7 Introduction to Differential Equations

In this module, you will be introduced to differential equations. The module content is split into four lessons.

Lessons

• Lesson 4.1: Differential Equations

• Lesson 4.2: Exponential Growth and Decay

• Lesson 4.3: Other Elementary Differential Equations

• Lesson 4.4: Introduction to Direction Fields (also called Slope Fields)

Module Start & End Dates

See your course syllabus for module start and end dates.

Show Your Work Problems

Module 4 assignment

Other Information

Project 4:

• 1. Do a search on the internet to find fairly reliable estimates for the world's human population in the years 1960, 1970, 1980, and 1990.

  2. Assuming that the world's human population follows an exponential model P(t)=P₀e^kt, use the 1960 figure as the initial population P0 and the 1970 population figure to find k, the growth rate constant. Note that if t is measured in years and 1960 is the starting year, 1970 corresponds to t=10.

  3. Compare the populations you found for 1980 and 1990 in part 1 to the values the exponential model you found in part 2 would have predicted.

  4. Do a search on the internet to find what you consider to be a reliable estimate of the carrying capacity of the earth. Use the model in #2 to estimate when we will reach the carrying capacity.