nicefa
.
Library
YouTube
Library
/
Mathematics
/
Calculus
Calculus
.
Explore 23 formal proofs and analytical renders within the discipline of Calculus.
Foundational
The Definition of a Limit
Visualizing limits.
Study Proof →
Foundational
The Power Rule & Slope
Seeing the derivative.
Study Proof →
Foundational
The Chain Rule Geometry
Explore the geometric intuition of the Chain Rule in calculus, understanding how rates of change compose through nested functions.
Study Proof →
Foundational
The Product Rule
Geometry of expanding rectangles.
Study Proof →
Foundational
The Quotient Rule
Rate of change of ratios.
Study Proof →
Foundational
Mean Value Theorem
The average-to-instant bridge.
Study Proof →
Foundational
L'Hopital's Rule
Solving indeterminate forms.
Study Proof →
Foundational
The Squeeze Theorem
Inevitable convergence tunnel.
Study Proof →
Foundational
Integration by Parts
Reversing product rule.
Study Proof →
Foundational
U-Substitution Intuition
Changing variables.
Study Proof →
Foundational
Trigonometric Substitution
Mapping circles to integrals.
Study Proof →
Foundational
Partial Fraction Decomposition
Breaking complex ratios.
Study Proof →
Foundational
The Disc Method
Rotating areas.
Study Proof →
Foundational
The Shell Method
Nesting cylindrical shells.
Study Proof →
Foundational
Arc Length Formula
Distance along a curve.
Study Proof →
Foundational
Surface Area of Revolution
Area of rotated curves.
Study Proof →
Foundational
Fundamental Theorem
The rate-accumulation bridge.
Study Proof →
Intermediate
Taylor Series Expansion
Polynomial approximation.
Study Proof →
Intermediate
Partial Derivatives
Slicing 3D surfaces.
Study Proof →
Intermediate
The Gradient Vector
Points of steepest ascent.
Study Proof →
Intermediate
Lagrange Multipliers
Constrained optimization.
Study Proof →
Intermediate
Triple Integrals
3D density accumulation.
Study Proof →
Intermediate
Flux & Surface Integrals
Flow through nets.
Study Proof →
