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Taylor Series Lesson Plan

Lesson Plan · University (Grade 14) · English

Taylor Series Lesson Plan

At a Glance

  • Grade Level: University (Grade 14)
  • Subject: Calculus / Mathematical Analysis
  • Lesson Title: Introduction to Taylor Series
  • Class Duration: 40 minutes

Objectives & Learning Outcomes

By the end of this lesson, students will be able to:
  1. Define a Taylor series and explain its purpose in approximating functions.
  1. Derive the Taylor series expansion for basic functions such as
    
    ,
    
    , and
    
    around a given point.
  1. Compute the
    
    th-degree Taylor polynomial for a specified function at
    
    .
  1. Analyze the error (remainder term) in Taylor polynomial approximations and explain its significance.
  1. Apply Taylor series to approximate function values and solve related problems in calculus and applied mathematics.

Standards Addressed

  • MAA Curriculum Guide to Undergraduate Majors in the Mathematical Sciences:
  • Standard C.1: "Students will demonstrate the ability to construct and analyze mathematical models, including series expansions, for real-world phenomena."
  • Standard A.4: "Students will develop proficiency in single-variable calculus, including series and approximations."
  • ABET Criteria for Mathematics (when applicable):
  • Criterion 3 (Student Outcomes): "An ability to apply knowledge of mathematics, science, and engineering, including series and approximations, to solve problems."
  • No specific K-12 standards addressed as this is a university-level topic.