Unit 1
Differential Equations Foundations
- First-order differential equations
- Slope fields
- Separable equations
- Initial-value problems
- Equilibrium solutions
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College Mathematics
MATH 213 — Survey of Calculus 2
A continuation emphasizing differential equations, multivariable ideas, optimization, sequences and series, approximation, and probability in applications.
Course overview
A continuation emphasizing differential equations, multivariable ideas, optimization, sequences and series, approximation, and probability in 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
Exponential & Logistic Models
- Exponential growth/decay
- Logistic growth
- Carrying capacity
- Parameter interpretation
- Business and social-science applications
Unit 3
Multivariable Functions
- Functions of two variables
- Partial derivatives
- Geometric interpretation
- Tangent planes
- Rates of change in several variables
Unit 4
Constrained Optimization
- Critical points in two variables
- Constraint equations
- Lagrange multipliers
- Economic optimization
- Interpreting feasible solutions
Unit 5
Sequences & Series
- Sequences and limits
- Geometric sequences and series
- Convergence and divergence
- Series notation
- Applications of recurrence models
Unit 6
Approximation & Numerical Methods
- Linear approximation
- Taylor-style local approximation
- Numerical integration ideas
- Error and accuracy
- Using approximation in models
Unit 7
Probability Foundations
- Basic probability concepts
- Expected value
- Discrete probability models
- Conditional probability in context
- Risk in business/social science
Unit 8
Integrated Applications
- Combining calculus and models
- Interpreting parameters
- Optimization under constraints
- Approximation and decision-making
- Written quantitative reasoning
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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