Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Schrödinger equation wikipedia , lookup
Debye–Hückel equation wikipedia , lookup
Two-body problem in general relativity wikipedia , lookup
Derivation of the Navier–Stokes equations wikipedia , lookup
Maxwell's equations wikipedia , lookup
Schwarzschild geodesics wikipedia , lookup
Calculus of variations wikipedia , lookup
Equations of motion wikipedia , lookup
Differential equation wikipedia , lookup
Warm Up NO CALCULATOR Homework Answers pg366 x2 1) y 2x C 2 3) y Ce x 2 1 2 5 2 5) y x C 2 2 7) y Ce (2/3)x3/2 2 9) y C (1 x ) x2 2) y 4x C 2 4) y 4 Ce x 3 2 2 32 6) y x C 2 3 8) y Ce 10) y Ce x2 /2 x2 /2 1 100 Pg378 2 x 55) y 2e 14 60) 1 y2 1 x2 1 1 58) y (ln x)2 2 2 64) y 70e kt 70 Slope Fields A slope field is a graphical picture of a derivative that projects the curve within the picture. Or a bunch of little line segments that show the slope of the curve (y = ) at different points. dy 1 x 1 dx 2 The slope field for a certain differential equation is shown. Which of the following could be a particular solution to that differential equation? y = x2 y = ex y = e –x y = cos x y = ln x Make your own slope field… dy x dx 2y x -2 -2 -1 y 0 1 2 -1 0 1 2 Make your own slope field… dy x dx 2y Sketch a short line segment with the slope at each point. Where are the tangent lines horizontal? Why? Where are the tangent lines vertical? Why? dy x dx 2y Solve the differential equation to find the particular solution with initial condition y(1) = 2. Sketch the particular solution on your slope field. Group Activity Make your own… Student 1 dy 1 y dx Student 3 dy 2 y dx Student 2 dy 1 x dx Student 4 dy 2 x dx • What do you notice about the slope fields whose differential equation had only x’s? • What do you notice about the slope fields whose differential equation had only y’s? How to pick out a multiple choice answer (equation) for a slope field… • pay attention to whether you need just the x- or y-values or both • Look for places where the slope is 0 • Look at the slopes along the x-axis (where y = 0) • Look for slopes along the y-axis (where x = 0) • Notice where the slopes are positive and where they are negative Shown is a slope field for which of the following differential equations? A) B) dy 1 y dx dy 2 y 2 dx x dy C) y2 dx dy x D) dx y dy E) yx dx Shown is a slope field for which of the following differential equations? dy x y dx dy x2 dx dy ey dx dy x y dx dy 2x dx y Which of the following differential equations matches the slope field given? dy 1 x dx dy x y dx dy ln y dx dy 2 x dx dy x dx y Which of the following differential equations matches the slope field given? dy y dx dy 1 x 1 dx 2 dy 2 xy dx dy y dx x dy x dx