Reading Assignments for the Differential Equations Unit TTH version The main ideas and skills you should take away from this part of the course include Modeling a situation using a differential equation or system of differential equations Knowing what it means to be a solution to a differential equation Being able to do qualitative analysis of solutions and being able to interpret solutions particularly for autonomous differential equations and systems This includes recognizing the difference between y f t and y f y Solving separable and first order linear differential equations Solving 2nd order homogeneous differential equations with constant coefficients 17 For Tuesday November 30 No homework give thanks 18 For Thursday December 2 Section 7 1 Modeling with Differential Equations Section 7 2 Direction Fields and Euler s Method Section 7 3 Separation of Variables Reading All of 7 1 In 7 2 skip Euler s method Read up until the middle of p 516 In 7 3 read pp 522 524 This means that in these three sections you ll read 11 pages in all Key areas of focus What is a differential equation What does it mean to be a solution to the differential equation What is the difference between a general solution and a particular solution How can the differential equation itself give you information about the solutions Understand direction fields and their relation to the differential equation and its solutions Begin to be familiar with modeling In 7 3 Learn the technique of separation of variables Reading Questions 1 7 1 1 3 4 2 7 3 6 3 What was the most confusing thing about the reading This question is now optional Read below Based on the midterm questionnaire responses we will do an experiment for this differential equations unit You do NOT need to answer the what is the most confusing thing question in order to get the pre class reading question credit Instead the credit will be based on whether or not you take a good try at the content pre class questions If you have questions and want them addressed in class get them in before the 11 00 pm deadline on your section s website You will NOT lose credit for not entering questions on the reading in the section website Let s also expand this questions part so that you can write in questions on the material from the previous class as well as on the pre class reading on the condition that you did indeed attend that previous class Let s see how this goes If you have questions about this change in policy please ask your section leader directly 19 For Tuesday December 7 Section 7 3 Separation of Variables p 526 7 Section G 31 3 Qualitative Analysis of Solutions to Autonomous Differential Equations Key areas of focus Focus on the material in the supplement 7 3 Orthogonal trajectories pp 525 6 are fascinating and are very useful in physics but we won t devote course time to them Let your interests determine how diligently to read that part Pay attention to p 526 7 we do want you to be able to do mixture problems You might want to supplement the page in Stewart with pp 1011 1014 in the Supplement Reading Questions 1 What does it mean for a first order differential equation to be autonomous 2 7 5 1a just the carrying capacity don t worry about k and 1b use the direction field to help you answer this There is no need to read 7 5 in order to do this The supplement will be fine 3 Optional What was the most confusing part of the reading 20 For Thursday December 9 Section 7 4 Exponential Growth and Decay Section 7 5 Logistic Growth Class will be on material given on a handout on Solving First Order Linear Differential Equations supplements page You can read this before class or after class as you see fit There are no pre class reading questions on this material Reading In 7 4 read the whole thing for the gist of it and especially look at continuously compounded interest so you see the non differential equation perspective on it Our perspective in class will be different from that in the text In 7 5 read all except p 543 Euler s method Key areas of focus We ve covered 7 4 and 7 5 from a different perspective Take a look at how Stewart talks about these topics De emphasize pp 546 7 Reading Questions 1 7 4 2 2 Optional What was the most confusing part of the reading 21 For Tuesday December 14 Section G 31 5 Systems of Differential Equations Section 7 6 Predator Prey Reading Questions 1 Look at example 31 24 on p 1025 Explain what it mean to say that in the Figure 31 19 each of the horizontal lines correspond to three different trajectories For the sake of being concrete look at the horizontal line at y 10 2 31 5 1 3 7 6 4a 4 Optional What was the most confusing part of the reading 22 For Thursday December 16 Section G 31 6 Second Order Homogeneous Differential Equations with Constant Coefficients p 1045 1047 Reading pp 1045 1047 Reading Questions 1 Solve y 4y 5y 0 2 Optional What was the most confusing part of the reading 23 For Tuesday December 21 Section G 31 6 Second Order Homogeneous Differential Equations with Constant Coefficients pp 1047 1049 Reading Questions 1 At this point in the course right about at the end you know how to solve separable first order linear and second order homogeneous constant coefficient differential equations What is the method for solving each of the types Write it down for yourself and turn it in 2 Some first order linear differential equations are also separable Give an example of one Would it be easiest for you to solve it as a first order linear or as a separable differential equation 3 Optional What was the most confusing part of the reading