## Week 25

NOTE: The reading assignments from Stewart Chapter 10 are not to be taken overly seriously at this point. Put your primary effort into reading the Web page and the attached material instead! We will come back to the end of Chapter 10 in sequence at the end of the semester.

Reference: Stewart 2.9 (review, emphasis on quadratic approximations), 10.10 (ignore infinite sums for now), 10.11, CalcLabs 10.5

Keywords: Taylor polynomial, Taylor expansion or series, Maclaurin expansion or series, geometric series, binomial series

Learning Objectives: The student will be able to:

• Compute Taylor polynomials, of a given degree n, about a given point a, for a given function f
• Know and use the Maclaurin series of exp, sin, and cos, and the geometric series
• Use Maple's taylor command to find Taylor polynomials
• Use Maple to plot graphs of functions and their Taylor polynomials

25.R Mean value theorem, Taylor's theorem (<-READ ME)

Reference: Stewart 3.2, 10.9, 10.12 (ignore infinite sums for now)

Keywords: Rolle's theorem, mean value theorem (MVT), Taylor series, Taylor's theorem with remainder, error term, perturbation theory

Learning Objectives: The student will be able to:

• State Rolle's Theorem and the Mean Value Theorem
• Verify whether or not a given function satisfies the hypotheses of the MVT
• State Taylor's formula with remainder
• Use the remainder to estimate the error when using Taylor polynomials
• Use Taylor polynomials in applications