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  4. Understanding Calculus: Problems, Solutions, and Tips

TELEVISION

Understanding Calculus: Problems, Solutions, and Tips

Series: Understanding Calculus: Problems, Solutions, and Tips
4.9
(55)
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Episodes
36
Rating
TVPG
Year
2008
Language
English
Publisher
The Great Courses

About

These 36 episodes cover all the major topics of a full-year calculus course in high school at the College Board Advanced Placement AB level or a first-semester course in college. Award-winning Professor Bruce H. Edwards guides you through hundreds of examples and problems, each of which is designed to explain and reinforce the major concepts of this vital mathematical field.

Related Subjects

  • Educational

Episodes

1. A Preview of Calculus

33m

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Calculus is the mathematics of change, a field with many important applications in science, engineering, medicine, business, and other disciplines. Begin by surveying the goals of the series. Then get your feet wet by investigating the classic tangent line problem, which illustrates the concept of limits.

2. Review - Graphs, Models, and Functions

30m

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In the first of two review episodes on precalculus, examine graphs of equations and properties such as symmetry and intercepts. Also explore the use of equations to model real life and begin your study of functions, which Professor Edwards calls the most important concept in mathematics.

3. Review - Functions and Trigonometry

30m

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Continue your review of precalculus by looking at different types of functions and how they can be identified by their distinctive shapes when graphed. Then review trigonometric functions, using both the right triangle definition as well as the unit circle definition, which measures angles in radians rather than degrees.

4. Finding Limits

31m

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Jump into real calculus by going deeper into the concept of limits introduced in the first episode. Learn the informal, working definition of limits and how to determine a limit in three different ways: numerically, graphically, and analytically. Also discover how to recognize when a given function does not have a limit.

5. An Introduction to Continuity

31m

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Broadly speaking, a function is continuous if there is no interruption in the curve when its graph is drawn. Explore the three conditions that must be met for continuity, along with applications of associated ideas, such as the greatest integer function and the intermediate value theorem.

6. Infinite Limits and Limits at Infinity

31m

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Infinite limits describe the behavior of functions that increase or decrease without bound, in which the asymptote is the specific value that the function approaches without ever reaching it. Learn how to analyze these functions, and try some examples from relativity theory and biology.

7. The Derivative and the Tangent Line Problem

31m

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Building on what you've learned about limits and continuity, investigate derivatives, which are the foundation of differential calculus. Develop the formula for defining a derivative, and survey the history of the concept and its different forms of notation.

8. Basic Differentiation Rules

30m

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Practice several techniques that make finding derivatives relatively easy: the power rule, the constant multiple rule, sum and difference rules, plus a shortcut to use when sine and cosine functions are involved. Then see how derivatives are the key to determining the rate of change in problems involving objects in motion.

9. Product and Quotient Rules

31m

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Learn the formulas for finding derivatives of products and quotients of functions. Then use the quotient rule to derive formulas for the trigonometric functions not covered in the previous episode. Also investigate higher-order derivatives, differential equations, and horizontal tangents.

10. The Chain Rule

31m

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Discover one of the most useful of the differentiation rules, the chain rule, which allows you to find the derivative of a composite of two functions. Explore different examples of this technique, including a problem from physics that involves the motion of a pendulum.

Extended Details

  • SeriesUnderstanding Calculus: Problems, Solutions, and Tips
  • Closed CaptionsEnglish

Artists

The Great CoursesDirector
The Great CoursesProducer
Bruce H. EdwardsActor