AP®︎ Calculus AB Unit 7: Notes & Study Guide
Prepare for your quiz, test, or the AP exam with a comprehensive review on Unit 7 of AP Calculus AB – Differential Equations.
Unit 7: Differential Equations
Solve separable differential equations and model exponential growth with slope fields.
Begin with Topic 7.1: Modeling Situations with...To review Unit 7, go through each of the 7 topics below.
Everything you actually need to know for your Unit 7 test, pulled directly from the AP® Calculus AB curriculum.
Modeling Situations with Differential Equations
Modeling Situations with Differential Equations
- What a Differential Equation Is in a Modeling Context
- Translating Verbal Statements into Differential Equations
- Finding the Constant of Proportionality \(k\)
Verifying Solutions for Differential Equations
Verifying Solutions for Differential Equations
- What It Means to Be a Solution to a Differential Equation
- General Solutions and Families of Curves
- How to Verify a Solution
Sketching Slope Fields
Sketching Slope Fields
- What a Slope Field Is
- How to Construct a Slope Field by Hand
- Sketching a Solution Curve
Reasoning Using Slope Fields
Reasoning Using Slope Fields
- What a Slope Field Shows
- Solutions Are Functions and Families of Functions
- Estimating Solutions from a Slope Field
Finding General Solutions Using Separation of Variables
Finding General Solutions Using Separation of Variables
- What a General Solution to a Differential Equation Is
- Separable Differential Equations
- The Separation of Variables Process
Finding Particular Solutions Using Initial Conditions and Separation of Variables
Finding Particular Solutions Using Initial Conditions and Separation of Variables
- General vs. Particular Solutions
- Separation of Variables with an Initial Condition
- Writing a Particular Solution as an Integral
Exponential Models with Differential Equations
Exponential Models with Differential Equations
- The Exponential Differential Equation
- Solving the Equation
- Finding a Particular Model from Data
Notes
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