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3Blue1Brown
Taylor series: Essence of Calculus - Part 11 of 11
Taylor series are extremely useful in engineering and math, but what are they? This video shows why they're useful, and how to make sense of the formula.
3Blue1Brown
Taylor series | Chapter 10, Essence of calculus
Taylor series are extremely useful in engineering and math, but what are they? This video shows why they're useful, and how to make sense of the formula.
Professor Dave Explains
Power Series Solutions Part 1: Leibniz Method
One technique for solving differential equations is to use power series. Hopefully we remember Maclaurin series and Taylor series from our study of calculus. These will actually have an important application here, as we can use infinite...
Professor Dave Explains
Power Series Solutions Part 2: Frobenius Method
We just learned how to solve differential equations using power series. However the simpler approached we used assumed that all the functions involved are infinitely differentiable at the point we are expanding about. This will not...
Zach Star
Dear Calculus 2 Students, This is why you're learning Taylor Series
Dear Calculus 2 Students, This is why you're learning Taylor Series
Khan Academy
Khan Academy: Calculus: Polynomial Approximation of Functions (Part 2)
Video lesson finishing the derivation of the formula for the Maclaurin series and then applying it to find the polynomial approximation for e^x. [10:09]
Khan Academy
Khan Academy: Calculus: Polynomial Approximations of Functions (Part 5)
Video lesson using a Maclaurin series to approximate a sine function by using a polynomial function. Generalizes the expansion of sine using sigma notation and relates it to the expansion for cosine. [9:24]
Khan Academy
Khan Academy: Calculus: Polynomial Approximation of Functions (Part 7)
Video continues a discussion about the relationship between the polynomial approximations for the sine, cosine and e^x functions from Maclaurin series and uses those to derive Euler's formula and Euler's identity. [10:18]
Khan Academy
Khan Academy: Calculus: Polynomial Approximation of Functions (Part 4)
Video lesson using a Maclaurin series to approximate a cosine function by using a polynomial function. Generalizes the expansion of cosine using sigma notation. [9:59]
Khan Academy
Khan Academy: Calculus: Polynomial Approximation of Functions (Part 6)
Video lesson relating the polynomial approximations for the sine, cosine and e^x functions from Maclaurin series. [9:59]
Khan Academy
Khan Academy: Calculus: Polynomial Approximation of Functions (Part 1)
Video lesson showing how to approximate a function at 0 using a polynomial by deriving the first three terms for the formula of a Maclaurin series. [9:45]
Khan Academy
Khan Academy: Calculus: Approximating Functions With Polynomials (Part 3)
Video lesson using a Maclaurin series to approximate an exponential function by using a polynomial expansion. Provides two different definitions for e. [7:13]
Khan Academy
Khan Academy: Calculus: Visualizing Taylor Series Approximations
Video lesson using the Wolfram Alpha website to show the graphs of the Maclaurin series expansion of the sine function, demonstrating that approximations with more terms are better approximations of the sine curve. [6:01]
Khan Academy
Khan Academy: Calculus: Maclaurin and Taylor Series Intuition
Video lesson showing how to approximate a function at 0 using a polynomial by deriving the formula for a Maclaurin series. [12:58]
Khan Academy
Khan Academy: Calculus: Taylor Series at 0 (Maclaurin) for E to the X
Video lesson using a Maclaurin series to approximate an exponential function by using a polynomial function and relates its polynomial approximation to that for the sine and cosine functions. [6:10]
Khan Academy
Khan Academy: Calculus: Sine Taylor Series at 0 (Maclaurin)
Video lesson using a Maclaurin series to approximate a sine function by using a polynomial function. [6:33]
Khan Academy
Khan Academy: Calculus: Euler's Formula and Euler's Identity
Video lesson using the polynomial approximations for the sine, cosine and exponential functions from Maclaurin series to derive Euler's formula and Euler's identity. [11:27]
Khan Academy
Khan Academy: Calculus: Cosine Taylor Series at 0 (Maclaurin)
Video lesson using a Maclaurin series to approximate a cosine function by using a polynomial function. [5:37]
Khan Academy
Khan Academy: Taylor Series at 0 (Maclaurin) for E to the X
Video lesson using a Maclaurin series to approximate an exponential function by using a polynomial function and relates its polynomial approximation to that for the sine and cosine functions.
Khan Academy
Khan Academy: Maclaurin and Taylor Series: Sine Taylor Series at 0 (Maclaurin)
Video lesson using a Maclaurin series to approximate a sine function by using a polynomial function.