Chapter 7  Differential Equations and Mathematical Modeling"One of the early accomplishments of calculus was predicting the future position of a planet from its present position and velocity. Today this is just one of many situations in which we deduce everything we need to know about a function from one of its known values and its rate of change. From this kind of information, we can tell how long a sample of radioactive polonium will last; whether, given current trends, a population will grow or become extinct; and how large major league baseball salaries are likely to be in the year 2020. In this chapter, we examine the analytic, graphical, and numerical techniques on which such predictions are based."
(Finney, Ross L., Franklin D. Demana, Bert K. Waits, and Daniel Kennedy. "Chapter 7." Calculus: Graphical, Numerical, Algebraic. 5th ed. N.p.: Pearson Education, n.d. 329. Print. AP Edition.) 
Chapter 7 reallife math connection.

Lesson 7.1  Slope Fields and Euler's Method
This lesson will teach students to use slope fields to analyze solution curves to differential equations, and you will be able to use Euler's Method to construct solutions numerically. Lesson 7.2  Antidifferentiation by Substitution
This lesson will teach students to find antiderivatives of functions using the technique of substitution to reverse the effect of the chain rule in differentiation. Lesson 7.3  Antidifferentiation by parts
This lesson will teach students to find antiderivatives of functions using the technique of parts. 
Lesson 7.4  Exponential Growth and Decay
This lesson will teach students to solve separable differential equations, including those arising in problems of exponential growth, exponential decay, and logistic growth. Lesson 7.5  Logistic Growth
This lesson will teach students to solve the logistic differential equation using the technique of partial fractions and then by the general formula. 
Assessment Review Topics 
Scoring Practice 