Verifying Solutions to Differential Equations
Learn how to verify whether a function is a solution to a differential equation by differentiating, substituting, and checking that the equation is satisfied.
The Logistic Differential Equation: An Introduction
Understand the logistic differential equation, carrying capacity, equilibrium solutions, and how the logistic model describes population growth for AP Calculus AB & BC.
Solving Separable Differential Equations
How to solve separable differential equations step by step, including separation of variables, integration, initial conditions, and fully worked AP Calculus examples.
Sketching Slope Fields
Learn how to sketch slope fields for differential equations, interpret solution curves, and use slope fields to understand qualitative behavior in AP Calculus AB & BC.
Reasoning Using Slope Fields
Learn how to reason from slope fields, including estimating solution behavior, identifying increasing and decreasing intervals, equilibrium solutions, concavity, and initial-value solutions for AP Calculus AB & BC.
Practice Problem Set: Slope Fields and Euler’s Method
Practice slope fields and Euler
Practice Problem Set: Separable Differential Equations
Practice separable differential equations for AP Calculus AB & BC with worked solutions covering separation, integration, initial conditions, and interpreting solutions.
Practice Problem Set: Exponential and Logistic Growth
Practice exponential and logistic growth models with AP Calculus-style problems, worked answers, and applications of differential equations.
Newton’s Law of Cooling
Learn how to model heating and cooling with Newton
Modeling Situations with Differential Equations
Learn how to translate real-world situations into differential equations, identify appropriate models, use initial conditions, and interpret solutions for AP Calculus AB & BC.