About This Chapter
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.
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.
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.
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.
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.
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.
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.
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.
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