AP Calculus BC April 18, 2016 Mr. Agnew Modeling with Differential Equations AP Calculus BC April 18, 2016 Mr. Agnew

Essential stuff Essential Question Essential Vocabulary What is a differential equation and how do you find the solution to a differential equation? Essential Vocabulary Differential Equation Models of population growth Integration Family of Functions

Modeling with Differential equations Differential equations is an important application of calculus Differential Equation: an equation that contains an unknown function and some of its derivatives Real world problems involve change; we want to predict future behavior on the basis of current change values.

Differential equations The order of a differential equation is the order of the highest derivative that occurs in the equation. A function f is called a solution of a differential equation if the equation is satisfied when y = f(x) and its derivative are substituted into the equation. When solving a DE, you must find all possible solutions of the equation.

Familiar d.E. problems Find all functions y that satisfy dy/dx = sec2x + 2x + 5 Find a particular solution to the equation dy/dx = ex – 6x2 whose graph passes through the point (0,1).

Solving D.E. Problems When solving differential equations, we typically look for a solution that satisfies some additional requirement. Also known as the “initial condition” Guided Practice page 511 – 512 #2 – 10 (Even)

Homework: April 18, 2016 Page 511 – 512 #1 – 11 (Odd)