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Calculus
Chapter Overview
Concept of derivative as rate of change. Differentiation of polynomials, exponentials. Tangents and optimization. Indefinite and definite integrals for area. Kinematics. Differential equations for modeling (HL).
Topics Covered
- Rate of Change
- Differentiation
- Tangents
- Optimization
- Integration
- Area Under Curve
- Kinematics
- Differential Equations (HL)
Key Formulas
ddx(xn) = nxn-1
ddx(ex) = ex
int xn dx = xn+1/(n+1) + C
Real-World Applications
Applications: Economics (marginal analysis), biology (population rates), engineering.
Study Tips
Tip: Focus on applying calculus to real problems
Tip: Use technology for complex calculations
Tip: Practice from a modeling perspective