Created on: August 6, 2010

Website Address: https://library.curriki.org/oer/Polynomial-Approximations

TABLE OF CONTENTS

- Limits
- Derivatives
- The Chain Rule
- Derivatives of Special Functions
- Implicit Differentiation
- Minima and Maxima
- Optimization Problems
- Indefinite Integrals
- Definite Integrals
- Solids of Revolution
- Sequences and Series
- Polynomial Approximations
- Partial derivatives
- AP Calculus BC
- Partial Derivatives
- Double Integrals
- Line Integrals I
- Vectors
- Line Integrals II
- Green's Theorem
- L'Hospital's Rule

- Proof: d/dx(x^n)
- Proof: d/dx(sqrt(x))
- Proof: d/dx(ln x) = 1/x
- Proof: d/dx(e^x) = e^x
- Proofs of Derivatives of Ln(x) and e^x
- Calculus: Derivative of x^(x^x)
- Extreme Derivative Word Problem (advanced)

- Introduction to the Line Integral
- Line Integral Example 1
- Line Integral Example 2 (part 1)
- Line Integral Example 2 (part 2)

- Maxima Minima Slope Intuition
- Inflection Points and Concavity Intuition
- Monotonicity Theorem
- Calculus: Maximum and minimum values on an interval
- Calculus: Graphing Using Derivatives
- Calculus Graphing with Derivatives Example
- Graphing with Calculus

- Polynomial approximation of functions (part 1)
- Polynomial approximation of functions (part 2)
- Approximating functions with polynomials (part 3)
- Polynomial approximation of functions (part 4)
- Polynomial approximations of functions (part 5)
- Polynomial approximation of functions (part 6)
- Polynomial approximation of functions (part 7)
- Taylor Polynomials
- Exponential Growth

Taylor Series

This video begins the task of approximating an arbitrary function by polynomials.

This video continues the effort to approximate a function with polynomials and applies it to an exponential.

This video continues approximating exp x with a series and describes McLauren series.

This video develops a McLauren representation of cos x.

This video derives the McLauren series for sin x.

This video takes MacLauren's representation of exp(x) and extracts sin(x) and cos(x)

This video presents Euler's Mystical Formula.

This video presents Taylor's Theorem and Taylor representation of some functions.

This video presents a word problem involving exponential growth of a bacterial colony.