290Afall 2010

Math 290A: Methods in Applied Mathematics. Lec A

Meeting Information

• Room: RH440R
• Time: M W F 8:00 am - 8:50 am
• Office hour: Tu Th 9:00 am - 10:00 am
• Mail List: 45150-F10@classes.uci.edu

Homework

Only 5 problems will be graded.

1. Ch1 - S1.1: 5; S1.2: 3(a), 6; S1.3: 4, 6(c), 8; S1.4: 6; S1.5: 3,4; S1.7: 4(a); S1.10: 3.
   Due: Oct 12.
2. Ch2 - S2.2: 1(a), 3, 5; S2.3: 2(a), 3, 5, 6*; S2.4: 2(a), 5; S2.5: 1, 5; S2.6: 2.
   Due: Oct 22.
3. Ch2 - S2.7 3, 6; S2.9 2(b), 4(c); Ch3 - S3.1 2, 5, 6; Sec 3.2 1, 4, 5.
   Due: Nov 3
4. Ch3 - S3.3 1(a), 3(b); S3.4 2, 3(b); S3.5 1, 6; S3.7 1, 6(a), 7; Ch4 - S4.1 2, 3(a), 10
   Due: Nov 24.

Exam

1. Take-home Exam. Due: Dec 10. Please make an appointment to present your solutions.
2. There will be a in-class exam on Dec 10 right after the lecture. More information will be provided soon.

Textbook

This textbook presents a systematic study of the qualitative and geometric theory of nonlinear differential equations and dynamical systems. Although the main topic of the book is the local and global behavior of nonlinear systems and their bifurcations, a thorough treatment of linear systems is given at the beginning of the text. All the material necessary for a clear understanding of the qualitative behavior of dynamical systems is contained in this textbook, including an outline of the proof and examples illustrating the proof of the Hartman-Grobman theorem, the use of the Poincare map in the theory of limit cycles, the theory of rotated vector fields and its use in the study of limit cycles and homoclinic loops, and a description of the behavior and termination of one-parameter families of limit cycles. In addition to minor corrections and updates throughout, this new edition includes materials on higher order Melnikov theory and the bifurcation of limit cycles for planar systems of differential equations, including new sections on Francoise's algorithm for higher order Melnikov functions and on the finite codimension bifurcations that occur in the class of bounded quadratic systems.

Schedule

• Linear Systems. 1 week.
• Nonlinear Systems: Local Theory. 3.5 weeks.
• Nonlinear Systems: Global Theory. 3 weeks.
• Nonlinear Systems: Bifurcation Theory. 2.5 weeks.

Grading

Your course grade will be determined by your cumulative average at the end of the term:

• 50% Homework
• 50% Final Exam/Project