Unit 7 Summary

AP Calculus · Axiom Academy

Review of differential equations Visual representation of a DE. Solution curves follow the segments. Isoclines show where slopes are constant. Numerical approximation: . Smaller steps = better accuracy. Factor as g(x)h(y) , separate, integrate both sides. Always apply IC to find C . dy/dt = ky gives y = y_0e^ kt . Know half-life and doubling time formulas. dP/dt = kP(1-P/L) gives sigmoid curve approaching L . Max growth at P = L/2 . General solution + initial condition = particular (unique) solution. Solutions don't cross.

This is the written version of the interactive lesson above. See the full AP Calculus course.