Math 123: Ordinary Differential Equations

Instructor: Di Fang         Please read the Syllabus carefully!

Lecture: Tuesdays and Thursdays, 2:00--3:29pm, 3111 Etcheverry ⇒ Berkeley time!

Office Hours: Tuesday 3:40-4:39pm and Wednesday 3:00-3:59pm, 843 Evans Hall ⇒ Not Berkeley time!

Textbook: The Qualitative Theory of Ordinary Differential Equations by Fred Brauer and John A. Nohel.

Email: difang@berkeley.edu ⇒ Please kindly include Math 123 in the subject line when emailing.

 

Course Outline:

  • Teminology; Review: techniques and tricks; the need for theory
  • Theory of ODEs: existence, uniqueness, continuation.
  • Linear Systems (with an intro to phase space analysis)
  • Stability theory and Lyapunov method
  • Applications and additional topics as time permits, e.g. biological models (flocking of birds), control theory.
  • (Things are subject to change. Once it happens I will let you know.)

 

Week Tuesday Topics Thursday Topics HW (posted on bCourse)
    1 Policy, Philosophy, Terminology
(not all in book) Lecture Notes
None!  
Happy labor day!
    2 How to solve ODEs? A Review of some techniques from [Calc/54] -- Old and New Lecture Notes Review of techniques continued, some basic theorem/proof of the structure of the solution space, the need for theory [BN 1.5]
Lecture Notes
HW1 (due Sept 10th)
    3 (Picard's) Existence theorem & proof (under the Lipschitz condition) [BN 3.1] -- Picard iteration, Uniform Convergence Finish proof & (Peano's) Existence theorem, generalization to higher Dimension [BN 3.2], Gronwall Ineq [BN 1.7] & Uniqueness Theorem [BN 3.3]
HW2 (due Sept 19th)
    4 Continuation of Solutions, Global existence, a priori estimate [BN 3.4] Dependence on initial condition and parameters [BN 3.5], How equilibrium depends on parameter -- an intro to bifurcation analysis
Chaotic system (sensitivity of initial data) -> try it here!
HW3 (due Sept 26th)

 

 

True or False: I do not need to take notes in class, because Di will always post her notes.

False!! Di is posting the notes for the first three lectures for easier reference because it was a review and material is not in the book. So take notes after the first three lectures.

(By Di on Sept. 3)

Wecome to the class. Wish we have a pleasant and productive semester together!

Please email me about the time conflicts with the office hour by Monday (Sept. 1st), so that we could settle the final office hours.

(By Di on August. 30)