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Course Curricula à la LiveMath

We proudly present these course curriculum projects that utilize LiveMath. These e-texts feature LiveMath notebooks, screencast recordings discussing the topics in the LiveMath notebooks, which also serve as a tutorial on using LiveMath, and "by hand" videos as complimentary instruction for certain topics where hand calculations are important for mathematical literacy.

These course packages have served as the core curricula for the Distance Calculus project for the past 20+ years.

You may view a selection of topics for DEMO purposes. If you like what you see, then you may purchase full access to one (or all) of the e-textbooks to gain access to all of the LiveMath notebooks and help movies.

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When Distance Calculus was launched back in 1997, the first courses were Calculus I and higher. As enrollment grew, it became clear that a number of students needed more Precalculus practice before jumping into the Calculus curriculum.

Out of this necessity was born the comprehensive (and exhaustive!) The Primitives of Precalculus, bridging the gap between a varied high school math background and the core skill requirements of the Calculus I course.

We begin with hand-calculations of solving basic equations from Algebra I level, all the way through conic sections, series, vectors, and polar equations - topics usually found in a precalculus textbook but never actually covered in class.

The pedagogical approach is dual in nature:

  • Hand-Calculations
    With hand-calculation videos, start the explanation of precalculus topics. If a student has already mastered such calculations, this part goes more quickly;
  • LiveMath Calculations
    Moving towards LiveMath usage, the topics are more thoroughly investigated, with the added challenge of learning how to drive LiveMath to obtain calculations equivalent to the hand calculations, and then beyond what you may accomplish by hand.
Not boring review as is usually the case in these courses, but a fresh and alive approach that allows students with weaker Precalculus skills to progress along with students whose skills are stronger, all of which are reinforced via the expanded LiveMath investigations.

Using both hand-skills and LiveMath skills as the foundation, we then advance through the Precalculus curriculum eventually leaning towards LiveMath and advanced and unique topics that cannot be studied without a technological tool.

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Such unique and advanced topics include:

  • Determining the polynomial formula for a mystery function with complex roots by vertically shifting the graph to create real roots in the shift, reading off those real roots visually, and then shifting back to obtain the factorization with complex roots and finding the mystery polynomial through this analysis.
  • Discovering trigonometric identities through the usage of 3D graphical comparisons.
  • Applying rotation of axes to analyze a tilted conic section

>>>Show Table of Contents (With Demo Sections & Content)