Calculus

Board: IB Class: AA

Chapter Overview

Limits and continuity. Differentiation from first principles, rules (product, quotient, chain). Applications: tangents, normals, optimization, kinematics. Integration: indefinite, definite, substitution, integration by parts (HL). Area and volume. Differential equations (HL). Maclaurin/Taylor series (HL).

Topics Covered

Limits and Continuity
Differentiation Rules
Tangents and Normals
Optimization
Kinematics
Integration
Definite Integrals
Area and Volume
Differential Equations (HL)
Maclaurin Series (HL)

Key Formulas

ddx(xⁿ) = nx^n-1

ddx(sin x) = cos x

int xⁿ dx = xⁿ⁺¹/(n+1) + C

int_a^b f(x) dx = F(b) - F(a)

Real-World Applications

Applications: Engineering, physics, economics, optimization in business, machine learning.

Study Tips

Tip: Master differentiation before integration

Tip: Practice many past paper questions

Tip: HL students should understand proofs