Calculus Separation of Variables with Lesson Video (Unit 7)

Separation of Variables and Differential Equations Lesson:

Your AP Calculus AB and BC students will use separation of variables to find general solutions of differential equations. They will use initial conditions to find particular solutions of differential equations.

What is included in this resource?

⭐ Guided Student Notes

⭐ Fully-editable SMART Board® Slides

⭐ Google Slides®

⭐ Homework/Practice assignment

⭐ Content quiz

⭐ Video Lesson Link for Distance Learning - Flipped Classroom models

⭐ Full solution set

Lesson Objective:

★ Use separation of variables to solve simple differential equations.

College Board® Topics:

Topic 7.6: Finding General Solutions Using Separation of Variables

Topic 7.7: Finding Particular Solutions Using Initial Conditions and Separation of Variables

College Board® Learning Objectives:

FUN-7: Solving differential equations allows us to determine functions and develop models.

FUN-7.D: Determine general solutions to differential equations.

FUN-7.D.1: Some differential equations can be solved by separation of variables.

FUN-7.D.2: Antidifferentiation can be used to find general solutions to differential equations.

FUN-7.E: Determine particular solutions to differential equations.

FUN-7.E.1: A general solution may describe infinitely many solutions to a differential equation. There is only one particular solution passing through a given point.

FUN-7.E.2: The function F defined by F(x)= y_0+∫1_a^xf(t) dt is a particular solution to the differential equation dy/dx=f(x), satisfying F(a)=y.

FUN-7.E.3: Solutions to differential equations may be subject to domain restrictions.

The unit includes:

1) Intro to Differential Equations

2) Slope Fields

3) Separation of Variables

4) Exponential Models with Differential Equations

5) Euler's Method (BC Only)

6) Logistic Growth (BC Only)

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AP® is a registered trademark of the College Board® which was not involved in the creation of, and does not endorse this product.

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