Unit route
Complete lessons in sequence, use diagnostic evidence to select a pathway, conduct the investigation, submit corrected work, and demonstrate mastery at 80% or above.
Weeks 35, 36 · 8 college lessons
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?
Pathways
Lesson 01 · Week 35
Power Series & Radius of Convergence
Using ratio or root behavior to determine where a power series converges.
Lesson 02 · Week 35Endpoint Testing & Interval of Convergence
Testing boundary points separately after finding radius.
Lesson 03 · Week 35Operations on Power Series
Differentiating, integrating, multiplying, and shifting within convergence intervals.
Lesson 04 · Week 35Taylor Polynomials & Local Approximation
Matching derivatives at a center.
Lesson 05 · Week 36Benchmark Maclaurin Series
Using canonical series for exponential, trigonometric, logarithmic, and inverse-trigonometric functions.
Lesson 06 · Week 36Taylor Remainder & Error Bounds
Using derivative bounds to certify approximation accuracy.
Lesson 07 · Week 36Series in Integration & Differential Equations
Using series where elementary antiderivatives or closed forms are unavailable.
Lesson 08 · Week 36Capstone Synthesis, Oral Defense & Calculus III Bridge
Integrating methods, convergence, modelling, communication, and responsible technology use.