Course Title:	Chaos Theory
Course Number:	MATH 5470 - 002;    meets with MATH 6440 - 002
Instructor:	Andrejs Treibergs
Home Page:	http://www.math.utah.edu/~treiberg/M5471.html
Place & Time:	T, H 12:25 - 1:45 PM in JWB 208
Office Hours:	12:55 - 1:45 M, W and 2:00 - 2:50 T in JWB 224 (tent.)
E-mail:
Prerequisites:	"C" or better in MATH 2250 OR MATH 2280 or MATH 2281 or consent of instructor.
Main Text:	Stephen H. Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity) 2nd ed., Westview Press; 2014
	ISBN-13: 978-0813349107

We shall basically follow the text. Here is a partial list of alternative sources that cover the material. Many Ordinary Differential Equations texts contain some chaos material, such as Hirsch, Smale and Devaney's text which is used for Math 5410. This is my second time teaching math 5470. I have also taught Math 5410 six times. Math 5410 is more mathematically demanding than math 5470. It emphasizes the theorems of ODE's about existence, uniqueness and well posedness of solutions, as well as many applications. A second semester of ordinary differential equations, Math 5420, is rarely offered.

Chaos Theory Math 5470, taught in the spring, may be viewed as a companion course to Math 5470. It also deals mostly with differential equations, often using the text of Strogatz. It covers many applications using the theory from Math 5410 but does not provide proofs. The two courses usually have disjoint audiences, with Chaos Theory attracting students with majors other than math. An alternative text for Math 5470 may be Robinson.

I have also taught Math 6410 several times and have tried various texts: Amann, Barriera & Valls, Chicone, Cronin, Liu, Perko, Sideris and Teschl. Perhaps not so unexpectedly, the texts the students liked the best, Perko and Liu, are not the ones I liked the best, Amann and Chicone and Sideris. None of the texts perfectly covered the syllabus of math 6410. Grant's notes as far as they go are modeled on the course he took as a graduate student here at Utah. All the texts cover about two thirds of the course, and the rest has to be supplemented. The authors all have their hobby horses, and they discuss their favorite special topics beyond what would be appropriate for a beginning course. Most texts for Math 6410 emphasize theory. But a couple of the others, Jordan &. Smith , and Schaeffer & Cain are especially good at explaining examples and applications.

Texts Suitable for an Undergraduate Course in Chaos.

• R. Clark Robinson, An Introduction to Dynamical Systems: Continuous and Discrete Pearson Prentice Hall, 2004.
• Steven Strogatz, Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Studies in Nonlinearity) 2nd ed., Westview Press; 2014.

Texts Suitable for an Undergraduate Course in ODE's.

• Fred Bauer & John Nohel, Dover 1989; reprint of W. A. Benjamin, 1969.
• V. Dharmaiah, Introduction to Theory of Ordinary Differential Equations, PHI Learning, Private Limited, 2013.
• Roger Grimshaw, Nonlinear Ordinary Differential Equations, CRC Press, 1993.
• M. Hirsch, S. Smale & R. Devaney, Differential Equations, Dynamical Systems & an Introduction to Chaos 2nd. ed., Elsevier, 2004.
• Richard Miller & Anthony Michel, Ordinary Differential Equations, Dover, 2007; reprint of Academic Press 1982.
• David G. Schaefer & John W. Cain, Ordinary Differnetial Equations: Basics and Beyond, Texts in Applied Mathematics 65, Springer, 2010.
• Shlomo Sternberg, Dynamical Systems, Dover 2010.
• Michael Taylor, Introduction to Differential Equations, American Mathematical Society Pure and Applied Undergraduate Texts 14, 2010.

Texts Suitable for a Graduate Course for Students who have not Studied Measure Theory.

