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Maclaurin & Taylor Series

Lecture Notes

Analytic Functions

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Section 2, Page 2 to page 4

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

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: Power Series (section 1 of this lecture)
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Algorithm for Computing Taylor Series

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Section 3, Page 4 to page 5

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.

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: Power Series and Taylor Series (sections 1 and 2 of this lecture)
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More Examples of Taylor Series

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Section 4, Page 5 to page 9

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

Course: 18.01 Single Variable Calculus, Fall 2005
Instructor: Prof. Jason Starr
Prior Knowledge: Power Series and Taylor Series (sections 1 to 3 of this lecture)
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Exam Questions

Taylor Approximations and Power Series

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Problem 7C-1 (page 44) to problem 7C-5 (page 44)

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

Course: 18.01 Single Variable Calculus, Fall 2006
Instructor: Prof. David Jerison
Prior Knowledge: None

Solution (PDF - 4.0 MB) Pages 100 to 102

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