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Lesson Plan: Introduction to Taylor Series
Lesson Plan · University (Grade 16) · English
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:
- Define the Taylor series and explain its mathematical foundation.
- Derive the Taylor series expansion for elementary functions at a given point.
- Apply Taylor series to approximate non-polynomial functions near a specified value.
- Analyze the error (remainder) term in Taylor series approximations.
- 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.