Instructional priorities
- Power series
- Radius and interval of convergence
- Endpoint testing
- Termwise operations
- Taylor polynomials
- Maclaurin series
- Taylor remainder
- Series methods
- Mathematical modelling
Faculty planning and evidence
Power Series, Taylor Series & Modelling Capstone
How do power series represent functions, control approximation error, solve problems, and bridge single-variable calculus to advanced analysis?
Evidence expectations
Require method selection, exact notation, conditions, units, interpretation, and an independent verification. Score the reasoning chain, not only the final value.
Common interventions
Use retrieval diagnostics, smaller algebraic cases, multiple representations, worked-example fading, error comparison, and oral explanation before assigning more repetition.
Assessment sequence
Formative checks → pathway set → investigation → mastery check → correction → reassessment. Preserve both first-attempt and corrected evidence.