Unit 1
Integration Techniques
- Substitution review
- Integration by parts
- Trigonometric integrals
- Trigonometric substitution
- Partial fractions
← Back to College Mathematics
College Mathematics
MATH 222 — Calculus & Analytic Geometry 2
A second-semester calculus pathway covering integration techniques, improper integrals, differential equations, sequences and series, and vector geometry.
Course overview
A second-semester calculus pathway covering integration techniques, improper integrals, differential equations, sequences and series, and vector geometry.
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
Improper Integrals & Convergence
- Infinite intervals
- Infinite discontinuities
- Comparison of improper integrals
- Convergence interpretation
- Applications
Unit 3
Differential Equations
- Separable equations
- Initial-value problems
- Linear first-order equations
- Equilibrium and qualitative behavior
- Growth and decay models
Unit 4
Sequences
- Sequence notation
- Limits of sequences
- Monotone and bounded sequences
- Recursive definitions
- Applications and asymptotic behavior
Unit 5
Infinite Series
- Geometric series
- Series convergence tests
- Absolute and conditional convergence
- Power series
- Interval/radius of convergence
Unit 6
Taylor & Maclaurin Series
- Taylor polynomials
- Maclaurin series
- Remainder/error ideas
- Series representations of functions
- Applications and approximation
Unit 7
Vector Geometry in 2D & 3D
- Vectors and components
- Dot product
- Cross product
- Lines and planes
- Geometric and physical applications
Unit 8
Three-Dimensional Modeling
- Coordinates in space
- Distances and angles
- Vector equations
- Motion and force models
- Geometric interpretation
Unit 9
Cumulative Calculus II
- Choosing integration methods
- Series-based approximation
- ODE and series connections
- Model interpretation
- Preparation for multivariable calculus
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.
READY TO GET STARTED?
Want help with this course?
Tell Math Aficionado the exact class, unit, or problem set you are working on.