynamical Systems Approach, New York, NY: Springer-Verlag, 1991.

Miller, Richard K. Ordinary Differential Equations New York, NY: Academic Press, 1982.

** Redheffer, Ray and Port, Dan. Differential Equations: Theory and Applications Boston, MA: Jones and Bartlett, 1991.

Roberts, Charles E., Jr. Ordinary Differential Equations: A Computational Approach Englewood Cliffs, NJ: Prentice Hall, 1979.

** Simmons, George F. and Robertson, John S. Differential Equations with Applications and Historical Notes, New York, NY: McGraw-Hill, 1972, 1991. Second Edition.

** Zill, Dennis G. A First Course in Differential Equations with Applications, Boston, MA: PWS-Kent, 1980, 1989. Fourth Edition.

Differential Equations: Ordinary Differential Equations

** Arnold, V.I. Geometrical Methods in the Theory of Ordinary Differential Equations, New York, NY: Springer-Verlag, 1983, 1988. Second Edition.

* Arnold, V.I. Ordinary Differential Equations Cambridge, MA: MIT Press, 1973, 1978.

Bellman, Richard E. Stability Theory of Differential Equations Mineola, NY: Dover, 1969.

*** Birkhoff, Garrett and Rota, Gian-Carlo. Ordinary Differential Equations, New York, NY: John Wiley, 1969, 1989. Fourth Edition.

** Brauer, Fred and Nohel, John A. The Qualitative Theory of Ordinary Differential Equations: An Introduction Mineola, NY: Dover, 1989.

Carrier, George F. and Pearson, Carl E. Ordinary Differential Equations Philadelphia, PA: Society for Industrial and Applied Mathematics, 1991.

Cesari, Lamberto. Asymptotic Behavior and Stability Problems in Ordinary Differential Equations New York, NY: Springer-Verlag, 1963.

*** Coddington, Earl A. and Levinson, Norman. Theory of Ordinary Differential Equations Melbourne, FL: Robert E. Krieger, 1984.

Driver, Rodney D. Ordinary and Delay Differential Equations New York, NY: Springer-Verlag, 1977.

* Hale, Jack K. Ordinary Differential Equations Melbourne, FL: Robert E. Krieger, 1980.

Hale, Jack K., ed. Studies in Ordinary Differential Equations Washington, DC: Mathematical Association of America, 1977.

* Hartman, Philip. Ordinary Differential Equations, New York, NY: Birkhauser, 1973, 1982. Second Edition.

Hille, Einar. Ordinary Differential Equations in the Complex Domain New York, NY: John Wiley, 1976.

*** Hirsch, Morris W. and Smale, Stephen. Differential Equations, Dynamical Systems, and Linear Algebra New York, NY: Academic Press, 1974.

Hurewicz, Witold. Lectures on Ordinary Differential Equations Mineola, NY: Dover, 1990.

* Ince, Edward L. Ordinary Differential Equations Mineola, NY: Dover, 1956.

Jordan, D. and Smith, P. Nonlinear Ordinary Differential Equations, New York, NY: Clarendon Press, 1987. Second Edition.

Lakin, William D. and Sanchez, David A. Topics in Ordinary Differential Equations Mineola, NY: Dover, 1982.

* Lefschetz, Solomon. Differential Equations: Geometric Theory Mineola, NY: Dover, 1977.

Nemytskii, V.V. and Stepanov, V.V. Qualitative Theory of Differential Equations Mineola, NY: Dover, 1989.

Pontrjagin, Lev S. Ordinary Differential Equations Reading, MA: Addison-Wesley, 1962.

Reid, William T. Sturmian Theory for Ordinary Differential Equations New York, NY: Springer-Verlag, 1980.

* Sanchez, David A. Ordinary Differential Equations and Stability Theory: An Introduction Mineola, NY: Dover, 1979.

Struble, Raimond A. Nonlinear Differential Equations Melbourne, FL: Robert E. Krieger, 1983.

** Waltman, Paul. A Second Course in Elementary Differential Equations New York, NY: Academic Press, 1986.

Wasow, Wolfgang. Asymptotic Expansions for Ordinary Differential Equations Mineola, NY: Dover, 1987.

