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Series: Calculus: Pre-Calculus Review

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About this Series

  • Lessons: 4
  • Total Time: 1h 16m
  • Use: Watch Online & Download
  • Access Period: Unlimited
  • Created At: 07/30/2009
  • Last Updated At: 07/21/2010

In this four-lesson series with Professor Burger, we'll review some of the material we learned in Pre-Calculus. Mastery of these areas is critical to success in Calculus. In this series, in particular, we'll review functions, the graphing of lines, parabolas, and an intro to Non-Euclidean Geometry.

A function pairs one object with another. A function will produce only one object for any pairing. A function can be represented by an equation. To evaluate the function for a particular value, substitute that value into the equation and solve. You can evaluate a function for an expression as well as for a number. Substitute the entire expression into the equation of the function. Be careful to include parentheses where needed.

A graph is a way of illustrating a set of ordered pairs. One of the easiest objectsto graph is the line. Lines have direction, but no thickness. The slope-intercept form, y = mx + b, and the point-slope form, ( y - y1 ) = m( x - x1 ), are two means of describing lines. When writing the equation of a line, the point-slope form is easier to use than the slope-intercept form, because you can use any point.

The graph of a second-degree polynomial expression is a parabola. A parabola consists of the set of all points in a plane that are equidistant from a fixed line (the directrix) and a fixed point not on the line (the focus). When graphing functions, start by looking for ways to simplify their expressions. Always promise that the denominator will not equal zero when you cancel. The distance formula is an application of the Pythagorean theorem. It states that d = [(x2-x1)^2 + (y2-y1)^2]^(1/2)

In Euclidean geometry, the shortest distance between two points is inevitably going to be a straight line. In Non-Euclidean geometry, however, this is not always the case.

Taught by Professor Edward Burger, this series comes from a comprehensive Calculus course. This course and others are available from Thinkwell, Inc. The full course can be found at http://www.thinkwell.com/student/product/calculus. The full course covers limits, derivatives, implicit differentiation, integration or antidifferentiation, L'Hopital's Rule, functions and their inverses, improper integrals, integral calculus, differential calculus, sequences, series, differential equations, parametric equations, polar coordinates, vector calculus and a variety of other AP Calculus, College Calculus and Calculus II topics.

About this Author

Thinkwell
Thinkwell
2174 lessons
Joined:
11/14/2008

Founded in 1997, Thinkwell has succeeded in creating "next-generation" textbooks that help students learn and teachers teach. Capitalizing on the power of new technology, Thinkwell products prepare students more effectively for their coursework than any printed textbook can. Thinkwell has assembled a group of talented industry professionals who have shaped the company into the leading provider of technology-based textbooks. For more information about Thinkwell, please visit www.thinkwell.com or visit Thinkwell's Video Lesson Store at http://thinkwell.mindbites.com/.

Thinkwell lessons feature a star-studded cast of outstanding university professors: Edward Burger (Pre-Algebra through...

Lessons Included

None of the lesson in this series have been reviewed.

Below are the descriptions for each of the lessons included in the series:

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