Ch 12: Fundamental Principles of Calculus

About This Chapter

Watch the engaging video lessons in this chapter to strengthen your knowledge of the fundamental principles of calculus. Our lessons, along with mini quizzes and a practice exam, can ensure you're ready and able to excel on an upcoming test.

Fundamental Principles of Calculus - Chapter Summary

Our instructors closely examine the fundamental principles of calculus, making it easy to improve your understanding of slopes, limits, derivatives and much more. By exploring entertaining video lessons, you will be prepared to do the following in no time:

  • Define limits using a graph
  • List and describe the properties of limits
  • Exhibit knowledge of slopes and the rate of change
  • Provide a description of the fundamental theorem of calculus
  • Calculate the derivative using limits
  • Apply the rules of differentiate in order to calculate derivatives
  • Solve integration problems in calculus

Lessons in this chapter are available to view in two formats: videos and transcripts. Videos are fun to watch and feature clickable timelines that make it easy to skip to key concepts, and transcripts make it possible to read the lessons online or print to review offline. Accompanying each lesson is a short quiz you can take at your convenience to gauge your understanding of concepts covered. A practice exam is available to ensure you have complete knowledge of the fundamental principles of calculus before the day of your test.

7 Lessons in Chapter 12: Fundamental Principles of Calculus
Test your knowledge with a 30-question chapter practice test
Using a Graph to Define Limits

1. Using a Graph to Define Limits

My mom always said I tested the limits of her patience. Use graphs to learn about limits in math. You won't get grounded as we approach limits in this lesson.

Understanding the Properties of Limits

2. Understanding the Properties of Limits

Graphically we can see limits, but how do we actually calculate them? Three words: Divide and Conquer. In this lesson, explore some of the properties that we can use to find limits.

Slopes and Rate of Change

3. Slopes and Rate of Change

If you throw a ball straight up, there will be a point when it stops moving for an instant before coming back down. Consider this as we study the rate of change of human cannonballs in this lesson.

The Fundamental Theorem of Calculus

4. The Fundamental Theorem of Calculus

The fundamental theorem of calculus is one of the most important equations in math. In this lesson we start to explore what the ubiquitous FTOC means as we careen down the road at 30 mph.

Using Limits to Calculate the Derivative

5. Using Limits to Calculate the Derivative

If you know the position of someone as a function of time, you can calculate the derivative -- the velocity of that person -- as a function of time as well. Use the definition of the derivative and your knowledge of limits to do just that in this lesson.

Applying the Rules of Differentiation to Calculate Derivatives

6. Applying the Rules of Differentiation to Calculate Derivatives

In this lesson, we'll review common derivatives and their rules, including the product, quotient and chain rules. We'll also examine how to solve derivative problems through several examples.

Integration Problems in Calculus: Solutions & Examples

7. Integration Problems in Calculus: Solutions & Examples

In this lesson, you'll learn about the different types of integration problems you may encounter. You'll see how to solve each type and learn about the rules of integration that will help you.

Chapter Practice Exam
Test your knowledge of this chapter with a 30 question practice chapter exam.
Not Taken
Practice Final Exam
Test your knowledge of the entire course with a 50 question practice final exam.
Not Taken

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