Curriculum Syllabus & Outline
Markdown Syllabus# Calculus II Outline
1. Integration Techniques
2. Improper Integrals
3. Sequences & Series
4. Parametric & Polar
5. Applications
Educational Context & Standards
Calculus II tutoring: advanced integration, convergence, parametric/polar coordinates.
Cross-Curriculum Equivalents
Canada/BC: BC University Calculus Prep & Tutoring
CA-BC-TUT
Canada/ON: Ontario Collegiate Advanced Tutoring
CA-ON-TUT
US/National: AP & Collegiate Advanced Mathematics
US-ADV-MTH
Structured Lesson Modules (5 Lessons)
1
Integration Techniques
Parts, trig sub, partial fractions.
2
Improper Integrals
Convergence tests.
3
Series
Tests, Taylor.
4
Parametric
Derivatives, arc length.
5
Polar
Area, arc length.
Assessments & Check-for-Understanding
Q1
∫ 1/(x ln x) dx = ?
Answer
ln|ln x|+C
Q2
Geometric series sum a/(1-r) if |r|<1?
Answer
Yes
Q3
Taylor for sin x?
Answer
x - x³/3! + x⁵/5! - ...
Q4
Parametric dy/dx = ?
Answer
(dy/dt)/(dx/dt)
Q5
Polar arc length?
Answer
∫√(r²+(dr/dθ)²) dθ
Q6
Alternating series test?
Answer
Terms decrease to 0