Calculus
Map
Arrows point from what you learn first to what it opens.
- Proven to level123
- Open
- Locked
- Comes back deeper
Learning path
In the order the concepts build on each other.
- SequencesLockedAn infinite ordered list of numbers, like 1, 1/2, 1/4, 1/8, ... - the raw material for talking about "getting closer and closer".Opens after: Rational numbers, Functions
- LimitsLockedThe value a sequence or function gets arbitrarily close to. Limits are how mathematics talks precisely about the infinite and the infinitely small.Opens after: Sequences
- DerivativesLockedThe instantaneous rate of change of a function - the slope of its graph at a single point, defined as a limit.Opens after: Functions, Limits
- IntegralsLockedThe accumulated total of a quantity - the area under a curve - found as a limit of sums of thin slices.Opens after: Limits
Connections to other domains
- Limits leads to Real numbersNumber Systems
- Derivatives needs FunctionsAlgebra
- Sequences needs Rational numbersNumber Systems
- Sequences needs FunctionsAlgebra
- Derivatives leads to AccelerationMechanics
- Derivatives leads to VelocityMechanics
- Limits leads to FunctionsAlgebra