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

2. 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

3. 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.

4. 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.

5. 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).

6. 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)

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