Maclaurin & Taylor Series

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Analytic Functions
Algorithm for Computing Taylor Series

More Examples of Taylor Series
Taylor Approximations and Power Series

Analytic Functions

Analytic functions and Taylor series are defined, including the concept of an infinitely differentiable function.

18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr

Course Material Related to This Topic:

Read lecture notes, section 2 on pages 2–4

Algorithm for Computing Taylor Series

Step-by-step method for computing a Taylor series, with example of finding the Taylor series expansion of f(x) = (1-x)^-1 about x = 0.

18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr

Course Material Related to This Topic:

Read lecture notes, section 3, pages 4–5

More Examples of Taylor Series

Taylor series expansions of (1-x)^-1, e^x, sin(x), and cos(x) about any point x=a.

18.01 Single Variable Calculus, Fall 2005
Prof. Jason Starr

Course Material Related to This Topic:

Read lecture notes, section 4, pages 5–9

Taylor Approximations and Power Series

Five questions which involve Taylor series approximations for sine, cosine, exponential, logarithmic, and other functions, as well as finding error bounds on these approximations.

18.01 Single Variable Calculus, Fall 2006
Prof. David Jerison

Course Material Related to This Topic:

Complete exam problems 7C-1 to 7C-5 on page 44
Check solution to exam problems 7C-1 to 7C-5 on pages 100–2