Ch 12: Differential Equations & Applications

About This Chapter

Let us help you boost your understanding of differential calculus and its applications and equations with this chapter. Use these lessons and videos to build confidence in the subject before you take a placement exam or complete a homework assignment.

Differential Equations & Applications - Chapter Summary

Our instructors will define differential calculus and explain its varied applications. The concepts of separation of variables and how to calculate exponential growth are discussed. You will also learn how to solve seemingly complicated problems involving the distance between two moving points by using differentiation.

As you move through the lessons, several methods you can use to solve systems of linear differential equations are also covered. This chapter will teach you to:

  • Describe how differential equations describe what is happening in the world around you
  • Use the separation of variables technique to solve equations
  • Understand how differential equations predict exponential growth
  • Solve the draining tank problem
  • Define the Newton-Raphson method
  • Outline several ways to solve linear differential equations

Our instructors are available to help you as you move through the lessons. Simply contact one of them if you need additional help. You can access these study materials at any time, 24 hours a day, seven days a week. Use the quizzes and tests to measure how well you've retained the information that you've learned.

9 Lessons in Chapter 12: Differential Equations & Applications
Test your knowledge with a 30-question chapter practice test
Differential Calculus: Definition & Applications

1. Differential Calculus: Definition & Applications

This lesson is an introduction to differential calculus, the branch of mathematics that is concerned with rates of change. If you ever wanted to know how things change over time, then this is the place to start!

Differential Notation in Physics

2. Differential Notation in Physics

Stop. Look around. Everything is changing. In this lesson, you'll learn what a differential equation is and how these equations can describe the world around you.

Separation of Variables to Solve System Differential Equations

3. Separation of Variables to Solve System Differential Equations

In this lesson, we discuss how to solve some types of differential equations using the separation of variables technique. We'll ponder the dastardly deeds of a mad scientist, using his chemical concoction as an example for how to use separation of variables.

Calculating Rate and Exponential Growth: The Population Dynamics Problem

4. Calculating Rate and Exponential Growth: The Population Dynamics Problem

You know how the world population keeps increasing? It's increasing faster now than it was 100 or 1,000 years ago. In this lesson, learn how differential equations predict this type of exponential growth.

Related Rates: The Draining Tank Problem

5. Related Rates: The Draining Tank Problem

Grab an empty cup and pour some water into it. In this lesson we will watch how the height of the water changes as we learn about related rates of change and learn how to solve the draining tank problem.

Related Rates: The Distance Between Moving Points Problem

6. Related Rates: The Distance Between Moving Points Problem

Remember the classic problem of math horror stories everywhere? You know, where one train leaves Kentucky at 2 p.m. and another leaves Sacramento at 4 p. m.? In this lesson, tame the horror and learn how to solve these problems using differentiation and related rates.

Newton-Raphson Method for Nonlinear Systems of Equations

7. Newton-Raphson Method for Nonlinear Systems of Equations

Solving a system of nonlinear equations might sound complicated! But anyone who can multiply and add can get a solution by following the Newton-Raphson method. In this lesson, we will explain step-by-step just how this is done.

Solving Systems of Linear Differential Equations

8. Solving Systems of Linear Differential Equations

In this lesson, we will look at two methods for solving systems of linear differential equations: the eigenvalue method and the Laplace transform method.

Solving Systems of Linear Differential Equations by Elimination

9. Solving Systems of Linear Differential Equations by Elimination

Solving linear differential equations may seem tough, but there's a tried and tested way to do it! We'll explore solving such equations and how this relates to the technique of elimination from algebra. We will also solve a population growth system problem using what we've learned.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
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Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
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