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Lesson Plan: Introduction to Taylor Series

Lesson Plan
University (Grade 16)
English

Lesson Plan: Introduction to Taylor Series

Objectives & Learning Outcomes

By the end of this lesson, students will be able to:
  1. Define the Taylor series and explain its mathematical foundation.
  1. Derive the Taylor series expansion for elementary functions at a given point.
  1. Apply Taylor series to approximate non-polynomial functions near a specified value.
  1. Analyze the error (remainder) term in Taylor series approximations.
  1. Solve problems involving function approximation and convergence of Taylor series.

Material & Resources Needed

  • Whiteboard and markers or chalkboard and chalk
  • Projector and computer for presentation of examples
  • Calculators or mathematical software (e.g., MATLAB, Mathematica, or Desmos)
  • Handouts with guided practice problems and summary tables of common Taylor series
  • Student notebooks
  • Access to internet or digital resources for further exploration

Assessment and Evaluation Plan

  • Formative Assessment:
  • In-class questioning and discussion to gauge understanding of Taylor series concepts and derivations.
  • Short, guided practice problems where students expand given functions using Taylor series.
  • Summative Assessment:
  • Completion of an exit ticket where students must derive the Taylor series for a specified function and estimate its error for a given value.
  • Homework assignment with more complex Taylor series problems, including analyzing convergence and approximation errors.
  • Diagnostic Assessment:
  • Quick review quiz at the beginning of class to assess prerequisite knowledge of derivatives and series expansions.