Unit 1
Limits & Continuity
- Functions and graphical analysis
- Limit laws and techniques
- One-sided and infinite limits
- Continuity
- Intermediate Value Theorem
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College Mathematics
MATH 221 — Calculus & Analytic Geometry 1
The principal first-semester calculus pathway covering differential and integral calculus, analytic geometry, transcendental functions, and applications.
Course overview
The principal first-semester calculus pathway covering differential and integral calculus, analytic geometry, transcendental functions, and applications.
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
Derivative Definition & Rules
- Difference quotients
- Derivative from first principles
- Power/product/quotient rules
- Chain rule
- Implicit differentiation
Unit 3
Transcendental Derivatives
- Exponential and logarithmic derivatives
- Inverse functions
- Inverse trigonometric derivatives
- Higher-order derivatives
- Related rates
Unit 4
Applications of Differentiation
- Linearization
- Critical points and extrema
- Mean Value Theorem
- Curve analysis
- Optimization and modeling
Unit 5
Integration & Accumulation
- Antiderivatives
- Riemann sums
- Definite integrals
- Accumulation functions
- Fundamental Theorem of Calculus
Unit 6
Techniques & Applications of Integration
- Substitution
- Areas between curves
- Volumes by slicing and washers
- Average value
- Physical applications
Unit 7
Analytic Geometry & Transcendental Modeling
- Coordinate geometry in calculus
- Parametric-style interpretation
- Trigonometric modeling
- Exponential/logarithmic models
- Cumulative real-world applications
Unit 8
Cumulative Calculus Problem Solving
- Graphical, numerical, and analytical representations
- Units and interpretation
- Justification and mathematical communication
- Mixed derivative/integral problems
- Calculus modeling
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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