Unit 1
Calculus Foundations & Limits
- Functions and calculus language
- Average versus instantaneous rate of change
- Limit notation and numerical limits
- One-sided and infinite limits
- Continuity and asymptotic behavior
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College Mathematics
MATH 211 — Survey of Calculus 1
A survey calculus pathway without trigonometry, designed around differential and introductory integral calculus and applications.
Course overview
A survey calculus pathway without trigonometry, designed around differential and introductory integral calculus 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
Derivatives & Rates of Change
- Derivative from first principles
- Basic derivative rules
- Product and quotient rules
- Chain rule
- Tangent lines and rates
Unit 3
Derivative Applications
- Increasing and decreasing functions
- Critical points and extrema
- First and second derivative tests
- Optimization
- Economic and physical applications
Unit 4
Exponential & Logarithmic Calculus
- Derivatives of exponential functions
- Derivatives of logarithms
- Elasticity and relative rates
- Growth and decay models
- Applications in business and economics
Unit 5
Antiderivatives & Definite Integrals
- Antiderivatives
- Indefinite integrals
- Riemann sums
- Definite integrals
- Accumulation functions
Unit 6
Fundamental Theorem & Applications
- Fundamental Theorem of Calculus
- Net change
- Areas under curves
- Average value
- Basic accumulation models
Unit 7
Integration & Modeling
- Substitution concept
- Integration by basic algebraic methods
- Economic accumulation models
- Consumer/producer-style applications
- Interpreting units and totals
Unit 8
Functions of Several Variables
- Surfaces and contour ideas
- Partial derivatives
- Tangent planes
- Two-variable optimization
- Economic interpretation of multivariable models
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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