3Blue1Brown
How (and why) to raise e to the power of a matrix | DE6
Exponentiating matrices, and the kinds of linear differential equations this solves.
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.
3Blue1Brown
Taylor series | Essence of calculus, chapter 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
Higher order derivatives | Footnote, Essence of calculus
What is the second derivative? Third derivative? How do you think about these?
3Blue1Brown
Higher order derivatives: Essence of Calculus - Part 10 of 11
What is the second derivative? Third derivative? How do you think about these?
3Blue1Brown
Higher order derivatives | Essence of calculus, chapter 10
What is the second derivative? Third derivative? How do you think about these?
Virtually Passed
3.1 Linearization PROOF | Nonlinear Dynamics
Nonlinear Dynamics mini-series Part 1: • 1.0 A better way ... Part 2: • 2.0 A better way ... Part 3: • 3.0 A better way ... This video shows a formal proof behind linearization for 2D flows: dx/dt = f(x,y) dy/dt = g(x,y) Step 1: Find...
Virtually Passed
1.1 Stability of Fixed Points PROOF | Nonlinear Dynamics
This video deals with nonlinear differential equations in the form: dx/dt = f(x) To find out whether a fixed point is stable or not, a linear stability analysis is done whereby the function is approximated as a line. If the slope of that...
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
Virtually Passed
Stability of Fixed Points PROOF | Nonlinear Dynamics (Part 1 extra)
This video deals with nonlinear differential equations in the form: dx/dt = f(x) To find out whether a fixed point is stable or not, a linear stability analysis is done whereby the function is approximated as a line. If the slope of that...
Virtually Passed
Linearization PROOF | Nonlinear Dynamics (Part 3 extra)
This video shows a formal proof behind linearization for 2D flows: dx/dt = f(x,y) dy/dt = g(x,y) Step 1: Find fixed points. This involves solving for where dx/dt and dy/dt both are equal to 0. Step 2: Approximate f(x,y) and g(x,y) as...
3Blue1Brown
Taylor Series | Essence of Calculus, Chapter 10
Sometimes close enough is just perfect. The last video in a series of 11 explores the Taylor series and its connection to derivatives. It shows the process for finding Taylor series approximations for y = sin x and for y = e^x.
Khan Academy
Khan Academy: Calculus: Taylor Polynomials
Video lesson showing the formula for a Taylor series expansion to five terms and uses it to approximate the cosine function. Includes the graphs of a specific number of terms of the approximate function using a graphing calculator. [18:05]
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #6A
Video shows how to write the first four nonzero terms of the Taylor series for a function. [7:42]
Khan Academy
Khan Academy: Calculus: Generalized Taylor Series Approximation
Video lesson showing how to approximate a function at any value using a polynomial by deriving the formula for a Taylor series. [7:27]
Khan Academy
Khan Academy: Calculus: Visualizing Taylor Series for E^x
Video lesson using a Taylor series to approximate e^x around x=3 by using a polynomial function and then showing some of the graphs of the expansion by using the Wolfram Alpha website. [6:38]
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #6C
Video shows how to use the Taylor series of a function which was found in the previous video to find the sixth derivative of the function at 0. [2:58]
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #6D
Video shows how to calculate the Lagrange error bound for a Taylor series polynomial approximation. [11:52]
Khan Academy
Khan Academy: Calculus: 2011 Calculus Bc Free Response #6B
Video shows how to find the first four nonzero terms of a Taylor series of cos x. Also shows how to combine Taylor series for parts of a function to create a Taylor series for the entire function. [9:59]
Khan Academy
Khan Academy: Calculus: Error or Remainder of a Taylor Polynomial Approximation
Video first reviews the formula for a Taylor series expansion and then defines the error function to be the difference between the polynomial approximation and the actual function. Properties of the derivatives of the error function are...
Khan Academy
Khan Academy: Calculus: Bounding the Error of a Taylor Polynomial Approximation
Video uses a property of the error function for a Taylor series expansion from the previous video to bound the (n+1)th derivative of the error function. Result is the Lagrange error bound. [15:08]
Khan Academy
Khan Academy: Maclaurin and Taylor Series: Visualizing Taylor Series for E^x
Video lesson using a Taylor series to approximate e^x around x=3 by using a polynomial function and then showing some of the graphs of the expansion by using the Wolfram Alpha website.