Differential Equations
IntermediateDifferential equations relate a function to its derivatives. This topic covers separable DEs, slope fields, Euler method, and exponential models for AP Calculus AB Unit 7.
Key concepts in this area include Differential Equation, Separable DE, Slope Field, and Euler Method. Differential Equation refers to an equation involving a function and its derivatives. Separable DE, meanwhile, involves a DE writable as g(y)dy = f(x)dx.
By studying differential equations, learners develop the ability to verify solutions by substitution and solve separable DEs analytically. These skills build analytical thinking and prepare students for more advanced work in Mathematics.
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Learning objectives
- •Verify solutions by substitution
- •Solve separable DEs analytically
- •Sketch and interpret slope fields
- •Apply Euler method
- •Model exponential growth/decay
- •Solve initial value problems
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