MATH 4B Midterm 1 Study Guide - MATH 4BDifferential...

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MATH 4B–Differential Equations, Spring 2016 Midterm 1 Study Guide GENERAL INFORMATION AND MIDTERM RULES The exam will have a duration of 50 minutes. No extra time will be given since there are classes in the classroom right after us. Failing to submit your solutions within 50 minutes will result in your exam not being graded. The material included for the first midterm corresponds to everything we have covered until Monday, April 11. The sections are 1.1–1.3, and 2.1–2.6. You can bring ONE index card of dimensions up to 4 00 × 5 00 . This index card should be handwritten and can be filled on both sides. However, note cards of higher dimensions than the ones mentioned above or typewritten WILL NOT be allowed. Calculators WILL NOT be needed, nor allowed for this exam. Last but not least, CHEATING WILL NOT BE TOLERATED. 1
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THINGS YOU NEED TO KNOW What is the order of an Ordinary Differential Equation (ODE). What is an Initial Value Problem (IVP). How to verify that something is a solution for an IVP. How to sketch the direction (slope) fields of an ODE. How to find equilibrium solutions for an Autonomous ODE, and determine if the equilibrium solution is semistable. How to identify separable equations. How to solve a separable ODE, and how to find the unique solution for a given IVP when the equation is separable. How to identify a linear ODE. How to find its integrating factor and corresponding solution. How to find the unique solution to a given IVP with linear ODE. How to determine if an ODE is exact. How to solve an exact ODE. How to read information from a word problem, and how to establish the corresponding ODE modeling the situation in the following cases: 1. Free falling object.
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