MATH 220- Midterm Exam Guide - Comprehensive Notes for the exam ( 33 pages long!)
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What is a differential equation: a differential equation is any equation that contains derivatives, both regular and partial derivatives count. Most people probably know a differential equation (or two!) off the top of their heads. Most of you probably know this equation from an introductory physics course. But you may be saying, hey wait a minute! I don"t see any derivatives! and to that i say, You don"t see any derivatives yet. that will soon change. Recall that acceleration is the derivative of velocity with respect to time. It is also the second derivative of position with respect to time or to put it in calculus terms: And now we have our first differential equations of this course: (cid:1853)=(cid:3049)(cid:3047) and (cid:1853)=(cid:3118)(cid:3046)(cid:3047)(cid:3118) More examples of diff eqs: (cid:1853)(cid:1877) +(cid:1854)(cid:1877) +(cid:1855)(cid:1877)=(cid:4666)(cid:4667) sin(cid:4666)(cid:1877)(cid:4667)(cid:3118)(cid:3052)(cid:3051)(cid:3118)=(cid:4666)(cid:883) (cid:1877)(cid:4667)(cid:3052)(cid:3051)+(cid:1877)(cid:2870) (cid:2873)(cid:3052) (cid:3119)(cid:3048)(cid:3118)(cid:3051)(cid:3047)=(cid:883)+(cid:3048)(cid:3052) The order of a differential equation is the largest derivative found in the equation.