I can describe slope fields Quick Lesson Plan. First, understanding direction fields and what they tell us about a differential equation and its solution is important and can be introduced without any knowledge of how to solve a differential equation and so can be done here before we get into solving them. Students should be able to do these types of problems without using a graphing calculator. Slope Fields and Differential Equations Students should be able to: Draw a slope field at a specified number of points by hand.

Slope Fields Date_____ Period____ Sketch the slope field for each differential equation. This topic is given its own section for a couple of reasons. (it says some of my answers are wrong) Match the slope fields shown below with the differential equations: As I mentioned above, it would be impossible to produce a slope field covering the entire, infinite, Cartesian plane. Click and drag the points A, B, C and D to see how the solution changes across the field. The first differential equation, , is rather easy to solve, we simply integrate both sides.This type of differential equation is called a pure-time differential equation.Pure-time differential equations express the derivative of the solution explicitly as a function of an independent variable. Slope Fields and Differential Equations Students should be able to: Draw a slope field at a specified number of points by hand. Any curve that follows the flow suggested by the directions of the segments is a solution to the differential equation. Solving 2 dy x dx = means “Name a function whose derivative is 2x”. Slope Fields on the AP Exams The availability of technology to draw slope fields is relatively new. Consider the following differential equations . (b) Sketch a solution curve that passes through the point (0, 1) on your slope field. Sketch a solution that passes through a given point on a slope field. Autonomous differential equations. (a) On the axes provided, sketch a slope field for the given differential equation. The Length slider controls the length of the vector lines. I can create a slope field given a differential equation in terms of one or two variables. Activity: Wiki Stix Slope Fields & 3x3 Match-Up Wiki Stix.
Draw conclusions about the solution curves by looking at the slope field. Match a slope field to a differential equation. Consider the following example: The slope, y'(x), of the solutions y(x), is determined once we know the values for x and y, e.g., if x=1 and y=-1, then the slope of the solution y(x) passing through the point (1,-1) will be . AP Slope Fields Worksheet Key S. Stirling 2011-12 Page 1 of 7 AP Slope Fields Worksheet Slope fields give us a great way to visualize a family of antiderivatives, solutions of differential equations. _____ 18. Some textbooks do not mention slope fields, so this is a topic that may need supplementing. Answers might includey =x2, yx=+2 3, yx= 2 −4, and so forth. Here's an online tool for drawing slope fields: You will be asked to match slope fields with their differential equations, or to match differential equations with their slope fields. A little practice looking at slope fields …

Let's continue to use the example of finding a slope field for the differential equation: dy/dx = x 2.

However, it is easy to calculate the slopes of these curves. Consider the differential equation givenby oy dx 2 (A) On the axes provided, sketch a slope field for the given differential equation. 3x3 Match-up. Slope fields are visual representations of differential equations of the form dy/dx = f(x, y). Differential Equations and Separation of Variables A differential equation is basically any equation that has a derivative in it. If you're seeing this message, it means we're having trouble loading external resources on our website. Work on the relationship between differential equations and the slope field that represents them. If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. Match a slope field to its differential equation. Sketch a solution that passes through a given point on a slope field. Overview. This section contains: Differential Equations and Separation of Variables Slope Fields When you start learning how to integrate functions, you’ll probably be introduced to the notion of Differential Equations and Slope Fields. Discover any solutions of the form y= constant. Match a slope field to its solution. Write an equation for the tangent line to the curve y (x) through the point (1, I). 1) dy dx = x x y −2 −1 1 2 −2 −1.5 −1 −0.5 0.5 1 1.5 2 2) dy dx = − x y x y −2 −1 1 2 −2 −1.5 −1 −0.5 0.5 1 1.5 2 For each problem, find a differential equation that could be represented with the given slope field. Section 1-2 : Direction Fields. Instead, for our example, let's restrict the section of the plane we consider to: -2 ≤ x ≤ 2, and -2 ≤ y ≤ 2 . Our stroll through the slope fields above gave some examples of things you can look for.

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