Unit 1
Precalculus Integration & Function Fluency
- Polynomial and rational review
- Exponential functions and inverses
- Trigonometric functions and identities
- Function composition
- Algebraic/trigonometric combinations
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College Mathematics
MATH 217 — Calculus with Algebra & Trigonometry II
A continuation pathway integrating algebra, trigonometry, precalculus and elementary differential calculus; completion is described by UW–Madison as satisfying the MATH 221/114 sequence requirements.
Course overview
A continuation pathway integrating algebra, trigonometry, precalculus and elementary differential calculus; completion is described by UW–Madison as satisfying the MATH 221/114 sequence requirements.
Math Aficionado uses this structure as a tutoring roadmap: lessons can be paced around the student's current level, school sequence, assignments, and assessment goals rather than forcing every student through the same timetable.
Units & topics
Unit 2
Limits & Continuity
- Limit laws
- Numerical and graphical limits
- Continuity
- Intermediate Value Theorem
- Asymptotic behavior
Unit 3
Derivative Foundations
- Derivative definition
- Basic derivative rules
- Product and quotient rules
- Chain rule
- Derivatives of exponential and trigonometric functions
Unit 4
Applications of Differentiation
- Tangent and normal lines
- Related rates
- Critical points
- First and second derivative tests
- Optimization and modeling
Unit 5
Integration & Accumulation
- Antiderivatives
- Riemann sums
- Definite integrals
- Fundamental Theorem of Calculus
- Accumulation and net change
Unit 6
Applications of Integration
- Area and signed area
- Volumes
- Average value
- Physical and biological applications
- Economic applications
Unit 7
Transcendental & Calculus Connections
- Inverse functions and derivatives
- Logarithmic differentiation
- Trigonometric applications
- Function behavior across representations
- Calculus with mixed function families
Unit 8
Bridge to MATH 222
- Integration fluency
- Modeling with differential equations
- Algebra/trigonometry review for integration
- Problem-solving strategies
- Preparation for techniques of integration and series
Curriculum reference: University of Wisconsin–Madison Guide / Department of Mathematics. The page is an independent tutoring roadmap and is not an official course page of the source institution.
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