Math 303: Fall 2007 Midterm 1: Review Sheet Summary: Math 303: Fall 2007 Midterm 1: Review Sheet No calculators, notes, or books will be allowed on the mid-term. The exam will consist of around 7 questions and last 55 minutes. It is essential that you clearly and neatly show all work in order to receive full or partial credit on the problems. Remember that your goal should not just be to arrive at the correct answer; you should convince the grader that you arrived at your answer by a correct (and followable) method. For Midterm 1, you may be asked to: · Write a differential equation which models a situation in the natural world. · Solve a first-order differential equation. This includes separable, linear, homogeneous, and exact equations. You should know how to find a general solution and solve an initial value problem. · Reduce certain second-order equations to first-order equations. · Find equilibrium solutions and their stability. You should understand their relationship to a physical situation which the equation models. · Determine the existence and uniqueness of solutions for a first-order equa- tion. The best way to study is by working problems, both old and new. Please review your old homeworks, including any comments, and work out new problems as Collections: Mathematics