Multivariable Calculus 17 | Taylor's Theorem - Examples

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This video is about examples of Taylor polynomials. We also discuss the Hessian matrix.

#MultivariableCalculus
#Analysis
#Integral
#Calculus
#Derivatives
#Mathematicspdt
#Lagrange

(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[sinanakhostin]

Excellent lecture... I ca not thank you enough for this great lecture. Very clear and organized deconstruction of second-order partial derivatives, Jacobian and Hessian matrices!

[sinanakhostin]

I just could not connect the last step of the example with the use of power series. I know the power series associated to the function cos(x). You mentioned them in in "Uniform convergence of Differentiable Functions" in Real Analysis. But I can not see why we use them here!?

[murongyunhai]

do you need infinitely differentiability when you only expand to order k? or differentiability up to order k+1 would suffice?

[NithinJune]

would have liked to seen like a more useful expansion point where it didn’t all just become the constant 1