Limits and Derivatives
Calculus helps us understand rates of change and accumulation, enabling optimization and modeling of real-world phenomena.
f'(x) = lim(h → 0) [f(x + h) - f(x)]/h
Integrals and Applications
Calculus provides tools for solving problems in physics, engineering, economics, and computer science, including area under curves and volumes of solids.
∫f(x) dx = F(x) + C
Real-World Impacts
Calculus is crucial in understanding population growth, electrical circuits, and mechanical systems, making it a fundamental tool for problem-solving.
y'' + 4y = 0