# Math 3410,  Spring 2019

There will be a midterm and a final, plus 4 quizzes.
Tentatively, homework 10%, each quiz 10%, midterm 20%, final 30%

Tentative dates: 2/5 (quiz), 2/19 (quiz), 3/12 (midterm), 4/9 (quiz), 4/30 (quiz), final exam
All of them on Tuesday.

Roughly, quizzes last for around 25-30 minutes. Midterm runs for the whole 75 minutes.
Homework policy will be announced later.

#### The exact outline will be updated as we go along.

 Week Section Topic Homework Exercises (turn in the red color ones) Lecture date H/W Due date Quiz/exam date Study guide 1 Read Chapter 4; theorems 4.1.2, 4.1.3, 4.2.1, 4.2.2. revision on existence and uniqueness of ODE 1/22 Read section 5.5 (p.93-100) revision on linear constant coeff  homogeneous ODE 1/24 p.119: B1-3, 8,14, 18, 24 5.1 linear homogeneous equations 1/24 2 5.2 linear independence and Wronskian 1/29 p.119: A2, A3, A10, A11 2/5 2/5 Quiz Constant coeff linear homogeneous ODE, definitions of linearly independence and Wronskian, use Abel's Theorem. 5.3 reduction of order 1/31 3 5.4.1 variation of parameter 2/5, 2/7 p.119: use variation of parameter to solve: C7 (cf example 5.4.5), 13, 17 5.5.1 Euler equation 2/7 p.119: D18, 19 2/12 5.6 Will skip that. But I expect you already know method of undetermined coeff. Do some revision and reading. 4 5.7 oscillatory behavior 2/12, 2/14 p.119: D1, 5, 6 2/19 5 5.8 nonlinear 2nd order eqn 2/19 p.119: D11 2/26 2/19 Quiz Reduction of order, Euler equation, variation of parameter 7.3 Wronskian of a system 2/21 6 7.4 revision on 1st order linear constant coeff homogeneous system and phase plane. Read 7.4 (for 2 by 2 systems) or your old text 2/21, 2/26 p.163: A4, B2, 3, 4, B11, D1 3/5 7 8.1 planar Hamiltonian system 2/28, 3/5 p.185: 6, 8, 10 3/14 8.2 prey-predator system 3/7 p.185: 14 3/14 8.3 phase plane analysis 3/7 8 3/12 3/12 Midterm. Covers Ch 5 and 7. Mainly on material after 2nd quiz, i.e. 5.7, 5.8.1, 5.8.2, 7.3, 7.4 Definition of oscillating solutions; Definitions of linearly independence and Wronskian for vector functions; 8.4 On x''=f(x) 3/14 3/17- 3/23 Spring Break 9 8.4 On x''=f(x) 3/26 p.185: 11, 20, 21, 30 3/28 more examples on x''=f(x); motivation of eigenfunction problem 3/28 10 Example 9.2.1 We deviate from the text. Basically we study 1 important example in depth. 4/2 p.196: 10, 11 4/4 Not in the text numerical series; series of functions 4/2 Not in the text brief discussion of Sturm Liouville Theorem 4/4 11 9.3 heat equation 4/9, 4/11 p.196: 16 4/16 4/9 Quiz Covers all  of Ch 8. That is, Hamiltonian systems, predator-prey, phase plane analysis. Formula for predator-prey is given in the revised formula sheet. Expect at least 1 problem for phase plane. Not in the text wave equation 4/11 12 10.2 power series 4/16 10.3 ordinary point 4/18, 4/23 p.223: 4 4/25 13 10.4 Frobenius method 4/23 10.4 4/25 p.223: 1, 7, 8 5/2 4/30 Quiz One question on the heat equation, the other on ordinary point. Calculate at least 3 non-zero terms in each power series. 14 10.5 Bessel equation 4/30 10.5 last date of class 5/2 p.223: 9, 10