1. Differentiation

Differentiation is the process of finding the rate at which a function changes. The derivative of a function gives the slope of the tangent line to the graph of the function at a particular point. It is denoted by f'(x) or dy/dx.

Key concepts:

Limits and continuity
Definition of the derivative
Rules of differentiation (product rule, quotient rule, chain rule)
Applications of derivatives (related rates, optimization)

2. Integration

Integration is the process of finding the accumulation of quantities. The definite integral of a function represents the area under the curve of the function between two points. It is denoted by ∫f(x) dx.

Key concepts:

Antiderivatives and indefinite integrals
Definite integrals and the fundamental theorem of calculus
Techniques of integration (substitution, integration by parts)
Applications of integrals (area between curves, volume of revolution)

3. Differential Equations

Differential equations involve functions and their derivatives, and they are used to model a wide variety of phenomena in science and engineering.

Key concepts:

First-order differential equations
Second-order linear differential equations
Applications of differential equations (growth and decay, simple harmonic motion)