AP®︎ Calculus BC Unit 7: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 7 of AP Calculus BC – Differential Equations.
Unit 7: Differential Equations
Solve separable differential equations and model exponential/logistic growth.
Begin with Topic 7.1: Modeling Situations with...To review Unit 7, go through each of the 9 topics below.
Everything you actually need to know for your Unit 7 test, pulled directly from the AP® Calculus BC curriculum.
Modeling Situations with Differential Equations
Modeling Situations with Differential Equations
- What a differential equation is
- Identifying the rate
- Proportional relationships
Verifying Solutions for Differential Equations
Verifying Solutions for Differential Equations
- What It Means to Be a Solution to a Differential Equation
- The Verification Process
- General Solutions and Families of Curves
Sketching Slope Fields
Sketching Slope Fields
- What a slope field is
- How to sketch a slope field
- Recognizing common patterns
Reasoning Using Slope Fields
Reasoning Using Slope Fields
- What a Slope Field Shows
- Sketching and Estimating a Solution
- Critical Points and Equilibrium Solutions
Approximating Solutions Using Euler’s Method
Approximating Solutions Using Euler’s Method
- Euler’s Method
- Running the Algorithm
- Why It Works
Finding General Solutions Using Separation of Variables
Finding General Solutions Using Separation of Variables
- What a General Solution to a Differential Equation Is
- What Makes a Differential Equation Separable
- How to Solve by Separation of Variables
Finding Particular Solutions Using Initial Conditions and Separation of Variables
Finding Particular Solutions Using Initial Conditions and Separation of Variables
- General solution vs particular solution
- Writing a particular solution with an integral
- Separation of variables with an initial condition
Exponential Models with Differential Equations
Exponential Models with Differential Equations
- The exponential growth and decay differential equation
- Solving \( \frac{dy}{dt} = ky \)
- Interpreting the model in context
Logistic Models with Differential Equations
Logistic Models with Differential Equations
- The Logistic Differential Equation
- Equilibrium Values and Carrying Capacity
- When the Population Is Growing Fastest
Notes
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