Differential Equations: Dynamical Systems

* Abraham, Ralph H. and Shaw, Christopher D., eds. Dynamics---The Geometry of Behavior, Santa Cruz, CA: Aerial Press, 1982--88. 4~Vols.

* Arrowsmith, D.K. and Place, C.M. An Introduction to Dynamical Systems New York, NY: Cambridge University Press, 1990.

Bhatia, Nam Parshad. Stability Theory of Dynamical Systems New York, NY: Springer-Verlag, 1970.

Burton, T.A. Stability and Periodic Solutions of Ordinary and Functional Differential Equations New York, NY: Academic Press, 1985.

Chow, S. and Hale, Jack K. Methods of Bifurcation Theory New York, NY: Springer-Verlag, 1982.

*** Guckenheimer, John and Holmes, Philip. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields New York, NY: Springer-Verlag, 1983.

Hale, Jack K.; Magalhaes, Luis T.; and Oliva, Waldyr M. An Introduction to Infinite Dimensional Dynamical Systems---Geometric Theory New York, NY: Springer-Verlag, 1984.

Hao, Bai-Lin. Chaos Teaneck, NJ: World Scientific, 1984.

Hazewinkel, M.; Jurkovich, R.; and Paelinck, J.H.P., eds. Bifurcation Analysis: Principles, Applications, and Synthesis Norwell, MA: D. Reidel, 1985.

* Iooss, Gerard and Joseph, Daniel D. Elementary Stability and Bifurcation Theory, New York, NY: Springer-Verlag, 1990. Second Edition.

LaSalle, Joseph P. The Stability of Dynamical Systems Philadelphia, PA: Society for Industrial and Applied Mathematics, 1976.

LaSalle, Joseph P. and Lefschetz, Solomon. Stability by Liapunov's Direct Method New York, NY: Academic Press, 1961.

Liapunov, A. Stability of Motion New York, NY: Academic Press, 1966.

* Marsden, Jerrold E. The Hopf Bifurcation and Its Applications New York, NY: Springer-Verlag, 1976.

Percival, Ian and Richards, Derek. Introduction to Dynamics New York, NY: Cambridge University Press, 1982.

Rouche, N.; Habets, P.; and Laloy, M. Stability Theory by Liapunov's Direct Method New York, NY: Springer-Verlag, 1977.

** Ruelle, David. Elements of Differentiable Dynamics and Bifurcation Theory New York, NY: Academic Press, 1989.

* Sparrow, Colin. The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors New York, NY: Springer-Verlag, 1982.

Verhulst, F. Nonlinear Differential Equations and Dynamical Systems, New York, NY: Springer-Verlag, 1985, 1990. Second Edition.

** Wiggins, Stephen. Introduction to Applied Nonlinear Dynamical Systems and Chaos New York, NY: Springer-Verlag, 1990.

Differential Equations: Partial Differential Equations

Andrews, Larry C. Elementary Partial Differential Equations with Boundary Value Problems New York, NY: Academic Press, 1986.

Baker, Bevan B. and Copson, E.T. The Mathematical Theory of Huygens' Principle New York, NY: Chelsea, 1987.

* Bergman, Stefan. Kernel Functions and Elliptic Differential Equations in Mathematical Physics New York, NY: Academic Press, 1953.

Bleistein, Norman. Mathematical Methods for Wave Phenomena New York, NY: Academic Press, 1984.

** Carrier, George F. and Pearson, Carl E. Partial Differential Equations: Theory and Technique, New York, NY: Academic Press, 1988. Second Edition.

Farlow, Stanley J. Partial Differential Equations for Scientists and Engineers New York, NY: John Wiley, 1982.

Friedman, Avner. Partial Differential Equations New York, NY: Holt, Rinehart and Winston, 1969.

** Garabedian, Paul R. Partial Differential Equations, New York, NY: Chelsea, 1986. Second Edition.

* Gustafson, Karl E. Introduction to Partial Differential Equations and Hilbert Space Methods, New York, NY: John Wiley, 1980, 1987. Second Edition.

* Haberman, Richard. Elementary Applied Partial Differential Equations with Fourier Series and Boundary Value Problems, Englewood Cliffs, NJ: Prentice Hall, 1983, 1987. Second Edition.

Hellwig, Gunter. Partial Differential Equations New York, NY: Blaisdell, 1964.

