Precalculus

Non-trigonometry pre-calculus topics. Solid understanding of all of the topics in the "Algebra" playlist should make this playlist pretty digestible.

Lectures

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   Lecture 1 - Introduction to Limits

   Introduction to the intuition behind limits.

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   Lecture 2 - Limit Examples (Part 1)

   Some limit exercises.

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   Lecture 3 - Limit Examples (Part 2)

   More limit exercises.

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   Lecture 4 - Limit Examples (Part 3)

   More limit exercises.

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   Lecture 5 - Limit Examples with Brain Malfunctions On

   3 interesting limit examples (correct answer for problem 1 is 3/16 (6/(4*8) NOT 6/(4+8)).

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   Lecture 6 - Squeeze Theorem

   Intuition (but not a proof) of the Squeeze Theorem.

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   Lecture 7 - Proof: lim (sin x)/x

   Using the squeeze theorem to prove that the limit as x approaches 0 of (sin x)/x =1.

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   Lecture 8 - More Limits

   More limit examples.

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   Lecture 9 - Sequences and Series Part 1

   Introduction to the arithmetic and geometric series.

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    Lecture 10 - Sequences and Series Part 2

    Finding the sum of an infinite geometric series.

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    Lecture 11 - Permutations

    Introduction to permutations.

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    Lecture 12 - Combinations

    Introduction to combinations.

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    Lecture 13 - Binomial Theorem Part 1

    Introduction to raising (a+b)^n.

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    Lecture 14 - Binomial Theorem Part 2

    Binomial Theorem and Pascal's Triangle.

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    Lecture 15 - Binomial Theorem Part 3

    Intuition behind why binomial expansion involves combinatorics.

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    Lecture 16 - Exponential Growth

    Exponential growth involving bacteria (some calculus in part c).

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    Lecture 17 - Polar Coordinates 1

    Introduction to polar coordinates.

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    Lecture 18 - Polar Coordinates 2

    Conversion from Cartesian to Polar Coordinates.

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    Lecture 19 - Polar Coordinates 3

    Converting between Cartesian and Polar functions.

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    Lecture 20 - Parametric Equations 1

    Introduction to parametric equations.

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    Lecture 21 - Parametric Equations 2

    Eliminating the parameter.

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    Lecture 22 - Parametric Equations 3

    Removing the parameter from a more interesting example.

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    Lecture 23 - Parametric Equations 4

    Parametric Equations that "move" along the same path.

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    Lecture 24 - Introduction to Function Inverses

    Introduction to Function Inverses.

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    Lecture 25 - Function Inverse Example 1

    Function Inverse Example 1.

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    Lecture 26 - Function Inverse Example 2

    Function Inverses Example 2.

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    Lecture 27 - Function Inverse Example 3

    Function Inverses Example 3.