Math 212: Exam I Preparation - Topics and Review, Exams of Differential Equations

Download Math 212: Exam I Preparation - Topics and Review and more Exams Differential Equations in PDF only on Docsity! Math 212: Exam I Review Exam I will be on Friday February 13 and it will cover sections 1.1-1.3, 2.1-2.8, and maybe 7.1 from the textbook. Your homework for the week is also due on Friday. These are some of the things I expect you to be able to do on the exam. (1) Identify different types of differential equations (1.3) (2) Model real world situations with differential equations (1.2, 2.3) (3) Sketch and interpret direction fields (1.1) (4) Use the methods we have discussed to solve a first order equation (1.2, 2.1, 2.2, 2.6) • integrating factors • separation of variables • homogeneous equations • exact equations • integrating factors to make an equation exact (5) Determine the interval on which a solution to a linear or nonlinear equation exists (2.4) (6) Understand autonomous equations (2.5) • solve them • sketch the graph (y, f(y)) • sketch the phase line • sketch solutions • equilibrium solutions and stability • determine concavity of solutions (7) Approximate a solution with Euler’s method and Picard’s method (2.7, 2.8) (8) (Maybe) change an equation of order n into n different first order equations and vice versa (7.1) The best way to study for the exam is to do as many problems as you can stand. Redo the homework problems and other problems like them. On Wednesday before the exam class will be devoted to answering questions. So if you have questions, bring them to class on Wednesday. You will not be allowed to use your calculator on the exam. You will not need to simplify your answers. But you will need to show all of your work: you will not receive credit if you do not show your work. 1