TELEVISION

Mathematics Describing the Real World: Precalculus and Trigonometry

Series: Mathematics Describing the Real World: Precalculus and Trigonometry
4.9
(58)
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Episodes
36
Rating
TVPG
Year
2008
Language
English
Publisher
The Great Courses

About

Finally make sense of the mysteries of precalculus and trigonometry in the company of master educator and award-winning professor Bruce Edwards. In 36 intensively illustrated episodes, he takes you through all the major topics of a typical precalculus course taught in high school or college. You'll gain new insights into functions, complex numbers, matrices, and much more.

Related Subjects

Episodes

1. An Introduction to Precalculus - Functions

31m

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Precalculus is important preparation for calculus, but it's also a useful set of skills in its own right, drawing on algebra, trigonometry, and other topics. As an introduction, review the essential concept of the function, try your hand at simple problems, and hear Professor Edwards's recommendations for approaching the series.

2. Polynomial Functions and Zeros

31m

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The most common type of algebraic function is a polynomial function. As examples, investigate linear and quadratic functions, probing different techniques for finding roots, or "zeros." A valuable tool in this search is the intermediate value theorem, which identifies real-number roots for polynomial functions.

3. Complex Numbers

31m

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Step into the strange and fascinating world of complex numbers, also known as imaginary numbers, where i is defined as the square root of -1. Learn how to calculate and find roots of polynomials using complex numbers, and how certain complex expressions produce beautiful fractal patterns when graphed.

4. Rational Functions

31m

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Investigate rational functions, which are quotients of polynomials. First, find the domain of the function. Then, learn how to recognize the vertical and horizontal asymptotes, both by graphing and comparing the values of the numerator and denominator. Finally, look at some applications of rational functions.

5. Inverse Functions

32m

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Discover how functions can be combined in various ways, including addition, multiplication, and composition. A special case of composition is the inverse function, which has important applications. One way to recognize inverse functions is on a graph, where the function and its inverse form mirror images across the line y = x.

6. Solving Inequalities

31m

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You've already used inequalities to express the set of values in the domain of a function. Now study the notation for inequalities, how to represent inequalities on graphs, and techniques for solving inequalities, including those involving absolute value, which occur frequently in calculus.

7. Exponential Functions

32m

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Explore exponential functions, which have a base greater than 1 and a variable as the exponent. Survey the properties of exponents, the graphs of exponential functions, and the unique properties of the natural base e. Then sample a typical problem in compound interest.

8. Logarithmic Functions

30m

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A logarithmic function is the inverse of the exponential function, with all the characteristics of inverse functions covered earlier. Examine common logarithms (those with base 10) and natural logarithms (those with base e), and study such applications as the "rule of 70" in banking.

9. Properties of Logarithms

32m

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Learn the secret of converting logarithms to any base. Then review the three major properties of logarithms, which allow simplification or expansion of logarithmic expressions and are widely used in calculus. Close by focusing on applications, including the pH system in chemistry and the Richter scale in geology.

10. Exponential and Logarithmic Equations

31m

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Practice solving a range of equations involving logarithms and exponents, seeing how logarithms are used to bring exponents "down to earth" for easier calculation. Then try your hand at a problem that models the heights of males and females, analyzing how the models are put together.

Extended Details

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