Calculus
Calculus is the mathematics of change and accumulation. It is built on two fundamental operations — differentiation (finding rates of change) and integration (finding accumulated quantities). From limits and derivatives to integrals and infinite series, this page links to every calculus term, formula, and worked example on Mathwords.
Key Concepts
Curve sketching is the systematic process of using calculus — specifically the first and second derivatives — to anal...
A deleted neighborhood of a point $a$ is the set of all points within a certain distance $\delta$ of $a$, but excludi...
Area between curves is the total region enclosed between two functions, calculated by integrating the absolute value ...
Absolute convergence is a property of an infinite series that converges even when every term is replaced by its absol...
Absolute convergence is a property of an infinite series that converges even when every term is replaced by its absol...
Absolute convergence is a property of an infinite series that converges even when every term is replaced by its absol...
Area under a curve is the region enclosed between the graph of a function y = f(x) and the x-axis over a given interv...
Area under a curve is the region enclosed between the graph of a function y = f(x) and the x-axis over a given interv...
The Alternating Series Remainder is the error bound that tells you how close the nth partial sum of a convergent alte...
Area Using Parametric Equations is a method for finding the area between a parametrically defined curve and the x-axi...
Area Using Parametric Equations is a method for finding the area between a parametrically defined curve and the x-axi...
The Washer Method is a technique for finding the volume of a solid of revolution when the region being rotated does n...
All Calculus Terms (233)
- Absolute Convergence
- Absolute Maximum
- Absolute Minimum
- Acceleration
- Algorithm
- Alternating Series
- Alternating Series Remainder
- Alternating Series Test
- Analytic Methods
- Annulus
- Antiderivative of a Function
- Approximation by Differentials
- ARC
- Arc Length of a Curve
- Area below a Curve
- Area between Curves
- Area of a Parabolic Segment
- Area of an Ellipse
- Area Using Parametric Equations
- Area Using Polar Coordinates
- Asymptote
- Average Value of a Function
- Axis of Rotation
- Boundary Value Problem
- Bounded Function
- Bounded Sequence
- Bounds of Integration
- Calculus
- Cartesian Form
- Cavalieri’s Principle
- Center of Mass Formula
- Centroid
- Chain Rule
- Comparison Test
- Concave
- Concave Down
- Concave Up
- Conditional Convergence
- Constant Term
- Continued Sum
- Continuous Function
- Continuously Differentiable Function
- Converge
- Convergence Tests
- Convergent Sequence
- Convergent Series
- Critical Number
- Critical Point
- Curly d
- Curve
- Curve Sketching
- Cusp
- Cylindrical Shell Method
- Decreasing Function
- Definite Integral
- Definite Integral Rules
- Degenerate
- Del Operator
- Deleted Neighborhood
- Delta (Δ δ)
- Derivative
- Derivative of a Power Series
- Derivative Rules
- Difference Quotient
- Differentiable
- Differential
- Differential Equation
- Differentiation
- Discontinuity
- Discontinuous Function
- Disk
- Disk Method
- Distance from a Point to a Line
- Diverge
- Divergent Sequence
- Divergent Series
- e
- Ellipsoid
- End Behavior
- Essential Discontinuity
- Explicit Differentiation
- Explicit Function
- Exponential Decay
- Exponential Growth
- Exponential Model
- Extreme Value Theorem
- Extreme Values of a Polynomial
- Extremum
- Factorial
- Falling Bodies
- First Derivative
- First Derivative Test
- First Order Differential Equation
- Fixed
- Function Operations
- Fundamental Theorem of Calculus
- GLB
- Golden Spiral
- Graphic Methods
- Harmonic Progression
- Harmonic Series
- Helix
- Higher Derivative
- Hole
- Homogeneous System of Equations
- Hyperbolic Trig
- Identity Function
- Implicit Differentiation
- Implicit Function or Relation
- Improper Integral
- Increasing Function
- Indefinite Integral
- Indeterminate Expression
- Infinite Geometric Series
- Infinite Limit
- Infinite Series
- Infinitesimal
- Infinity
- Inflection Point
- Initial Value Problem
- Instantaneous Acceleration
- Instantaneous Rate of Change
- Instantaneous Velocity
- Integrable Function
- Integral
- Integral Methods
- Integral of a Function
- Integral of a Power Series
- Integral Table
- Integral Test
- Integral Test Remainder
- Integrand
- Integration
- Integration by Parts
- Integration by Substitution
- Intermediate Value Theorem
- Interval of Convergence
- Iterative Process
- Jump Discontinuity
- Least Upper Bound
- Limit
- Limit Comparison Test
- Limit from Above
- Limit from Below
- Limit Test for Divergence
- Local Behavior
- Local Maximum
- Local Minimum
- Logarithmic Differentiation
- Logistic Growth
- Mathematical Model
- Maximize
- Maximum of a Function
- Mean Value Theorem
- Mean Value Theorem for Integrals
- Mesh
- Minimize
- Minimum of a Function
- Mode
- Moment
- Multivariable
- Multivariable Analysis
- n-tuple
- Neighborhood
- Normal
- nth Degree Taylor Polynomial
- nth Derivative
- nth Partial Sum
- Oblate Spheroid
- One-Sided Limit
- Order of a Differential Equation
- Ordinary Differential Equation
- p-series
- Parallel Cross Sections
- Parameter (algebra)
- Parametric Derivative Formulas
- Parametric Equations
- Parametrize
- Partial Fractions
- Partial Sum of a Series
- Partition of an Interval
- Piecewise Continuous Function
- Pinching Theorem
- Polar Derivative Formulas
- Positive Series
- Power Rule
- Power Series
- Power Series Convergence
- Product Rule
- Prolate Spheroid
- Quotient Rule
- Radius of Convergence
- Ratio Test
- Rationalizing Substitutions
- Reciprocal Rule
- Related Rates
- Remainder of a Series
- Riemann Sum
- Root Test
- Scalar
- Secant Line
- Second Derivative
- Second Derivative Test
- Second Order Critical Point
- Second Order Differential Equation
- Separable Differential Equation
- Sequence
- Sequence of Partial Sums
- Series
- Series Rules
- Simple Closed Curve
- Simple Harmonic Motion (SHM)
- Simpson's Rule
- Slope of a Curve
- Solid
- Solid of Revolution
- Solve Analytically
- Solve Graphically
- Speed
- Surface
- Surface Area of a Surface of Revolution
- Surface of Revolution
- Tangent Line
- Taylor Series
- Taylor Series Remainder
- Torus
- Trapezoid Rule
- Trig Substitution
- Uniform
- Velocity
- Volume
- Washer Method
- Work