• Ravi Agarwal & Donal O'Regan, An Introduction to Ordinary Differential Equations, Springer Universitext, 2008.
• Vladimir Arnold, Ordinary Differential Equations, 3rd. ed., Springer Universitext, 1992.
• K. S. Bhamra, Ordinary Differential Equations: A Graduate Text, Alpha Science International Ltd., 2015.
• Luis Barriera and Claudia Valls, Ordinary Differential Equations: Qualitative Theory, American Mathematical Society Graduate Studies in Mathematics 137, 2010.
• David Betounes, Differential Equations: Theory and Applications, 2nd. ed., Springer 2010.
• Jane Cronin, Ordinary Differential Equations: Introduction and Qualitative Theory, 3rd. ed., CRC Press, 2008.
• Paul Glendenning, Stability, Instability and Chaos: An Introduction to the Theory of Nonlinear Differential Equations, Cambridge, 1994.
• John R. Graef, Johnny Henderson, Lingju Kong and Xueyan Sherry Liu, Ordinary Differential Equations and Boundary Value Problems Vol. 1: Advanced Ordinary Differential Equations, World Scientific Pub. Co. 2018.
• Christopher Grant, Theory of Ordinary Differential Equations(chapter index), pdf(158 pages), on-line lecture notes with Solutions.
• Sze-Bi Hsu, Ordinary Differential Equations with Applications 2nd. ed., World Scientific, 2013.
• James Hetao Liu, A First Course in the Qualitative Theory of Differential Equations, Prentice Hall 2003.
• D. W. Jordan and P. Smith, Nonlinear Ordinary Differential Equations-- An Introduction for Scientists and Engineers, 4th ed., Oxford, 2007.
• Lawrence Perko, Differential Equations and Dynamical Systems, Springer Texts in Applied Mathematics 7, 1991.
• Qinghai Kong, A Short Course in Ordinary Differential Equations, Springer Universitext, 2014.
• Thomas Sideris, Ordinary Differential Equations and Dynamical Systems, Atlantis Press, 2013.
• Stephen Salaff and Shing-Tung Yau, Ordinary Differential Equations, 2nd ed., International Press, 1998.
• David G. Schaeffer and John W. Cain, Ordinary Differential Equations: Basics and beyond, Texts in Applied Mathematics 65, Springer, 2016.
• Gerald Teschl, Ordinary Differential Equations and Dynamical Systems, Studies in Mathematics 140, American Mathematical Society Graduate 2012.
• Ferdinand Verhulst, Nonlinear Differential Equations and Dynamical Systems, 2nd. ed., Springer Universitext, 2006.
• Marcello Viana and Jose M. Espinar, Differential Equations: A Dynamical Systems Approach to Theory and Practice , American Math. Soc., Graduate Studies in Maathematics 212, Providence 2021.

Texts Suitable for a Graduate Course for Students who have Studied Measure Theory.

• Herbert Amann, Ordinary Differential Equations--An Introduction to Nonlinear Analysis, Walter de Gruyter, 1990.
• Carmen Chicone, Differential Equations with Applications, Springer Texts in Applied Mathematics 34, 1999.
• Earl A. Coddington and Norman Levinson, Theory of Ordinary Differential Equations, Krieger Publishing Company, 1984; reprint of McGraw Hill, 1955.
• Jack Hale, Ordinary Differential Equations, 2nd. ed., Dover 2009; reprint of Krieger 1980; re-reprint of John Wiley & Sons, 1969.
• Philip Hartman, Ordinary Differential Equations, 2nd ed., SIAM 2002; reprint of Birkhaüser, 1982; re-reprint of John Wiley & Sons, 1964.
• Fritz John, Ordinary Differential Equations, Courant Institute of Mathematics Lecture Notes, 1965.
• Klaus Schmitt and Russell Thompson, Nolinear Analysis and Differential Equations: An Introduction, University of Utah Lecture Notes 2009.pdf.(152 pages.)
• Wolfgang Walter, Ordinary Differential Equations, Springer Graduate Texts in Mathematics 182, 1991.

Specialist's Books on Specific Topics. Unsuitable for Math 6410.

• Richard Bellman, Stability Theory of Differential Equations, Dover 1969; reprint of McGraw-Hill, 1953.
• Theodore A. Burton, Stability and Periodic Solutions of ordinary Differential Equations, Dover 2005; reprint of Academic Press, Inc., 1985.
• John Guckenheimer & Philip Holmes, Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields, Applied Mathematical Sciences 42, Springer, 1983.
• Yuri Kuznetsov, Elements of Bifurcation Theory, 3rd. ed., Applied Mathematical Sciences 112, Springer, 2010.
• Stephen Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, 2nd ed., Springer Texts in Applied Mathematics 2, 2000.

Last updated: 8 - 2 - 23