Calculus

Study of continuous change through derivatives and integrals.

Limits and ContinuityDerivatives and Rates of ChangeIntegrals and Area Under Curves
Applications of DerivativesTechniques of IntegrationInfinite Series and Convergence
Modeling MotionEconomics and OptimizationBiology and Population Growth
Breaking Down ProblemsMemorizing Key FormulasChecking Your Work
Limits and Continuit...Derivatives and Rate...Integrals and Area U...Applications of Deri...Techniques of Integr...Infinite Series and ...Modeling MotionEconomics and Optimi...Biology and Populati...Breaking Down Proble...Memorizing Key Formu...Checking Your Work
Practical Applications

Modeling Motion

Calculus in the Real World: Moving Objects

Calculus helps us understand and predict how things move. By using derivatives, we can analyze velocity and acceleration; with integrals, we can find total distance traveled, even when speed changes over time.

  • Sports: Predicting the path of a basketball shot
  • Space: Calculating the trajectory of satellites
  • Driving: Figuring out stopping distances

Calculus lets engineers and scientists build smarter, safer, and more efficient vehicles and technology.

Examples

  • Calculating how far a runner travels using the integral of their speed over time.

  • Predicting when and where a rocket will land by analyzing its motion with derivatives and integrals.

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Economics and Optimization