* Hormander, Lars. The Analysis of Linear Partial Differential Operators I: Distribution Theory and Fourier Analysis, New York, NY: Springer-Verlag, 1983, 1990. Second Edition.

John, Fritz. Partial Differential Equations, New York, NY: Springer-Verlag, 1971, 1982. Fourth Edition.

Littman, Walter, ed. Studies in Partial Differential Equations Washington, DC: Mathematical Association of America, 1982.

Pinsky, Mark A. Introduction to Partial Differential Equations with Applications, New York, NY: McGraw-Hill, 1984, 1991. Second Edition.

* Protter, Murray H. and Weinberger, Hans F. Maximum Principles in Differential Equations Englewood Cliffs, NJ: Prentice Hall, 1967.

Smoller, J. Shock Waves and Reaction Diffusion Equations New York, NY: Springer-Verlag, 1983.

Tikhonov, Andrei N. Partial Differential Equations of Mathematical Physics San Francisco, CA: Holden-Day, 1967.

Treves, Fran cois. Basic Linear Partial Differential Equations New York, NY: Academic Press, 1975.

** Weinberger, Hans F. A First Course in Partial Differential Equations with Complex Variables and Transform Methods Lexington, MA: Xerox College, 1965.

* Whitham, G. Linear and Nonlinear Waves New York, NY: John Wiley, 1974.

** Widder, David V. The Heat Equation New York, NY: Academic Press, 1975.

Williams, W.E. Partial Differential Equations New York, NY: Clarendon Press, 1980.

Zachmanoglou, E.C. and Thoe, Dale W. Introduction to Partial Differential Equations with Applications Mineola, NY: Dover, 1986.

* Zauderer, Erich. Partial Differential Equations of Applied Mathematics, New York, NY: John Wiley, 1983, 1989. Second Edition.

Differential Equations: Boundary Value Problems

*** Churchill, Ruel V. and Brown, James W. Fourier Series and Boundary Value Problems, New York, NY: McGraw-Hill, 1978. Third Edition.

Crank, John. Free and Moving Boundary Problems New York, NY: Clarendon Press, 1984.

Greenberg, Michael D. Application of Green's Functions in Science and Engineering Englewood Cliffs, NJ: Prentice Hall, 1971.

Hanna, J. Ray and Rowland, J.H. Fourier Series and Integrals of Boundary Value Problems, New York, NY: John Wiley, 1982, 1990. Second Edition.

* Powers, David L. Boundary Value Problems, New York, NY: Academic Press, 1979, 1987. Third Edition.

Roach, G.F. Green's Functions, New York, NY: Cambridge University Press, 1982. Second Edition.

** Stakgold, Ivar. Green's Functions and Boundary Value Problems New York, NY: John Wiley, 1979.

Differential Equations: Special Topics

* Gould, Sydney H. Variational Methods for Eigenvalue Problems: An Introduction to the Method Toronto: University of Toronto Press, 1957, 1966.

Hochstadt, Harry. Integral Equations New York, NY: John Wiley, 1973.

Ladde, G.S. Oscillation Theory of Differential Equations with Deviating Arguments New York, NY: Marcel Dekker, 1987.

Martin, Robert H., Jr. Nonlinear Operators and Differential Equations in Banach Spaces Melbourne, FL: Robert E. Krieger, 1987.

* Mickens, Ronald E. An Introduction to Nonlinear Oscillations New York, NY: Cambridge University Press, 1981.

Miller, Richard K. Nonlinear Volterra Integral Equations Reading, MA: W.A. Benjamin, 1971.

Smith, Donald R. Singular-perturbation Theory: An Introduction with Applications New York, NY: Cambridge University Press, 1985.

Tikhonov, Andrei N. and Samarskii, A.A. Equations of Mathematical Physics Mineola, NY: Dover, 1990.

Titchmarsh, Edward C. Eigenfunction Expansions Associated with Second-Order Differential Equations New York, NY: Clarendon Press, 1962.

* Tricomi, Francesco G. Integral Equations Mineola, NY: Dover, 1985.

Volterra, Vito. Theory of Functionals and of Integral and Integro-Differential Equations Mineola, NY: Dover, 1959.

* Yosida, Kosaku. Lectures on Differential and Integral Equations New York, NY: Interscience, 1960.