## Math 123, Spring 2014

Instructor: Daniel Tataru

Lectures: TuTh 9:30-11:00 am, 71 EVANS

Course Control Number: 54183

Office: 841 Evans, e-mail: tataru@math.berkeley.edu

Office Hours: Tuesday 10:30-11:30 or by appointment

Prerequisites: Math. 104

Textbook: Hirsch, Smale and Devaney, Differential Equations, Dynamical Systems, and an Introduction to Chaos, third edition

Further reading: M.E. Taylor, Introduction to Differential Equations

Syllabus: The course provides a more elementary yet rigorous introduction to Ordinary Differential Equations. We begin with linear systems of equations, first in the plane and then in higher dimension. Then we move on to nonlinear systems and study the existence and uniqueness of solutions, equilibrium and stability, as well as the Poincare-Bendixson theorem. Finally we consider some applications to biology and mechanics. Additional topics will be covered as time permits.

Grading: 40% homeworks, 20% midterm, 40% final.

Homework: Homework for each week will be assigned online, and due every Tuesday. The two lowest homework grades will be dropped.

Midterm: Thursday March 13. Here is an earlier midterm I gave for Math 123. Note that it has no problems from sections 7 and 8; in our midterm you will definitely get a problem from these sections.

Final: Friday May 16, 7-10pm, in the regular classroom Evans 71. Here is an earlier final I gave for Math 123. Office hours during the exam week: Tue. May 13, 9:30-10:30am and 1-2pm.

Homework assignments:

 No: Due Date: Problems: 1. 1/28 p.16: 2,3,5,9,11,12 2. 2/4 p.38: 2,3,6,7,9; p.57: 1,2(i)(ii)(iv),4,6,9,13 3. 2/11 p.104: 2(c,e),3,5(c,g),8(b),11,14 4. 2/25 p.135:1,6,7,11(a),12 5. 3/11 p.157: 1ade, 2,5, 7, p 408: 4abce, 10,14 8. 4/1 p.184: 1,2,5,7,9 9. 4/15 p. 211: 1(c), 4,5,6,7b,8bcd 10. 4/24 p. 230: : 1(cd), 7,8,10 11. not due p. 301:1,5,7,9,10 12. 4/29