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# review_1 - ODE(Section 2.5 6 Separable nonlinear ODE how to...

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Review list for Test 1, Math 2214 1. Basic concepts: order, linearity, autonomous ODE, homogenous ﬁrst order ODE, so- lution of an ODE, equilibrium solution. (Sections 1.2, 1.3) 2. Sketch of the direction ﬁeld for an ODE y 0 ( t ) = f ( t,y ( t )). How to read a direction ﬁeld? (Section 1.3) 3. Find the interval in which the IVP of a ﬁrst linear ODE has a unique solution. (Section 2.1) 4. What is the integrating factor and how to use it to ﬁnd the general solution of a linear ODE: y 0 + p ( t ) y = g ( t ) . How to use the general solution to solve the related IVP. (Section 2.2) 5. Determine the rectangle in the t - y plane to which the Theorem 2.2 can be applied to guarantee the existence and uniqueness of an IVP of a ﬁrst order nonlinear
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Unformatted text preview: ODE. (Section 2.5) 6. Separable nonlinear ODE, how to ﬁnd its general solution, and how to solve the related IVP. Implicit solution and explicit solution. (Section 2.6) 7. Set up the IVP of a ﬁrst order ODE to model certain procedures (decay, mixing, 1-D motion, etc.) (Sections 2.3, 2.4, 2.9) 8. Euler’s method for numerically solving IVP (Section 2.10): y = f ( t,y ) , y ( t ) = y . Note: • It is critical to review diﬀerentiation of simple functions and computing partial deriva-tives. • It is critical to review integration of simple functions and some of the basic integration techniques such as Integration by Parts and Change of Variable. 1...
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